## Go Math Grade 6 Answer Key Chapter 13 Variability and Data Distributions

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## Go Math Grade 6 Answer Key Chapter 13 Variability and Data Distributions

Before you start your preparation checkout the topic provided below. The Go Math Grade 6 Answer Key Chapter 13 Variability and Data Distributions helps the students to score good marks in exams. Click on the below links and download the solutions.

Chapter 13 – Lesson: 1

Chapter 13 – Lesson: 2

Chapter 13 – Lesson: 3

Chapter 13 – Lesson: 4

Chapter – 13 – Mid-Chapter Checkpoint

Chapter 13 – Lesson: 5

Chapter 13 – Lesson: 5

Chapter 13 – Lesson: 6

Chapter 13 – Lesson: 7

Chapter 13 – Review/Test

### Share and Show – Page No. 709

For 1–3, use the dot plot.

Question 1.
The dot plot shows the number of paintings students in the art club displayed at the art show. Does the dot plot contain any gaps?
If so, where?

Type below:
_________________

Answer: Between the intervals of 4 – 7 excluding 4 and 7

Explanation:

The dots are filled from 1 – 4 and 7 but the region between these two intervals is left unfilled so the region containing gaps is 5-6 including 5 and 6

Question 2.
Identify any clusters in the data.
Type below:
_________________

Explanation:
A group of dots is called a cluster
The dots form a cluster at 1 – 4

Question 3.
Summarize the information in the dot plot.
Type below:
_________________

Answer: It says about the number of paintings done by each student in the art club.

Explanation:
The number of paintings is represented by the number line. The dots represent the students.
Therefore we can say that It says about the number of paintings done by each student in the art club.

Question 4.
What patterns do you see in the histogram data?

Type below:
_________________

Explanation:
STEP 1 Identify any peaks in the data.
The histogram has 6 peaks.
The interval representing the greatest number of visitors is for ages between 60 and 69 age group.
STEP 2 The data changes across the intervals.
The number of visitors increases from 0 to 29 age group and from 40 to 69 age group.
So, the data values increase to one peak in the interval from 0 to 9 age group and then decrease.
The visitors of the age group 30 – 39 did not visit the zoo.

Question 5.
The dot plot shows the number of errors made by a baseball team in the first 16 games of the season. For numbers 5a-5e, choose Yes or No to indicate whether the statement is correct.

5a. There is a gap from 4 to 5.
5b. There is a peak at 0.
5c. The dot plot has symmetry.
5d. There are two modes.
5e. There is one cluster.
5a. __________
5b. __________
5c. __________
5d. __________
5e. __________

5a. Yes
5b. Yes
5c. No
5d. No
5e. No

Explanation:
5a. There are dots between 4-5 so we can say that there is a gap from 4 to 5.
5b. The number of dots is more at the interval 0 So we can say that there is a peak at 0.
5c. The symmetrical view is nothing but having the same number of dots on both sides of the figure but we cannot observe it in the above figure. Therefore we can say that the dot plot has no symmetry.
5d. The most frequently occurring observation is known as a mode. One dot repeats in all the intervals so we can say that the mode is 1.
5e. A group of observations form a cluster, there are more than 1 group of dots in the figure given above.

### Big Cats – Page No. 710

There are 41 species of cats living in the world today. Wild cats live in places as different as deserts and the cold forests of Siberia, and they come in many sizes. Siberian tigers may be as long as 9 feet and weigh over 2,000 pounds, while bobcats are often just 2 to 3 feet long and weigh between 15 and 30 pounds.

You can find bobcats in many zoos in the United States. The histogram below shows the weights of several bobcats. The weights are rounded to the nearest pound.

Use the histogram for 6 and 7.

Question 6.
Look for a Pattern Describe the overall shape of the histogram.
Type below:
_________________

Answer: The graph starts from a small interval and increases to the highest and then decreases to the smallest interval.
The histogram has rectangles which are closely packed.

Explanation:
STEP 1 Identify any peaks in the data.
The histogram has 1 peak(s).
The interval representing the greatest number of bobcats is for weights between 18 and 20 pounds.
STEP 2 Describe how the data changes across the intervals. The number of bobcats increases from 12 to 17 pounds and from 21 to 29 pounds.
STEP 3 Describe any symmetry the graph has. If I draw a vertical line through the interval for 18 to 20 pounds, the left and right parts of the histogram are very close to being mirror images. The histogram has line symmetry.

So, the data values increase to one peak in the interval for 18 to 20 pounds and then decrease. The data set has a vertical line
symmetry about the peak.

Question 7.
Sense or Nonsense? Sunny says that the graph might have a different shape if it was redrawn as a bar graph with one bar for each number of pounds. Is Sunny’s statement sense or nonsense? Explain.
Type below:
_________________

Explanation:
Bar graph also contains rectangles but they are not closely packed hence the statement is correct which is said by Sunny as a bar graph with one bar for each number of pounds.

### Patterns in Data – Page No. 711

For 1–2, use the dot plot.

Question 1.
The dot plot shows the number of omelets ordered at Paul’s Restaurant each day. Does the dot plot contain any gaps?
Type below:
_________________

Answer: Yes, the dot plot contain gaps

Explanation:
The dots are filled from 10 – 11, from 14 – 16 and from 18 – 19 but the region between these two intervals is left unfilled so the region containing gaps is 12-13 including 12 and 13, 17 is also left unfilled.

Question 2.
Identify any clusters in the data.
Type below:
_________________

Answer: 14 – 16 and 18 – 19

Explanation:
A group of dots is called a cluster. The dots which form a cluster are 14 – 16 and from 18 – 19.

For 3–4, use the histogram.

Question 3.
The histogram shows the number of people that visited a local shop each day in January. How many peaks does the histogram have?
Type below:
_________________

Answer: The histogram has only one peak.

Explanation:
The rectangle with tall length represents the highest peak in the graph given above.
The number of people who visited a local shop each day in January were among 0 – 9  visitors and this was the highest frequency having 14 days.
The highest peak is in the interval of 0 – 9.

Question 4.
Describe how the data values change across the intervals.
Type below:
_________________

Answer: They decrease from highest to low values in the given picture above.

Explanation:
The graph represents the number of visitors in the month of January the visitors of number 0 – 9 have the highest frequency,
10 – 19 are the second-highest among the visitors who went to the local shop in the month of January, followed by 20 – 29,
30 – 39

Problem Solving

Question 5.
Look at the dot plot at the right. Does the graph have symmetry? Explain.

Type below:
_________________

Answer: Yes, the graph has a symmetry

Explanation:
If I draw a vertical line through the interval for _ to_ pounds, the left and right parts of the histogram are very close to being mirror images. The histogram __ line symmetry.
A geometric figure has line symmetry if you can draw a line through it so that the two parts are mirror images of each other.
So, the data values increase to one peak in the interval for _ to _ pounds and then decrease. The data set __ line symmetry about the peak.

Question 6.
A histogram that shows the ages of students at a library has intervals 1–5, 6–10, 11–15, 16–20, and 21–25. There is a peak at 11–15 years and the graph is symmetric. Sketch what the histogram could look like and describe the patterns you see in the data.
Type below:
_________________

The histogram shows the ages of students at a library has intervals 1–5, 6–10, 11–15, 16–20, and 21–25. There is a peak at 11–15 years and the graph is symmetric.

Explanation:

The histogram is a graph with continuous rectangles which are closely packed.
The asymmetric graph is a graph which has a mirror-like view with equal rectangles on each side.
The graph with the highest peak represents the highest number of students who visit the library in that age group 11 – 15

### Lesson Check – Page No. 712

Question 1.
What interval in the histogram has the greatest frequency?

Type below:
_________________

Answer: 10 – 14 interval has highest frequency of 6

Explanation:
The rectangle with a peak can be said as it has the greatest frequency. The interval with a peak is 11 – 15 and the frequency of the peak is 6

Question 2.
Meg makes a dot plot for the data 9, 9, 4, 5, 5, 3, 4, 5, 3, 8, 8, 5. Where does a gap occur?
Type below:
_________________

Answer: 6 – 7 including 6 and 7

Explanation:
Let us consider an axis with 3 to 9 numbers on it plot the dots as given in the question at the points 3,4,5,8 and 9 the gap occurs between 6 and 7 including 6 and 7.

Spiral Review

Question 3.
A rectangular fish tank is 20 inches long, 12 inches wide, and 20 inches tall. If the tank is filled halfway with water, how much water is in the tank?
________ in.

Answer: 37500 cubic centimeter

Explanation:
The length of the rectangle of the rectangular fish tank = 20 inches x 2.5 cm = 50 cm (since 1 inch = 2.5 cm)
The breadth of the rectangle of the rectangular fish tank = 12 inches x 2.5 cm = 30 cm (since 1 inch = 2.5 cm)
The height of the rectangle of the rectangular fish tank = 20 inches x 2.5 cm = 50 cm (since 1 inch = 2.5 cm)
Water filled in the tank = Volume of the tank = 50 x 50 x 30 = 75000 cubic centimeter
If the tank is filled halfway = volume of the tank / 2 = 37500 cubic centimeter

Question 4.
Look at the histogram below. How many students scored an 81 or higher on the math test?
________ students

Explanation:
The interval 81 – 90 has 10 frequency and the interval 91 – 100 has 4 frequency. So the total number of students = 14

Question 5.
The Little League coach uses a radar gun to measure the speed of several of Kyle’s baseball pitches. The speeds, in miles per hour, are 52, 48, 63, 47, 47. What is the median of Kyle’s pitch speeds?
The median is ________ miles.

Answer: Median is 48

Explanation:
First, write the observations in ascending order or descending order.
The formula to calculate the median is (n+1/2)th observation, for odd number of observations
n = 5 (odd)
Median = (5 + 1 / 2) = (6/2) = 3rd observation = 48
Therefore the median is 48.

### Share and Show – Page No. 715

Find the median, lower quartile, and upper quartile of the data.

Question 1.
the scores of 11 students on a geography quiz:
87, 72, 80, 95, 86, 80, 78, 92, 88, 76, 90
Type below:
_________________

Answer: Median: 86, lower quartile: 72, upper quartile: 95

Explanation:
First, write the observations in ascending order or descending order.
The formula to calculate the median is (n+1/2)th observation, for odd number of observations
n = 11 (odd)
Median = (11 + 1 / 2) = (12/2) = 6th observation = 86
Therefore the median is 86.

Lower quartile: 72  Upper quartile: 95

Question 2.
the lengths, in seconds, of 9 videos posted online:
50, 46, 51, 60, 62, 50, 65, 48, 53
Type below:
_________________

Answer: Median: 51 Lower quartile: 46 Upper quartile: 65

Explanation:
First, write the observations in ascending order or descending order.
The formula to calculate the median is (n+1/2)th observation, for odd number of observations
n = 9 (odd)
Median = (9 + 1 / 2) = (10/2) = 5th observation = 51
Therefore the median is 51.

Lower quartile: 46 Upper quartile: 65

Question 3.
Make a box plot to display the data set in Exercise 2.
Type below:
_________________

Answer: The box plot is drawn on the topic: Lengths of the videos (in seconds) posted in the online.

Explanation:
The box is drawn to understand the clear view of the raw data, in a precise manner.
This box gives us information about lengths of the videos posted in the online. We can directly say the median, lower quartile, upper quartile seeing the box plot.

Find the median, lower quartile, and upper quartile of the data.

Question 4.
13, 24, 37, 25, 56, 49, 43, 20, 24
Type below:
_________________

Explanation:
First, write the observations in ascending order or descending order.
The formula to calculate the median is (n+1/2)th observation, for odd number of observations
n = 9 (odd)
Median = (9 + 1 / 2) = (10/2) = 5th observation =25
Therefore the median is 25.

Question 5.
61, 23, 49, 60, 83, 56, 51, 64, 84, 27
Type below:
_________________

Explanation:
First, write the observations in ascending order or descending order.
The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observations
n = 10 (even)
Median = Mean of (5)th and (6)th observations = 56 + 60 divided by 2 = 116/2 = 58
Therefore the median is 58.

Question 6.
The chart shows the height of trees in a park. Display the data in a box plot.

Type below:
_________________

Explanation:
Lower limit: 8
Upper limit: 30
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observations
n = 12 (even)
Median = Mean of (6)th and (7)th observations = 18 + 20 divided by 2 = 38/2 = 19
Therefore the median is 19.

Question 7.
Analyze Eric made this box plot for the data set below. Explain his error.

Type below:
_________________

Answer: The lower and upper limits are marked wrong.

Explanation:
The box drew above the number line is wrong.
It does not show the correct upper and lower limits.
The lower limit is 5 and the upper limit is 35.

### Problem Solving + Applcations – Page No. 716

Pose a Problem

Question 8.
The box plots show the number of flights delayed per day for two different airlines. Which data set is more spread out?

Airline A: greatest value − least value = _____
Airline B: greatest value − least value = _____
So, the data for _____ is more spread out.
Write a new problem that can be solved using the data in the box plots.
Type below:
_________________

Airline A: greatest value − least value = 8
Airline B: greatest value − least value = 10
The data for airline B is more spread out.

A problem which can be solved using the box plot can be:

Find the median, lower and upper limits.

Explanation:
The greatest value and lowest value can be identified by seeing the box drew above the number line. The ends represent the lower and upper limits in both the box plots.

The solution to the question framed:
The start and end of the rectangle represent the lower and upper limits. And the middle line represents the median.
The lower limit is 5
Upper limit is 35
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observations
n = 6 (even)
Median = Mean of (3)th and (4)th observations = 15 + 25 divided by 2 = 40/2 = 20
Therefore the median is 20.

Question 9.
The data set shows the cost of the dinner specials at a restaurant on Friday night.

The median is _____.
The lower quartile is _____.
The upper quartile is _____.

Median: 24
The lower quartile is 16.
The upper quartile is 30.

Explanation:
Seeing the data in the box we can identify the lower and upper quartiles.
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is (n+1/2)th observation, for odd number of observations
n = 11 (odd)
Median = (11 + 1 / 2) = (12/2) = 6th observation =24
Therefore the median is 24.

### Box Plots – Page No. 717

Find the median, lower quartile, and upper quartile of the data.

Question 1.
the amounts of juice in 12 glasses, in fluid ounces:
11, 8, 4, 9, 12, 14, 9, 16, 15, 11, 10, 7
Type below:
_________________

Median: 10.5
Lower quartile: 4
Upper quartile: 16

Explanation:
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observations
n = 12 (even)
Median = Mean of (6)th and (7)th observations = 10 + 11 divided by 2 = 21/2 = 10.5
Therefore the median is 10.5.
After writing in ascending or descending order the first and last terms justify the lower and upper limits respectively.
They are:
Lower quartile: 4
Upper quartile: 16

Question 2.
the lengths of 10 pencils, in centimeters:
18, 15, 4, 9, 14, 17, 16, 6, 8, 10
Type below:
_________________

Median: 12
Lower quartile: 4
Upper quartile: 18

Explanation:
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observations
n = 10 (even)
Median = Mean of (5)th and (6)th observations = 10 + 14 divided by 2 = 24/2 = 12
Therefore the median is 12.
After writing in ascending or descending order the first and last terms justify the lower and upper limits respectively.
They are:
Lower quartile: 4
Upper quartile: 18

Question 3.
Make a box plot to display the data set in Exercise 2.
Type below:
_________________

The above box plot represents the lower and upper quartiles, the median.

Explanation:
Box plot is drawn using the number line and the rectangle which is drawn above it.
The ends of the rectangles say about the lower and upper limits and the middle line indicates the median.

Question 4.
The numbers of students on several teams are 9, 4, 5, 10, 11, 9, 8, and 6. Make a box plot for the data.
Type below:
_________________

Explanation:
Box plot is drawn using the number line and the rectangle which is drawn above it.
The ends of the rectangles say about the lower and upper limits and the middle line indicates the median.
Therefore the lower and upper quartiles are 4 and 11 respectively.
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observations
n = 8 (even)
Median = Mean of (4)th and (5)th observations = 8 + 9 divided by 2 = 17/2 = 8.5
Therefore the median is 8.5.

Problem Solving

Question 5.
The amounts spent at a gift shop today are $19,$30, $28,$22, $20,$26, and $26. What is the median? What is the lower quartile? Type below: _________________ Answer: Median:$26
Lower quartile: $19 Upper quartile:$30

Explanation:
Median:
First, write the observations in ascending order or descending order.
The formula to calculate the median is (n+1/2)th observation, for odd number of observations
n = 7 (odd)
Median = (7 + 1 / 2) = (8/2) = 4th observation =26
Therefore the median is 26.
After writing in ascending or descending order the first and last terms justify the lower and upper limits respectively.
They are:
Lower quartile: $19 Upper quartile:$30

Question 6.
The weights of six puppies in ounces are 8, 5, 7, 5, 6, and 9. What is the upper quartile of the data?
Type below:
_________________

Answer: Upper quartile: 9

Explanation:
The highest value in the data is defined as the upper quartile.
The highest value in the raw data given is 9

Question 7.
Draw a box plot to display this data: 81, 22, 34, 55, 76, 20, 56.
Type below:
_________________

Explanation:
A box plot gives information about the lower and upper quartiles and about the median.
The box plot is drawn using a rectangle and the number line.

### Lesson Check – Page No. 718

Question 1.
The values in a data set are 15, 7, 11, 12, 6, 3, 10, and 6. Where would you draw the box in a box plot for the data?
Type below:
_________________

Answer: The box is drawn above the number line.

Explanation:
Example:

The rectangle which can be seen above the number line is the box plot which is drawn.
The box plot gives information about the lower and upper quartiles and about the median.

Question 2.
What is the lower quartile of the following data set?
22, 27, 14, 21, 22, 26, 18
Type below:
_________________

Explanation:
The value which is lowest in the given data is called the lowest quartile.
Therefore the lowest quartile in the given data is 14.

Spiral Review

Question 3.
Jenn says that “What is the average number of school lunches bought per day?” is a statistical question. Lisa says that “How many lunches did Mark buy this week?” is a statistical question. Who is NOT correct?
Type below:
_________________

Answer: Lisa’s statement is wrong.

Explanation:

Question 4.
The prices of several chairs are $89,$76, $81,$91, $88, and$70. What is the mean of the chair prices?
The mean is $_________ Answer:$82.5

Explanation:
Number of observations= 6
Mean of the observations= $89 +$76 + $81+$91+$88+$70/ 6= 495/6 = $82.5 Question 5. By how much does the mean of the following data set change if the outlier is removed? 13, 19, 16, 40, 12 Type below: _________________ Answer: The mean shows a difference if the lower limit is removed the mean increases and if the upper limit is removed the mean decreases. Explanation: Outliers are nothing but both upper and lower limits. The actual mean is 20 But when the lower limit is removed the mean increases to 22 while when the upper limit is removed the mean decreases to 15. Therefore, we can say that the mean shows a difference when the outliers are removed. Question 6. Where in the dot plot does a cluster occur? Type below: _________________ Answer: 52 – 54 Explanation: A cluster is nothing but a group of dots. In the intervals 52 – 54 a cluster has occurred. ### Share and Show – Page No. 721 Use counters, a dot plot, or iTools to find the mean absolute deviation of the data. Question 1. Find the mean absolute deviation for both data sets. Explain which data set is more spread out. the number of laps Shawna swam on 5 different days: 5, 6, 6, 8, 10 mean = 7 the number of laps Lara swam on 5 different days: 1, 3, 7, 11, 13 mean = 7 Type below: _________________ Answer: Case 2 is more spread out. Explanation: CASE1 The number of laps Shawna swam on 5 different days: 5,6,6,8,10 Mean = 7 Deviations: 7 – 5 = 2 7 – 6 = 1 7 – 6 = 1 7 -8 = -1 7 -10=-3 Mean of deviations = 2+1+1+1+3/5 = 8/5 = 1.6 CASE2 The number of laps Lara swam on 5 different days: 1, 3, 7, 11, 13 Mean = 7 Deviations: 7 – 1 = 6 7 – 3 = 4 7 – 7 = 0 7 -11= -4 7 -13= -6 Mean of deviations = 6+ 4 + 0 + 4 + 6 / 5 = 20/5 = 4 Use the dot plot to find the mean absolute deviation of the data. Question 2. mean = 7 books ______ books Answer: Mean absolute deviation is 2.4 Explanation: STEP 1 Label each dot with its distance from the mean. Starting from left to right: 4: 7-4=3 5: 7-5=2 6: 7-6=1 9: 7-9=-2 10: 7-10=-3 11: 7-11=-4 STEP 2 Find the mean of the distances. (3) + (2) +(2) +(2) +(2) +(1) + (2) +(3) +(3) +(4) / 10 = 24/10 = 2.4 So, the mean absolute deviation of the data is 2.4 Question 3. mean = 29 pounds _______ pounds Answer: Mean Absolute deviation is 3.2 Explanation: STEP 1 Label each dot with its distance from the mean. Starting from left to right: 26: 29-26=03 27: 29-27=02 32: 29-32=-3 33: 29-33=-4 35: 29-35=-6 STEP 2 Find the mean of the distances. (3) + (2) +(3) +(4) +(6) +(3) + (3) +(2) / 8 = 26/8 = 3.2 So, the mean absolute deviation of the data is 3.2 Question 4. The mean absolute deviation of the number of daily visits to Scott’s website for February is 167.7. In March, the absolute mean deviation is 235.9. In which month did the number of visits to Scott’s website vary more? Explain how you know. Type below: _________________ Answer: As the mean absolute deviation is more in the month of February we can say that there are more visitors in this month. Explanation: As the mean of the month of February is less it means that the number of observations are more. Similarly, as the mean of the month of March is more it means that the number of observations are less. Therefore we can say that the number of visitors were more in the month of February compared to March. Question 5. Write an Inequality Algebra In April, the data for Scott’s website visits are less spread out than they were in February. Use a to represent the mean absolute deviation for April. Write an inequality to describe the possible values of a. Type below: _________________ Answer: a < February Explanation: Since the data is more spread out in the month of April than they were in February. Therefore the inequality represents “less than” sign. ### Problem Solving + Applcations – Page No. 722 Question 6. Use the table. The mean of the data is 11. What is the mean absolute deviation of the data? _______ days Answer: 3 Explanation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 10: 11-10= 1 12: 11-12=-1 13: 11-13=-2 18: 11-18=-7 10: 11-10= 1 08: 11-08= 3 07: 11-07= 4 06: 11-06= 5 16: 11-16=-5 14: 11-14=-3 08: 11-08= 3 10: 11-10= 1 STEP 2 Find the mean of the distances. 1+1 +2 +7 +1 +3 +4 +5+5+3+3+1/ 12 = 36/12 = 3 So, the mean absolute deviation of the data is 3. Question 7. Suppose all of the players on a basketball team had the same height. Explain how you could use reasoning to find the mean absolute deviation of the players’ heights. Type below: _________________ Answer: 0 Explanation: If the players on a basketball team had the same height. The mean deviation will be equal to the 0 because the difference between the mean and the observations is 0. Let the observations be 2,2,2,2,2 Mean = 10/5 = 2 Mean deviation = (2-2)+(2-2)+(2-2)+(2-2)+(2-2)/5 = 0/5 = 0 Question 8. Explain Tell how an outlier that is much greater than the mean would affect the mean absolute deviation of the data set. Explain your reasoning. Type below: _________________ Answer: An outlier increases the mean absolute deviation of the data set. Explanation: The difference between the outlier and the mean is a greater number when added in the sum of observations the mean absolute deviation increases. Question 9. The data set shows the number of soccer goals scored by players in 3 games. For numbers 9a–9c, choose Yes or No to indicate whether the statement is correct. 9a. The mean absolute deviation of Player A is 1. 9b. The mean absolute deviation of Player B is 0. 9c. The mean absolute deviation of Player C is greater than the mean absolute deviation of Player A. 9a. __________ 9b. __________ 9c. __________ Answer: 9a. No 9b. Yes 9c. No Explanation: Player A Mean = 1+2+3/3 = 6/3 = 2 Mean absolute deviation = 1+0+1/3 = 2/3 = 0.6 Player B Mean =2+2+2/3 = 6?3 = 2 Mean absolute deviation = 0/3 = 0 Player C Mean = 1+2+1/3 = 4/3 = 1.3 Mean absolute deviation = 0.3+0+0.3/3 = 0.2 ### Mean Absolute Deviation – Page No. 723 Use counters and a dot plot to find the mean absolute deviation of the data. Question 1. the number of hours Maggie spent practicing soccer for 4 different weeks: 9, 6, 6, 7 mean = 7 hours _______ hour Answer: The mean absolute deviation of the data is 1. Explanation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 9: 7-9=-2 6: 7-6=-1 6: 7-6=-1 7: 7-7= 0 STEP 2 Find the mean of the distances. 2 +1 +1+0/ 4 = 4 /4 = 1 So, the mean absolute deviation of the data is 1. Question 2. the heights of 7 people in inches: 60, 64, 58, 60, 70, 71, 65 mean = 64 inches _______ inches Answer: The mean absolute deviation of the data is 4. Explanation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 60: 64-60= 4 64: 64-64= 0 58: 64-58= 6 60: 64-60= 4 70: 64-70=-6 71: 64-71=-7 65: 64-65=-1 STEP 2 Find the mean of the distances. 4+0+6+ 4+6+7+1/7 = 28/7 = 4 So, the mean absolute deviation of the data is 4. Use the dot plot to find the mean absolute deviation of the data. Question 3. mean = 10 _______ year Answer: The mean absolute deviation of the data is 1 Explanation: STEP 1 Label each dot with its distance from the mean. Starting from left to right: 08: 10-08=02 09: 10-09=01 10: 10-10= 0 11: 10-11=-1 12: 10-12=-2 STEP 2 Find the mean of the distances. (2) + (1) +(0) +(1) +(2) +(2)+(1)+(0)+(0)+(0)+(1)+(2) /12 = 12/12= 1 So, the mean absolute deviation of the data is 1 Question 4. mean = 8 _______ hours Answer: The mean absolute deviation of the data is 2.4 Explanation: STEP 1 Label each dot with its distance from the mean. Starting from left to right: 03: 8-03=05 04: 8-04=04 05: 8-05=03 07: 8-07=01 08: 8-08= 0 09: 8-09=-1 10: 8-10=-2 11: 8-11=-3 12: 8-12=-4 STEP 2 Find the mean of the distances. (5) + (4) +(3) +(1) +(0) +(1) + (2) +(3) +(4)+(5)+(0)+(1)+(1)+(2)+(4)/ 15 = 36/15 = 2.4 So, the mean absolute deviation of the data is 2.4 Problem Solving Question 5. In science class, Troy found the mass, in grams, of 6 samples to be 10, 12, 7, 8, 5, and 6. What is the mean absolute deviation? _______ grams Answer: The mean absolute deviation of the data is 2. Explanation: Mean = 10+12+7+8+5+6/6 = 48/6 = 8 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 10: 8-10= -2 12: 8-12= -4 07: 8-07= 01 08: 8-08= 0 05: 8-05=03 06: 8-06=02 STEP 2 Find the mean of the distances. 2+4+1+0+3+2/6 = 12/6 = 2 So, the mean absolute deviation of the data is 2. Question 6. Five recorded temperatures are 71°F, 64°F, 72°F, 81°F, and 67°F. What is the mean absolute deviation? _______ °F Answer: The mean absolute deviation of the data is 4.4. Explanation: Mean = 71+64+72+81+67/5 = 355/5 = 71 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 71: 71-71= 0 64: 71-64= 07 72: 71-72= -1 81: 71-81=-10 67: 71-67= 04 STEP 2 Find the mean of the distances. 0+7+1+10+4/5 = 22/5 = 4.4 So, the mean absolute deviation of the data is 4.4. Question 7. Make a dot plot of the following data: 10, 10, 11, 12, 12, 13, 13, 15. Use the dot plot to find the mean absolute deviation. Type below: _________________ Answer: The mean absolute deviation of the data is 1.25 Explanation: Mean = 10+10+11+12+12+13+13+15/8 = 96/8 = 12 Mean absolute deviation: Box plot: STEP 1 Label each dot with its distance from the mean. Starting from left to right: 10: 12-10=02 11: 12-11=01 12: 12-12=0 13: 12-13=-1 15: 12-15=-3 STEP 2 Find the mean of the distances. (2) + (2) +(1) +(0) +(0) +(1) + (1) +(3) / 8 = 10/8 = 1.25 So, the mean absolute deviation of the data is 1.25 ### Lesson Check – Page No. 724 Question 1. Six test grades are 86, 88, 92, 90, 82, and 84. The mean of the data is 87. What is the mean absolute deviation? _______ Answer: The mean absolute deviation of the data is 3.5 Explanation: Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 86: 87-86= 01 88: 87-88= -1 92: 87-92= -5 90: 87-81= 06 82: 87-82= 05 84: 87-84= 03 STEP 2 Find the mean of the distances. 1+5+1+6+5+3/6 = 21/6 = 3.5 So, the mean absolute deviation of the data is 3.5 Question 2. Eight heights in inches are 42, 36, 44, 46, 48, 42, 48, and 46. The mean of the data is 44. What is the mean absolute deviation? _______ inches Answer: Explanation: The mean absolute deviation of the data is 3 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 42: 44-42= 02 36: 44-36= 08 44: 44-44= 0 46: 44-46= -2 48: 44-48= -4 42: 44-42= 02 48: 44-48= -4 46: 44-46= -2 STEP 2 Find the mean of the distances. 2+8+2+4+0+2+4+2/8 = 24/8 = 3 So, the mean absolute deviation of the data is 3 Spiral Review Question 3. What is the volume of a rectangular prism with dimensions 4 meters, 1 $$\frac{1}{2}$$ meters, and 5 meters? _______ m3 Answer: 30m3 Explanation: Dimentions: 4 meters, 1 1/2 meters, 5 meters Change the mixed fraction into improper fraction = 3/2 Volume of the rectangle = 4 x 3/2 x 5 = 30m3 Question 4. Carrie is making a frequency table showing the number of miles she walked each day during the 30 days of September. What value should she write in the Frequency column for 9 to 11 miles? _______ Answer: 1 Explanation: Total number of days in the month of September = 30 Number of days given in the frequency table = 17+8+4 = 29 Frequency in the interval 9 – 11 = 30 – 29 = 1 day Question 5. The following data shows the number of laps each student completed. What number of laps is the mode? 9, 6, 7, 8, 5, 1, 8, 10 The mode is _______ laps. Answer: The mode is 8 laps. Explanation: The most frequently occurring observation is known as mode. 8 is the mode in the above raw data given. Question 6. What is the upper quartile of the following data? 43, 48, 55, 50, 58, 49, 38, 42, 50 The upper quartile is _______ Answer: The upper quartile is 58 Explanation: The highest observation in the data given is known as upper quartile. The upper quartile is 58 ### Share and Show – Page No. 727 Question 1. Find the range and interquartile range of the data in the box plot. The range is$ __________ .
The interquartile range is $__________ . Answer:$12, $3 Explanation: The difference between the highest observation and the lowest observation is called a range. Range = 19 – 7 =$12
The difference and the highest and the lowest dots of the dot plot is called as interquartile range.
Interquartile range = 15 – 12 = $3 Practice: Copy and Solve Find the mean absolute deviation for the data set. Question 2. heights in inches of several tomato plants: 16, 18, 18, 20, 17, 20, 18, 17 _______ inch Answer: The mean absolute deviation of the data is 1 Explanation: Mean: Mean = 16+18+18 +20+17+20+18+17/8 = 144/8 = 18 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 16: 18-16= 02 18: 18-18= 0 18: 18-18= 0 20: 18-20= -2 17: 18-17= 01 20: 18-20= -2 18: 18-18= 0 17: 18-17= 01 STEP 2 Find the mean of the distances. 2+0+0+2+1+2+0+1/8 = 8/8 = 1 So, the mean absolute deviation of the data is 1 Question 3. times in seconds for students to run one lap: 68, 60, 52, 40, 64, 40 _______ seconds Answer: The mean absolute deviation of the data is 10 Explanation: Mean: Mean = 68+60+52+40+64+40/6 = 54 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 68: 54-68= -14 60: 54-60= -6 52: 54-52= 02 40: 54-40= 14 64: 54-64= -10 40: 54-40= 14 STEP 2 Find the mean of the distances. 14+6+2+14+10+14/6 = 60/6 = 10 So, the mean absolute deviation of the data is 10 On Your Own Use the box plot for 4 and 5. Question 4. What is the range of the data?$ _______

Answer: $24 Explanation: The difference between the highest observation and the lowest observation is called a range. Range =$56 – $32 =$24

Question 5.
What is the interquartile range of the data?
$_______ Answer:$16

Explanation:
The difference and the highest and the lowest dots of the dot plot is called as interquartile range.
Interquartile range = $52 –$36 = $16 Practice: Copy and Solve Find the mean absolute deviation for the data set. Question 6. times in minutes spent on a history quiz: 35, 35, 32, 34, 34, 32, 34, 36 _______ minute Answer: The mean absolute deviation of the data is 1 Explanation: Mean: Mean = 35+ 35+ 32+ 34+34+ 32+ 34+36/8 = 272/8 = 34 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 35: 34-35= -1 35: 34-35= -1 32: 34-32= 02 34: 34-34= 0 34: 34-34= 0 32: 34-32=02 34: 34-34=0 36: 34-36=-2 STEP 2 Find the mean of the distances. 1+1+2+0+0+2+0+2/8 = 8/8 = 1 So, the mean absolute deviation of the data is 1 Question 7. number of excused absences for one semester: 1, 2, 1, 10, 9, 9, 10, 6, 1, 1 _______ Answer: The mean absolute deviation of the data is 3.8 Explanation: Mean: Mean =1+2+1+10+9+9+10+6+1+1 /10 = 50/10 = 5 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 1: 5-1= 4 2: 5-2= 3 1: 5-1= 4 10: 5-10= -5 9: 5-9= -4 9: 5-9=-4 10: 5-10=-5 6: 5-6=-1 1: 5-1=4 1: 5-1=4 STEP 2 Find the mean of the distances. 4+3+4+5+4+4+5+1+4+4/10 =38/10 = 3.8 So, the mean absolute deviation of the data is 3.8 Question 8. The chart shows the price of different varieties of dog food at a pet store. Find the range, interquartile range, and the mean absolute deviation of the data set. Type below: _________________ Answer: The mean absolute deviation of the data is 3.6 Range = 32-16 = 16 Interquartile range = 24 – 20 = 4 Explanation: Mean: Mean =18+24+20+26+24+20+32+20+16+20 /10 = 220/10 = 22 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 18: 22-18= 4 24: 22-24= -2 20: 22-20= 2 26: 22-26= -4 24: 22-24= -2 20: 22-20= 2 32: 22-32=-10 20: 22-20= 2 16: 22-16= 6 20: 22-20= 2 STEP 2 Find the mean of the distances. 4+2+2+4+2+2+10+2+6+2/10 =36/10 = 3.6 So, the mean absolute deviation of the data is 3.6 The difference between the highest observation and the lowest observation is called a range. Range = 32-16 = 16 The difference and the highest and the lowest dots of the dot plot is called as interquartile range. Interquartile range = 24 – 20 = 4 ### Problem Solving + Applications – Page No. 728 Question 9. Hyato’s family began a walking program. They walked 30, 45, 25, 35, 40, 30, and 40 minutes each day during one week. At the right, make a box plot of the data. Then find the interquartile range. _______ minutes Answer: 35 minutes Explanation: Ascending order: 25,30,30,35,40,40,45 n=7 (odd) Median= Number of (n+1/2) = 8/2 = 4th observation = 35 Median:(four terms of the data) Median = 30+30/2 = 60/2 = 30 Median:(last 3 terms of the data) Median = (n+1/2) = 2nd observation = 40 Interquartile range = 30+40/2 = 70/2 = 35 Question 10. Compare Jack recorded the number of minutes his family walked each day for a month. The range of the data is 15. How does this compare to the data for Hyato’s family? Type below: _________________ Answer: Jack’s family walked less number of minutes each day compared to Hyato’s family. Explanation: The range of Hyato’s family is 20 while the range of Jack’s family is 15. Therefore we can say that Hyato’s family walked more minutes compared to Jack’s family in a day. Range can define the data with large observations and the data with least observations. Question 11. Sense or Nonsense? Nathan claims that the interquartile range of a data set can never be greater than its range. Is Nathan’s claim sense or nonsense? Explain. Type below: _________________ Answer: Nonsense, Interquartile range of a data set can be less than or greater than range. Explanation: The interquartile range is the difference between the medians of the observations. Nathan’s claim is nonsense as he said that, ” The interquartile range can never be greater than its range.” The range is the difference between the highest observation and the lowest observation. The interquartile range can be less than greater than the range. Example: Ascending order: 25,30,30,35,40,40,45 n=7 (odd) Median= Number of (n+1/2) = 8/2 = 4th observation = 35 Median:(four terms of the data) Median = 30+30/2 = 60/2 = 30 Median:(last 3 terms of the data) Median = (n+1/2) = 2nd observation = 40 Interquartile range = 30+40/2 = 70/2 = 35 Range= 45-25 = 20 In the above case the interquartile range is more than the range proving that the given statement is nonsense. Question 12. The box plot shows the heights of corn stalks from two different farms. The range of Farm A’s heights is _____ the range of Farm B’s heights. Answer: greater than Explanation: The range is the difference between the highest and the lowest observations. Range of Farm A: 72-58 = 14 Range of Farm B: 70-55 = 15 Therefore, The range of Farm A’s heights is greater than the range of Farm B’s heights. ### Measures of Variability – Page No. 729 Question 1. Find the range and interquartile range of the data in the box plot. The range is __________ miles. The interquartile range is __________ miles. Answer: 16, 8 Explanation: The difference between the highest and the lowest observations is range. Range = 17 – 1 = 16 The difference between the highest and lowest observations of the box is the interquartile range. Interquartile range = 12 – 4 = 8 Use the box plot for 2 and 3. Question 2. What is the range of the data? _____ Answer: 35 Explanation: The difference between the highest and the lowest observations is range. Range = 95 – 60 = 35 Question 3. What is the interquartile range of the data? _____ Answer: 20 Explanation: The difference between the highest and lowest observations of the box is the interquartile range. Interquartile range = 90 – 70 = 20 Find the mean absolute deviation for the set. Question 4. heights in centimetres of several flowers: 14, 7, 6, 5, 13 _____ cm Answer: The mean absolute deviation of the data is 3.6 Explanation: Mean: Mean =14+7+ 6+5+13/5= 45/5 = 9 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 14: 9-14= -5 07: 9-07= 02 06: 9-06= 03 05: 9-05= 04 13: 9-13= -4 STEP 2 Find the mean of the distances. 5+2+3+4+4/5 = 18/5 = 3.6 So, the mean absolute deviation of the data is 3.6 Question 5. ages of several children: 5, 7, 4, 6, 3, 5, 3, 7 _____ years Answer: The mean absolute deviation of the data is 1.25 Explanation: Mean: Mean = 5+7+4+6+ 3+5+3+7/8 = 40/8 = 5 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 5: 5-5= 0 7: 5-7= -2 4: 5-4= 01 6: 5-6= -1 3: 5-3= 02 5: 5-5= 0 3: 5-3= 02 7: 5-7=-2 STEP 2 Find the mean of the distances. 0+2+1+1+2+0+2+2/8 = 10/8 = 1.25 So, the mean absolute deviation of the data is 1.25 Problem Solving Question 6. The following data set gives the amount of time, in minutes, it took five people to cook a recipe. What is the mean absolute deviation for the data? 33, 38, 31, 36, 37 _____ minutes Answer: The mean absolute deviation of the data is 2.4 Explanation: Mean: Mean = 33+38+31+36+37/5 = 175/5 = 35 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 33: 35-33= 02 38: 35-38= -3 31: 35-31= 04 36: 35-36= -1 37: 35-37= -2 STEP 2 Find the mean of the distances. 2+3+4+1+2/5 = 12/5 = 2.4 So, the mean absolute deviation of the data is 2.4 Question 7. The prices of six food processors are$63, $59,$72, $68,$61, and $67. What are the range, interquartile range, and mean absolute deviation for the data? Type below: _________________ Answer: Range =$9 The mean absolute deviation of the data is 4

Explanation:
The difference between the highest and the lowest observations is range.
Range = $68 –$59 = $9 The difference between the highest and lowest observations of the box is the interquartile range. Interquartile range = 12 – 4 = 8 Mean: Mean =$63+$59+$72+$68+$61+$67/6 = 390/6 = 65 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 63: 65-63= 02 59: 65-59= 06 72: 65-72= -7 68: 65-68= -3 61: 65-61= -4 67: 65-67= -2 STEP 2 Find the mean of the distances. 2+6+7+3+4+2/6 = 24/6 = 4 So, the mean absolute deviation of the data is 4 Question 8. Find the range, interquartile range, and mean absolute deviation for this data set: 41, 45, 60, 61, 61, 72, 80. Type below: _________________ Answer: The mean absolute deviation of the data is 9.7 Explanation: Mean: Mean = 41+45+60+61+61+72+80 /7 = 420/7 = 60 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 41: 60-41= 19 45: 60-45= 15 60: 60-60= 0 61: 60-61= -1 61: 60-61= -1 72: 60-72= -12 80: 60-80= -20 STEP 2 Find the mean of the distances. 19+15+0+1+1+12+20/7 = 68/7 = 9.7 So, the mean absolute deviation of the data is 9.7 ### Lesson Check – Page No. 730 Question 1. Daily high temperatures recorded in a certain city are 65°F, 66°F, 70°F, 58°F, and 61°F. What is the mean absolute deviation for the data? _____ °F Answer: The mean absolute deviation of the data is 3.6 Explanation: Mean: Mean = 65+66+70+58+61 /5 = 320/5 = 64 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 65: 64-65=-1 66: 64-66=-2 70: 64-70=-6 58: 64-58=06 61: 64-61=03 STEP 2 Find the mean of the distances. 1+2+6+6+3/5 = 18/5 = 3.6 So, the mean absolute deviation of the data is 3.6 Question 2. Eight different cereals have 120, 160, 135, 144, 153, 122, 118, and 134 calories per serving. What is the interquartile range for the data? _____ calories Answer: 42cereals Explanation: Ascending order of the data: 118,120,122,134,135,144,153,160 Median:(for first 4 terms) Median= 120+122/2 = 242/2 = 121 Median:(for first 4 terms) Median= 144+153/2 = 297/2 = 148.5 The difference and the highest and the lowest dots of the dot plot is called as interquartile range. Interquartile range = 148.5 – 121 = 27.5 Spiral Review Question 3. Look at the histogram. How many days did the restaurant sell more than 59 pizzas? ________ Answer: 20 Explanation: After 59 there is 1 interval 60-79 Number of days the restaurant sell more than 59 pizzas = 20 Question 4. Look at the histogram. Where does a peak in the data occur? Type below: _________________ Answer: 20 – 39 Explanation: Number of days the restaurant sold the maximum pizzas = 30 Number pizzas sold in each day = 20 – 39 Question 5. What is the mode of the data set? 14, 14, 18, 20 The mode is ________ Answer: 14 Explanation: The most frequently occurring observation is known as a mode. In the above data mode is 14. Question 6. The data set below lists the ages of people on a soccer team. The mean of the data is 23. What is the mean absolute deviation? 24, 22, 19, 19, 23, 23, 26, 27, 24 ________ Answer: The mean absolute deviation of the data is 2 Explanation: Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 24: 23-24=-1 22: 23-22= 1 19: 23-19= 4 19: 23-19= 4 23: 23-23=0 23: 23-23=0 26: 23-26=-3 27: 23-27=-4 24: 23-24=-1 STEP 2 Find the mean of the distances. 1+1+4+4+3+4+1+0+0/9 = 18/9 = 2 So, the mean absolute deviation of the data is 2 ### Mid-Chapter Checkpoint – Vocabulary – Page No. 731 Choose the best term from the box to complete the sentence. Question 1. The _____ is the difference between the upper quartile and the lower quartile of a data set. Type below: _________________ Answer: Range Explanation: The difference between the upper and lower quartiles of the data is known as range. Question 2. A graph that shows the median, quartiles and least and greatest values of a data set is called a(n) _____. Type below: _________________ Answer: Box plot Explanation: The figure which shows the median, quartiles and least and greatest values of a data set is called a box plot, a box plot is a figure which represents median with a horizontal line and the starting and ending line represents the upper and lower quartiles and the end dots represent the upper limit and the lower limit. Question 3. The difference between the greatest value and the least value in a data set is the _____. Type below: _________________ Answer: Range Explanation: Each data set consists of upper and lower limits the difference between these limits is called as range. Question 4. The _____ is the mean of the distances between the values of a data set and the mean of the data set. Type below: _________________ Answer: Mean absolute Explanation: Mean absolute deviation is calculated by subtracting each observation from the mean and then the mean is calculated for these observations. Therefore we can say that the mean absolute is the mean of the distances between the values of a data set and the mean of the data set. Concepts and Skills Question 5. Make a box plot for this data set: 73, 65, 68, 72, 70, 74. Type below: _________________ Answer: Median = 71 Explanation: Median: Ascending order: 65, 68, 70, 72, 73,74 n = even = 6 Median = Mean of 3rd and 4th terms = 70+72/2 = 142/2 = 71 Find the mean absolute deviation of the data. Question 6. 43, 46, 48, 40, 38 ________ Answer: The mean absolute deviation of the data is 3.2 Explanation: Mean: Mean = 43+46+48+40+38/5 = 215/5 = 43 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 43: 43-43=0 43: 43-46=-3 43: 43-48=-5 43: 43-40= 3 43: 43-38= 5 STEP 2 Find the mean of the distances. 0+3+5+3+5/5 = 16/5 = 3.2 So, the mean absolute deviation of the data is 3.2 Question 7. 26, 20, 25, 21, 24, 27, 26, 23 ________ Answer: The mean absolute deviation of the data is 2.125 Explanation: Mean: Mean = 26+20+25+21+24+27+26+23/8 = 192/8 = 24 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 26: 24-26=-3 20: 24-20= 4 25: 24-25= -1 21: 24-21= 3 24: 24-24=0 27: 24-27=-3 26: 24-26=-2 23: 24-23=1 STEP 2 Find the mean of the distances. 3+4+1+3+0+3+2+1/8 = 17/8 = 2.125 So, the mean absolute deviation of the data is 2.125 Question 8. 99, 70, 78, 85, 76, 81 ________ Answer: The mean absolute deviation of the data is 2 Explanation: Mean: Mean = 99+70+78+85+76+81/6 = 489/6 = 81.5 Mean absolute deviation: STEP 1 Label each observation with its distance from the mean. Starting from left to right: 24: 23-24=-1 22: 23-22= 1 19: 23-19= 4 19: 23-19= 4 23: 23-23=0 23: 23-23=0 26: 23-26=-3 27: 23-27=-4 24: 23-24=-1 STEP 2 Find the mean of the distances. 1+1+4+4+3+4+1+0+0/9 = 18/9 = 2 So, the mean absolute deviation of the data is 2 Find the range and interquartile range of the data. Question 9. 2, 4, 8, 3, 2 The range is _________ . The interquartile range is _________ . Answer: 6 Explanation: The difference between the upper quartile and lower quartile. Range = 8 – 2 =6 Question 10. 84, 82, 86, 87, 88, 83, 84 The range is _________ . The interquartile range is _________ . Answer: 6 Explanation: The difference between the upper quartile and lower quartile. Range = 88 – 82 = 6 Question 11. 39, 22, 33, 45, 42, 40, 28 The range is _________ . The interquartile range is _________ . Answer: 23 Explanation: The difference between the upper quartile and lower quartile. Range = 45 – 22 = 23 ### Page No. 732 Question 12. Yasmine keeps track of the number of hockey goals scored by her school’s team at each game. The dot plot shows her data. Where is there a gap in the data? Type below: _________________ Answer: There is a gap in the data in the intervals: between 1 and 2 Explanation: As shown in the dot plot there is a gap between 1 and 2. This means that Yasmine’s team did not score only one goal when they played the game. Question 13. What is the interquartile range of the data shown in the dot plot with Question 12? The interquartile range is _________ . Answer: 2 Explanation: The interquartile range is the difference between the lower and upper quartiles. Interquartile range = 3-1 = 2 Question 14. Randall’s teacher added up the class scores for the quarter and used a histogram to display the data. How many peaks does the histogram have? Explain how you know. Type below: _________________ Answer: The graph has only one peak Explanation: In the given graph there is are rectangles out of which one has a tall rectangle which can be addressed as peak. Question 15. In a box plot of the data below, where would the box be drawn? 55, 37, 41, 62, 50, 49, 64 Type below: _________________ Answer: The box is drawn above the number line and this represents the median and the lower and upper limits. Explanation: A box is drawn to represent the median and the upper and lower limits in a box plot. ### Share and Show – Page No. 735 Question 1. The distances in miles students travel to get to school are 7, 1, 5, 9, 9, and 8. Decide which measure(s) of center best describes the data set. Explain your reasoning. Type below: _________________ Answer: Mean: 6.5 Median: 7.5 Mode: 9 Explanation: Mean: 7+1+5+9+9+8/6 = 39/6 = 6.5 Median: Ascending order: 1,5,7,8,9,9 Median = Mean of 7 and 8 = 7+8/2 = 15/2 = 7.5 Mode: The most frequently occurring observation is known as the mode. The mode is 9. Question 2. Use Graphs The numbers of different brands of orange juice carried in several stores are 2, 1, 3, 1, 12, 1, 2, 2, and 5. Make a box plot of the data and find the range and interquartile range. Decide which measure better describes the data set and explain your reasoning. Type below: _________________ Answer: Range: 11 Interquartile: 3 Interquartile range is the best way to represent the data. Explanation: Range = 12 – 1 = 11 Interquartile range : Median(of first 4 terms): Median = 1+1/2 = 2/2 = 1 Median (of last 4 terms): Median = 3+5/2 = 8/2 = 4 Interquartile range = 4 – 1 = 3 On Your Own Question 3. Use Reasoning The ages of students in a computer class are 14, 13, 14, 15, 14, 35, 14. Decide which measure of center(s) best describes the data set. Explain your reasoning. Type below: _________________ Answer: Mean:17 Median:14 Mode:14 Median and mode is the best ways to represent the data. Explanation: Mean: 14+13+14+15+14+35+14/7 = 119/7 = 17 Median: Ascending order: 13,14,14,14,14,15,35 Median = 14 Mode: The most frequently occurring observation is known as the mode. The mode is 14. Question 4. Mateo scored 98, 85, 84, 80, 81, and 82 on six math tests. When a seventh math test score is added, the measure of center that best describes his scores is the median. What could the seventh test score be? Explain your reasoning. Type below: _________________ Answer: Median is the best way to represent the data. Explanation: Median: Ascending order: 80,81,82,84,85,98 Median = Mean of 3 and 4 = 82+84/2 = 166/2 = 83 The seventh score can be 83 ### Unlock the Problem – Page No. 736 Question 5. Jaime is on the community swim team. The table shows the team’s results in the last 8 swim meets. Jaime believes they can place in the top 3 at the next swim meet. Which measure of center should Jaime use to persuade her team that she is correct? Explain. a. What do you need to find? Type below: _________________ Answer: Mean, median,mode Explanation: Mean= 1+2+2+3+3+1+18+2/8 = 32/8 = 4 Median: Ascending order: 1,1,2,2,2,3,3,18 Median = 2+2/2 = 2 Mode: The most frequently occurring observation is called a mode. Mode=2 Question 5. b. What information do you need to solve the problem? Type below: _________________ Answer: We need to have the data to find the centre of tendencies. Explanation: The given data can be used to find the mean, median and mode. Question 5. c. What are the measures of center? Type below: _________________ Answer: Mean = 4 Median = 2 Mode = 2 Explanation: There are three measures to calculate their approximate values. Question 5. d. Which measure of center should Jaime use? Explain. Type below: _________________ Answer: Median or mode Explanation: Median or mode are nearer to the solution, therefore, they can be used. Question 6. The numbers of sit-ups students completed in one minute are 10, 42, 46, 50, 43, and 49. The mean of the data values is 40 and the median is 44.5. Which measure of center better describes the data, the mean or median? Use words and numbers to support your answer. Type below: _________________ Answer: Median is the better way to represent the data. Explanation: 44.5 is closer and represents the more number of observations compared to the mean. ### Choose Appropriate Measures of Center and Variability – Page No. 737 Question 1. The distances, in miles, that 6 people travel to get to work are 14, 12, 2, 16, 16, and 18. Decide which measure(s) of center best describes the data set. Explain your reasoning. Type below: _________________ Answer: Mean= 13 miles Median= 15 miles Mode= 16 miles Explanation: Mean is less than the data points. Median describes the data in the best way compared to mean and mode. Question 2. The numbers of pets that several children have are 2, 1, 2, 3, 4, 3, 10, 0, 1, and 0. Make a box plot of the data and find the range and interquartile range. Decide which measure better describes the data set and explain your reasoning. Type below: _________________ Answer: Range = 10-0 = 10 Interquartile range = 3.5 – 0.5 = 3 The interquartile range is the best way to represent the data. Explanation: Ascending order: 0,0,1,1,2,2,3,3,4,10 Median = 2+2/2 = 2 Lower quartile = 0.5 Upper quartile= 7/2 = 3.5 Highest observation= 10 Lowest observation = 0 Range = 10-0 = 10 Interquartile range = 3.5 – 0.5 = 3 The interquartile range is the best way to represent the data. Problem Solving Question 3. Brett’s history quiz scores are 84, 78, 92, 90, 85, 91, and 0. Decide which measure(s) of center best describes the data set. Explain your reasoning. Type below: _________________ Answer: Mean is the best measure of centre to describe the data set. Explanation: Mean: Mean= 84+78+92+90+85+91+0/7 = 74.2 Median: Ascending order: 0,78,84,85,90,91,92 Median = 4th observation = 85 Question 4. Eight students were absent the following number of days in a year: 4, 8, 0, 1, 7, 2, 6, and 3. Decide if the range or interquartile range better describes the data set, and explain your reasoning. Type below: _________________ Answer: 8 represents all the terms range is more preferable compared to the interquartile range. Explanation: Ascending order: 0,1,2,3,4,6,7,8 Range = 8-0 = 8 Median = Mean of 3 and 4 = 3+4/2 = 7/2 = 3.5 Median of first 3 terms = 1 Median of last 3 terms = 7 Interquartile range = 7-1 = 6 Since 8 represents all the terms range is more preferable compared to the interquartile range. Question 5. Create two sets of data that would be best described by two different measures of centre. Type below: _________________ Answer: The given below are the examples of two sets of data that would be best described by two different measures of centre. Explanation: Example 1: The numbers of pets that several children have are 2, 1, 2, 3, 4, 3, 10, 0, 1, and 0. Make a box plot of the data and find the range and interquartile range. Decide which measure better describes the data set and explain your reasoning. Type below: _________________ Answer: Range = 10-0 = 10 Interquartile range = 3.5 – 0.5 = 3 The interquartile range is the best way to represent the data. Explanation: Ascending order: 0,0,1,1,2,2,3,3,4,10 Median = 2+2/2 = 2 Lower quartile = 0.5 Upper quartile= 7/2 = 3.5 Highest observation= 10 Lowest observation = 0 Range = 10-0 = 10 Interquartile range = 3.5 – 0.5 = 3 The interquartile range is the best way to represent the data. Example 2: Brett’s history quiz scores are 5,6,7,8,9,10. Decide which measure(s) of centre best describes the data set. Explain your reasoning. Type below: _________________ Answer: Mean and median are the best measure of centre to describe the data set. Explanation: Mean: Mean= 5+6+7+8+9+10/6 = 7.5 Median: Ascending order: 5,6,7,8,9,10 Median = Mean of 7 and 8 = 15/2 = 7.5 ### Lesson Check – Page No. 738 Question 1. Chloe used two box plots to display some data. The box in the plot for the first data set is wider than the box for the second data set. What does this say about the data? Type below: _________________ Answer: The graphs say that the interquartile range is more for the second graph compared to the first. Explanation: The interquartile range is the difference between the lower and upper quartiles. It is more for wider data compared to the compact data. Question 2. Hector recorded the temperature at noon for 7 days in a row. The temperatures are 20°F, 20°F, 20°F, 23°F, 23°F, 23°F, and 55°F. Which measure of center would best describe the data? Type below: _________________ Answer: Mode Explanation: The most frequently occurring observation is known as mode. The mode of the above data describes the data well, the mode of the data is 20°F Spiral Review Question 3. By how much does the median of the following data set change if the outlier is removed? 13, 20, 15, 19, 22, 26, 42 Type below: _________________ Answer: 0.5 Explanation: Median: Ascending order: 13,15,19,20,22,26,42 Median = 20 If the outlier is removed then the median= 19+20/2 = 39/2 = 19.5 The difference in the medians = 0.5 Question 4. What percent of the people surveyed spent at least an hour watching television? _______ % Answer: 8 people Explanation: Total number of people= 40 Percentage = 8/40 x 100 = 20% Question 5. What is the lower quartile of the following data? 12, 9, 10, 8, 7, 12 The lower quartile is _______ . Answer: Explanation: Ascending order: 7,8,9,10,12,12 Median = 9+10/2 = 9.5 Lower quartile = 8 Question 6. What is the interquartile range of the data shown in the box plot? The interquartile range is _______ . Answer: 5 Explanation: The difference between the upper and lower quartiles is called as interquartile range. Interquartile range = 14 – 9 = 5 ### Share and Show – Page No. 741 Question 1. Zoe collected data on the number of points her favourite basketball players scored in several games. Use the information in the table to compare the data. The mean of Player 1’s points is __ the mean of Player 2’s points. The interquartile range of Player 1’s points is __ the interquartile range of Player 2’s points. So, Player 2 typically scores __ points than Player 1, but Player 2’s scores typically vary __ Player 1’s scores Type below: _________________ Answer: less than ; less than ; more ; more Explanation: The mean of Player 1’s points is less than the mean of Player 2’s points. The interquartile range of Player 1’s points is less than the interquartile range of Player 2’s points. So, Player 2 typically scores more points than Player 1, but Player 2’s scores typically vary in more Player 1’s scores Question 2. Mark collected data on the weights of puppies at two animal shelters. Find the median and range of each data set, and use these measures to compare the data. Type below: _________________ Answer: They differ slightly but on an average we can say that shalter B is more as compared to shelter A Explanation: Shelter A Median: Ascending order: 5,7,7,7,10,12,15 Median = 4th observation = 7 Range = 15-5 = 10 Shelter B Median: Ascending order: 4,5,5,11,11,13,15 Median = 4th observation = 11 Range = 15-4 = 11 On Your Own Kwan analyzed data about the number of hours musicians in her band practice each week. The table shows her results. Use the table for Exercises 3–5. Question 3. Which two students typically practised the same amount each week, with about the same variation in practice times? Type below: _________________ Answer: Sally and Jennifer Explanation: They are slightly different but on a whole, the average shows no difference and we can say that Sally and Jennifer practised for the same amount each week Question 4. Which two students typically practised the same number of hours, but had very different variations in their practice times? Type below: _________________ Answer: Tim and Sally Explanation: They are different in range but on a whole, the average shows no difference and we can say that Sally and Tim practised for the same number of hours, but had very different variations in their practice times. Question 5. Which two students had the same variation in practice times, but typically practised a different number of hours per week? Type below: _________________ Answer: Matthew and Tim Explanation: Matthew and Tim practised for the same number of hours but they had a high variation in the range. ### Problem Solving + Applications – Page No. 742 Question 6. Compare The table shows the number of miles Johnny ran each day for two weeks. Find the median and the interquartile range of each data set, and use these measures to compare the data sets. Type below: _________________ Answer: Interquartile range is the best way to compare the data in the week 1 While the median is the best way to compare the data in the week 2 Explanation: Week 1 Median: Ascending order: 1,2,2,3,3,4,5 Median = 4th observation = 3 Lower quartile range= 2 Upper quartile range= 4 Interquartile range = 4-2 = 2 Week 2 Median: Ascending order: 1,1,1,3,3,8,8 Median = 4th observation = 3 Lower quartile range= 1 Upper quartile range= 8 Interquartile range = 8-1 = 7 Question 7. Sense or Nonsense? Yashi made the box plots at right to show the data he collected on plant growth. He thinks that the variation in bean plant growth was about the same as the variation in tomato plant growth. Does Yashi’s conclusion make sense? Why or why not? Type below: _________________ Answer: Sense Explanation: Yashi said that thinks that the variation in bean plant growth was about the same as the variation in tomato plant growth. It is a true statement because the range of both bean and tomato plants growth is the same and they have the same medians. Question 8. Kylie’s teacher collected data on the heights of boys and girls in a sixth-grade class. Use the information in the table to compare the data. The mean of the boys’ heights is _____ the mean of the girls’ heights. The range of the boys’ heights is _____ the range of the girls’ heights. Answer: more than ; more than Explanation: Mean of boys height: Mean = 72+68+70+56+58+62+64/7 = 64.2 Range= 72-56 = 16 Mean of girls height: Mean = 55+60+56+51+60+63+65/7 = 58.5 Range= 65-51 = 14 The mean of the boys’ heights is _more than____ the mean of the girls’ heights. The range of the boys’ heights is _more than____ the range of the girls’ heights. ### Apply Measures of Center and Variability – Page No. 743 Solve. Question 1. The table shows temperature data for two cities. Use the information in the table to compare the data. The mean of City 1’s temperatures is the ———————– mean of City 2’s temperatures. The ———————- of City 1’s temperatures is————— the —————–of City 2’s temperatures. So, City 2 is typically —————-City 1, but City 2’s temperatures vary ——————-City 1’s temperatures. Type below: _________________ Answer: less than; interquartile range; less than; interquartile range; warmer than; more than Explanation: The mean of City 1’s temperatures is the —-less than———- mean of City 2’s temperatures. The –interquartile range——— of City 1’s temperatures is—less than—– the —-interquartile range—–of City 2’s temperatures. So, City 2 is typically —warmer than—–City 1, but City 2’s temperatures vary —–more than——-City 1’s temperatures. Question 2. The table shows weights of fish that were caught in two different lakes. Find the median and range of each data set, and use these measures to compare the data. Type below: _________________ Answer: Lake A’s average is greater but varies more. Explanation: Lake A Median: Ascending order: 4,6,7,9,10,12 Median = Mean 3rd and 4th observation = 7+9/2 = 8 Range = 12 – 4 = 8 Lake B Median: Ascending order: 4,4,5,6,6,7 Median = Mean 3rd and 4th observation = 5+6/2 = 5.5 Range = 7 – 3 = 4 Problem Solving Question 3. Mrs. Mack measured the heights of her students in two classes. Class 1 has a median height of 130 cm and an interquartile range of 5 cm. Class 2 has a median height of 134 cm and an interquartile range of 8 cm. Write a statement that compares the data. Type below: _________________ Answer: Class 2 is greater but varies more. Explanation: The interquartile range is the difference between the lower and upper quartiles. Since the interquartile range is more for class 2 we can say that the extremes are greater while the interquartile range is less for class 1 which means that the data is compact. Question 4. Richard’s science test scores are 76, 80, 78, 84, and 80. His math test scores are 100, 80, 73, 94, and 71. Compare the medians and interquartile ranges. Type below: _________________ Answer: Medians are equal but the interquartile range varies a large, math test scores are more spread out compared to science test scores. Explanation: Science test scores: Median: Ascending order: 76,78,80,80,84 Median = 3rd observation = 80 Interquartile range = 84 – 76 = 10 Math test scores: Median: Ascending order: 71,73,80,94,100 Median = 3rd observation = 80 Interquartile range = 100 – 71 = 29 Medians are equal but the interquartile range varies a large, math test scores are more spread out compared to science test scores. Question 5. Write a short paragraph to a new student that explains how you can compare data sets by examining the mean and the interquartile range. Type below: _________________ Answer: average and consistency Explanation: If the mean is more it means that the data has more observations or observations with more value. Interquartile range and median range say about the consistency. ### Lesson Check – Page No. 744 Question 1. Team A has a mean of 35 points and a range of 8 points. Team B has a mean of 30 points and a range of 7 points. Write a statement that compares the data. Type below: _________________ Answer: Similar variation but team A average is more than team B Explanation: The range has only a difference of 1 point which can be said as a slight variation but while the average/ mean has a large variation. Question 2. Jean’s test scores have a mean of 83 and an interquartile range of 4. Ben’s test scores have a mean of 87 and an interquartile range of 9. Compare the students’ scores. Type below: _________________ Answer: Ben’s average is more than Jean’s but Ben is less consistent compared to Jean. Explanation: Ben’s average score is more than the average scores of Jean while the interquartile range Spiral Review Question 3. Look at the box plots below. What is the difference between the medians for the two groups of data? _______ students Answer: 2 students Explanation: Median of students in a class of school A = 24 Median of students in a class of school B = 26 Difference between the medians of the schools = 26-24 = 2 students Question 4. The distances in miles that 6 people drive to get to work are 10, 11, 9, 12, 9, and 27. What measure of center best describes the data set? Type below: _________________ Answer: Median is the centre best describes the data set Explanation: Median: AScending order: 9,9,10,11,12,27 Median= 3rd and 4th observations = 10+11/2 = 21/2 = 10.5 Question 5. Which two teams typically practice the same number of hours, but have very different variations in their practice times? Type below: _________________ Answer: Team A and C Explanation: Team A and C have medians which nare only slightly different but the consistency varies a lot that is range. ### Share and Show – Page No. 747 Connie asked people their ages as they entered the food court at the mall. Use the histogram of the data she collected for 1–5. Question 1. What statistical question could Connie ask about her data? Type below: _________________ Answer: Mean, Median, Mode Explanation: The graph shows the age and number of people. The questions which can be asked can be of mean, median, mode. Question 2. Describe any peak or gap in the data. Type below: _________________ Answer: Peak : 21-30 Gap : 61-70 Explanation: There is a peak in the graph at the interval 21-30 There is a gap in between the bars of the histogram the bar which had a gap before it was 61-70 Question 3. Does the graph have symmetry? Explain your reasoning. Type below: _________________ Answer: No the graph doesn’t have symmetry Explanation: The symmetry of the graph means there must be equal parts of the graph on both the sides of the line of the graph. This is not possible in the above situation. On Your Own Question 4. The lower quartile of the data set is 16.5 years, and the upper quartile is 51.5 years. Find the interquartile range. Is it a better description of the data than the range? Explain your reasoning. Type below: _________________ Answer: Interquartile range = 35; The interquartile range is better than the range. Explanation: The interquartile range is the difference between the upper quartile and the lower quartile. Interquartile range = 51.5-16.5 = 35 The interquartile range is better than the range because if we take the example of the above graph we can see thatthe most of the data fall in the range of the interquartile range ie. 35. Therefore we can say that the interquartile range is better than the range. Question 5. Make Arguments The mode of the data is 16 years old. Is the mode a good description of the center of the data? Explain Type below: _________________ Answer: No mode is not a good description of the data. Explanation: The mode is just a frequently occurring observation. It cannot be the best way to describe the data. ### Problem Solving + Applications – Page No. 748 Use the dot plot for 6–8. Question 6. Make Arguments Jason collected data about the number of songs his classmates bought online over the past 3 weeks. Does the data set have symmetry? Why or why not? Type below: _________________ Answer: No, the data has no symmetry. Explanation: No, the data has no symmetry. Because there are gaps between the dots drawn. Question 7. Jason claims that the median is a good description of his data set, but the mode is not. Does his statement make sense? Explain. Type below: _________________ Answer: Median can be a better centre of description. Therefore his statement makes a sense. Explanation: Median = 7+8/2 = 15/2 = 7.5 The number 7.5 represents more number of observations. Question 8. Trinni surveyed her classmates about how many siblings they have. A dot plot of her data increases from 0 siblings to a peak at 1 sibling and then decreases steadily as the graph goes to 6 siblings. How is Trinni’s dot plot similar to Jason’s? How is it different? Type below: _________________ Answer: Trinni graph represents a part of Jason’s graph Explanation: In Jason’s graph, there is a peak in the middle and then it decreases on both sides. But according to Trinni graph, there is no peak in the middle. Question 9. Diego collected data on the number of movies seen last month by a random group of students. Draw a box plot of the data and use it to find the interquartile range and range. Type below: _________________ Answer: Range = 12 Interquartile range = 2 Explanation: The range is the difference between the highest and lowest observations. Range = 12-0 = 12 The interquartile range is the difference between the upper and lower quartiles. Ascending order: 0,0,1,1,2,2,2,2,3,3,3,5,12 Lower quartile = 1+1/2 = 2/2 = 1 Upper quartile = 3+3/2 = 6/2 = 3 Interquartile range = 3-1 = 2 ### Describe Distributions – Page No. 749 Chase asked people how many songs they have bought online in the past month. Use the histogram of the data he collected for 1–4. Question 1. What statistical question could Chase ask about the data? Type below: _________________ Answer: What is the median number of songs purchased? Explanation: Many questions can be formed from the data given to us We can ask about the mean, median, mode. Question 2. Describe any peaks in the data. Type below: _________________ Answer: Peak : 0-4 Explanation: The peak is a bar in the histogram which has the highest value. The peak of the given graph is 0-4 Question 3. Describe any gaps in the data. Type below: _________________ Answer: There are no gaps in the graph. Explanation: The gap is something between a bar of the histogram and all the other adjacent bars. There no such case in the graph. Therefore there are no gaps in the graph. Question 4. Does the graph have symmetry? Explain your reasoning. Type below: _________________ Answer: No the graph doesn’t have symmetry Explanation: The symmetry of the graph means there must be equal parts of the graph on both the sides of the line of the graph. This is not possible in the above situation. Problem Solving Question 5. Mr. Carpenter teaches five classes each day. For several days in a row, he kept track of the number of students who were late to class and displayed the results in a dot plot. Describe the data. Type below: _________________ Answer: Peaks: At 6 and 8 Gaps: Between 3 and 5 , 6 and 8 Clusters: Between 0-3 ; 9-11 Explanation: The highest points in the graph are known as peaks. They are at 6 and 8 in this graph. The space between the dots in the dot plot graph is known as gaps. Gaps are between 3 and 5; 6 and 8 The group of the dots in the dot plot are known as clusters. The clusters are at the 0-3; 9-11 Question 6. Describe how a graph of a data set can be used to understand the distribution of the data. Type below: _________________ Answer: Mean, median, mode Explanation: There are three measures of centre which can be used to describe the data given in the form of a graph. The three measures of centre are mean, median, mode. ### Lesson Check – Page No. 750 Question 1. The ages of people in a restaurant are 28, 10, 44, 25, 18, 8, 47, and 30. What is the median age of the people in the restaurant? _______ years old Answer: Median age of the people in the restaurant is 26.5 approximately 27 Explanation: Median: Ascending order: 8,10,18,25,28,30,44,47 Median = Mean of 4th and 5th observations = 25+28/2 = 53/2 = 26.5 Question 2. What is the median in the dot plot?$ ________

Explanation:
Median is the middlemost value and it is 11 in the above graph.
We need to consider the middle value by neglecting the same number on both the sides.

Spiral Review

Question 3.
Look at the dot plot. Where does a gap occur in the data?

Type below:
_________________

Explanation:
The gap is a space between the intervals.
The intervals are 30-33.

Question 4.
Look at the dot plot. Where does a peak occur in the data?

Type below:
_________________

Explanation:
The highest point in the graph is known as the peak.
The peak in the dot plot is 37.

Question 5.
Which two teams had similar variations in points earned, but typically earned a different number of points per game?

Type below:
_________________

Answer: Red and blue

Explanation:
The difference between the upper and lowest observations is called a range.
The range (consistency) in the data given is the same but they vary in the mean.
But we can say that Red and Blue teams typically earned a different number of points per game.

Question 6.
Manny’s monthly electric bills for the past 6 months are $140,$165, $145,$32, $125, and$135. What measure of center best represents the data?
Type below:
_________________

Answer: Median is the best way to represent the data. Median= 137.5

Explanation:
Median:
Ascending order: 32,125,135,140,145,165
Median = 135+140/2 = 275/2 = 137.5

### Share and Show – Page No. 753

Question 1.
Josh is playing a game at the carnival. If his arrow lands on a section marked 25 or higher, he gets a prize. Josh will only play if most of the players win a prize. The carnival worker says that the average (mean) score is 28. The box plot shows other statistics about the game. Should Josh play the game? Explain your reasoning.

First, look at the median. The median is _ points.
Next, work backwards from the statistics.
The median is the __ value of the data.
So, at least __ of the values are scores
less than or equal to _.
Finally, use the statistics to draw a conclusion.
Type below:
_________________

Answer: middlemost value; 20; 15

Explanation:
First, look at the median. The median is 20 points.
Next, work backwards from the statistics.
The median is the middlemost value of the data.
So, at least 20 of the values are scores
less than or equal to 15.
Finally, use the statistics to draw a conclusion.

Question 2.
What if a score of 15 or greater resulted in a prize? How would that affect Josh’s decision? Explain.
Type below:
_________________

Answer: It doesn’t affect his decision.

Explanation:
Josh wanted to play only when most of the prizes were awarded.
Therefore if the minimum score was 15 or greater than it then they would get the prize. So there will be no difference in his decision.

Question 3.
A store collects data on the sales of DVD players each week for 3 months. The manager determines that the data has a range of 62 players and decides that the weekly sales were very inconsistent. Use the statistics in the table to decide if the manager is correct. Explain your answer.

Type below:
_________________

Answer: No the manager is not correct.

Explanation:
The range is given to be 62.
The range is correct when we check it with the help of the given data, therefore, the data is not inconsistent.

### On Your Own – Page No. 754

Question 4.
Gerard is fencing in a yard that is 21 feet by 18 feet. How many yards of fencing material does Gerard need? Explain how you found your answer.
_______ yards

Answer: 78 yards of the fencing material is required

Explanation:
Length = 21 feet  Breadth = 18 feet
The perimeter of the rectangle = The number of yards of fencing material required = 2(l+b) = 2(21+18) = 2(39) = 78 yards

Question 5.
Susanna wants to buy a fish that grows to be about 4 in. long. Mark suggests she buys the same type of fish he has. He has five of these fish with lengths of 1 in., 1 in., 6 in., 6 in., and 6 in., with a mean length of 4 in. Should Susanna buy the type of fish that Mark suggests? Explain.
Type below:
_________________

Answer: Yes Susanna buy the type of fish that Mark suggests

Explanation:
The length of fish suggested by Mark is 4 in. long.
Mark has 5 fishes with a mean length of 4 in.
To buy a fish of that grows to be about 4 in. long. Susanna should buy the fishes suggested by Mark.

Question 6.
Look for a Pattern The graph shows the number of stamps that Luciano collected over several weeks. If the pattern continues, how many stamps will Luciano collect in Week 8? Explain.

_______ stamps

Explanation:
In week 4 and 6, the number of stamps are 4, 5. Therefore in week 6 and 8, the number of stamps are 5, 7

Question 7.
The data set shows the number of hours Luke plays the piano each week. Luke says he usually plays the piano 3 hours per week. Why is Luke’s statement misleading?

Type below:
_________________

Answer: According to the question he should spend 3 hours per week. His statement is correct.

Explanation:
Sum of the data = 1+2+1+3+2+10+2 = 21
Number of days in a week = 7
Mean = 21/7 = 3 hours

### Problem Solving Misleading Statistics – Page No. 755

Mr Jackson wants to make dinner reservations at a restaurant that has most meals costing less than $16. The Waterside Inn advertises that they have meals that average$15. The table shows the menu items.

Question 1.
What is the minimum price and the maximum price?
minimum: $_________ maximum:$ _________

Answer: minimum: $6 maximum:$19

Explanation:
The minimum value is the most minimum price in the given data.
The maximum value is the most maximum price in the given data.

Question 2.
What is the mean of the prices?
$________ Answer:$15

Explanation:
Mean = sum of all the observations/ total number of observations = 6+16+18+16+18+19/6 = 93/6 = 15.2
Approximately therefore the mean of the observations is $15 Question 3. Construct a box plot for the data. Type below: _________________ Answer: The box plot is a diagram which signifies the information about the data. Explanation: The box plot represents the range, lower and upper quartiles. Question 4. What is the range of the prices?$ ________

Answer: the range is $13 Explanation: The difference between the upper and lower observations is known as the range. Range = 19-6 =$13

Question 5.
What is the interquartile range of the prices?
$________ Answer:$7.5

Explanation:
Ascending order: $6,$16, $16,$18, $18,$19
Median = 16+18/2 = 34/2 = 17
Lower quartile = 6+16/2 = 11
Upper quartile = 18+19/2 = 18.5
Interquartile range = 18.5-11 = 7.5

Question 6.
Does the menu match Mr. Jackson’s requirements? Explain your reasoning.
Type below:
_________________

Answer: Yes the menu matches Mr Jackson’s requirements.

Explanation:
Mr Jackson wants to make dinner arrangements with cost less than $16. The mean of the items in the menu: Mean =$6+$16+$16+$18+$18+$19/6 = 93/6 =$15.5
Therefore the requirements of Mr Jackson is satisfied.

Question 7.
Give an example of a misleading statistic. Explain why it is misleading.
Type below:
_________________

Explanation:
According to the information given in the question, The Waterside Inn advertises that they have meals that average $15. But it is more than that, so this is the misleading statement. The mean of the items in the menu: Mean =$6+$16+$16+$18+$18+$19/6 = 93/6 =$15.5
Therefore the requirements of Mr Jackson is satisfied.

### Lesson Check – Page No. 756

Question 1.
Mary’s science test scores are 66, 94, 73, 81, 70, 84, and 88. What is the range of Mary’s science test scores?
________

Explanation:
The difference between the highest and the lowest observations is called a range.
Range = 94 – 66 = 28

Question 2.
The heights in inches of students on a team are 64, 66, 60, 68, 69, 59, 60, and 70. What is the interquartile range?
________

Answer: Interquartile range = 9

Explanation:
Ascending order: 59,60,60,64,66,68,69,70
Median = Mean of 64 and 66 = 64+66/2 = 130/2 = 65
Lower quartile = 60
Upper quartile = 69
Interquartile range = 69 – 60 = 9

Spiral Review

Question 3.
By how much does the median of the following data set change if the outlier is removed?
26, 21, 25, 18, 0, 28
Type below:
_________________

Answer: The median changes by 3.5

Explanation:
Ascending order: 0,18,21,25,26,28
Median = 21+28/2 = 49/2 = 24.5
If the outlier is removed then the
Median = 21
Difference between the 1st and 2nd median = 24.5 – 21 = 3.5

Question 4.
Look at the box plot. What is the interquartile range of the data?

________

Answer: Interquartile range = 6

Explanation:
The difference between the lower and upper quartiles is known as the interquartile range.
Interquartile range = 50 – 44 = 6

Question 5.
Erin is on the school trivia team. The table shows the team’s scores in the last 8 games. Erin wants to build confidence in her team so that they will do well in the last game. If a score of 20 is considered a good score, what measure of center would be best for Erin to use to motivate her teammates?

Type below:
_________________

Answer: Mean and median are the best centre of tendencies to compare the data.

Explanation:
Mean = 20+20+18+19+23+40+22+19/8 = 181/8 = 22.6
Median:
Ascending order: 18,19,19,20,20,22,23,40
Median = 40/2 = 20

### Chapter 13 Review/Test – Page No. 757

Question 1.
The dot plot shows the number of chin-ups done by a gym class.

For numbers 1a–1e, choose Yes or No to indicate whether the statement is correct.
1a. There are two peaks.
1b. There are no clusters.
1c. There is a gap from 6 to 8.
1d. The most chin-ups anyone did was 15.
1e. The modes are 3, 4, and 9.
1a. ____________
1b. ____________
1c. ____________
1d. ____________
1e. ____________

1b. No
1c. Yes
1d. No
1e. Yes

Explanation:
1a. The highest point in the dot plot is called the peak. The peak in the given dot plot is at 5 and 11 the value of the peak is 3
1b. The group of dots form a cluster with 3 or more intervals.
1c. There is a gap between the intervals 6-8
1d. The maximum number of people did 11 chin-ups while only a single person did 15 chin-ups.
1e. The most frequently occurring observation is known as mode.
The mode of the given data is at the intervals 3,4 and 9.

Question 2.
The histogram shows the high temperatures in degrees Fahrenheit of various cities for one day in March.

Select the best word to complete each sentence.
The histogram has _____ peak(s).
The histogram _____ symmetry.

Answer: The histogram has 1 peak(s).
The histogram is symmetry.

Explanation:
The is one and only one peak at the interval 41 – 50
We can say that the graph is symmetrical because if we draw a line between the graph we can observe that the graph has two parts symmetric to each other.

### Chapter 13 Review/Test – Page No. 758

Question 3.
The data set shows the scores of the players on the winning team of a basketball game.

The median is _____.
The lower quartile is _____.
The upper quartile is _____.

Lower quartile = 1
Upper quartile =19.5

Explanation:
Ascending order: 0,0,1,1,4,5,6,9,13,17,22,30,47
Median = 6
Lower quartile = Mean of 1 and 1 = 1+1/2 = 2/2 = 1
Upper quartile = Mean of 17 and 22 = 17+22/2 = 39/2 = 19.5

Question 4.
The data set shows the number of desks in 12 different classrooms.

Find the values of the points on the box plot.

Type below:
_________________

Answer: A= 16 B=17 C= 20 D= 21 E=24

Explanation:
Ascending order: 16,17,17,18,19,20,20,21,21,21,22,24
Median = 20+20/2 = 20
Lower quartile = 17
Upper quartile = 21

Question 5.
The box plot shows the number of boxes sold at an office supply store each day for a week.

For numbers 5a–5d, select True or False for each statement.
5a. The median is 18.
5b. The range is 15.
5c. The interquartile range is 9.
5d. The upper quartile is 18.
5a. ____________
5b. ____________
5c. ____________
5d. ____________

5b. true
5c. true
5d. true

Explanation:
Median is the middlemost value of the given data.
Median of the data is 14
The range is the difference between the upper and lower observations.
Range = 21-6 = 15
The interquartile range is the difference between the upper and lower observations.
Upper quartile range: 18
Interquartile range = 18-9 = 9

### Chapter 13 Review/Test – Page No. 759

Question 6.
The data set shows the number of glasses of water Dalia drinks each day for a week.

Part A
What is the mean number of glasses of water Dalia drinks each day?
_______ glasses

Answer: The mean number of glasses of water Dalia drinks each day is 8 glasses.

Explanation:
Mean = sum of all the observations/ total number of observations= 6+7+9+9+8+7+10/7 = 8

Question 6.
Part B
What is the mean absolute deviation of the number of glasses of water Dalia drinks each day? Round your answer to the nearest tenth. Use words and numbers to support your answer.
_______

Answer: Mean absolute deviation is 1.14

Explanation:

Mean:
Mean = sum of all the observations/ total number of observations= 6+7+9+9+8+7+10/7 = 8

Mean absolute deviation:

STEP 1 Label each observation with its distance from the mean.
Starting from left to right:
06: 8-6  = 02
07: 8-7  = 01
09: 8-9  = -1
09: 8-9  = -1
08: 8-8  =  0
07: 8-7  = 01
10: 8-10= -2

STEP 2 Find the mean of the distances.
2+1+1+1+0+1+2/7
= 8/7 = 1.14

So, the mean absolute deviation of the data is 1.14

Question 7.
The numbers of emails Megan received each hour are 9, 10, 9, 8, 7, and 2. The mean of the data values is 7.5 and the median is 8.5. Which measure of center better describes the data, the mean or median? Use words and numbers to support your answer.
Type below:
_________________

Answer: Mean is the best centre of tendency to represent the data given in the question

Explanation:
Ascending order of the data: 2,7,8,9,9,10
Mean = 7.5
Mean represents the observations 8,9,9,10 which come after 7.5
Therefore mean is the best way to represent the data.

Question 8.
The number of miles Madelyn drove between stops was 182, 180, 181, 184, 228, and 185. Which measure of center best describes the data?
Options:
a. mean
b. median
c. mode

Explanation:
Ascending order: 180,181,182,184,185,228
Median = 182+184/2 = 183
183 represents all the observations after 182
So the median is the best way to represent the data.

### Chapter 13 Review/Test – Page No. 760

Question 9.
The histogram shows the weekly earnings of part-time workers. What interval(s) represents the most common weekly earnings?

Type below:
_________________

Answer: 321-330 ; 341-350

Explanation:
The histogram has 2 intervals which show equal heights which means that the monthly earnings of these intervals is the same.

Question 10.
Jordan surveyed a group of randomly selected smartphone users and asked them how many applications they have downloaded onto their phones. The dot plot shows the results of Jordan’s survey. Select the statements that describe patterns in the data. Mark all that apply.

Options:
a. The modes are 37 and 42.
b. There is a gap from 38 to 40.
c. There is a cluster from 41 to 44.
d. There is a cluster from 35 to 36.

Answer: b. There is a gap from 38 to 40.

Explanation:
The dot plot represents a gap between 38-40. So we can say that there is a gap between the intervals 38 to 40.

### Chapter 13 Review/Test – Page No. 761

Question 11.
Mrs. Gutierrez made a histogram of the birth month of the students in her class. Describe the patterns in the histogram by completing the chart.

Type below:
_________________

Answer: There are 2 peaks, Yes there is an increase across the intervals, Yes there is a decrease across the intervals

Explanation:
The highest point in the histogram is called is as a peak.
There is a peak near the month’s May and August.

There is an increase between the bars in the bar graph.
At the months February, March, November there is an increase in the graph.

There is a decrease between the bars in the bar graph.
At the months September, October, December.

Question 12.
Ian collected data on the number of children in 13 different families.

Draw a box plot of the data and use it to find the interquartile range and range.
Type below:
_________________

Answer: Range = 8-0 = 8 Interquartile range = 3-1 = 2

Explanation:

Ascending order:
0,0,1,1,1,1,2,2,2,3,3,4,8
Median = 2
Lower quartile = 1+1/2 = 1
Upper quartile = 3+3/2 = 3
Range = 8-0 = 8
Interquartile range = 3-1 = 2

### Chapter 13 Review/Test – Page No. 762

Question 13.
Gavin wants to move to a county where it rains about 5 inches every month. The data set shows the monthly rainfall in inches for a county. The mean of the data is 5 and the median is 4.35. After analyzing the data, Gavin says that this county would be a good place to move. Do you agree or disagree with Gavin? Use words and numbers to support your answer.

Type below:
_________________

Answer: Yes I agree that it is a good place to move.

Explanation:
After analyzing the data we can say that this country would be a good place to move for Gavin.
Gavin wants to move to a place which has an average of 5 cm rainfall. So this country is the best choice because it has a mean equal to 5 and median equal to 4.35

Question 14.
The data set shows the number of books Peyton reads each month. Peyton says she usually reads 4 books per month. Why is Peyton’s statement misleading?

Type below:
_________________

Answer: No Peyton’s statement is not misleading because the mean of the data is 4.
Therefore Peyton says she usually reads 4 books per month.

Explanation:
Mean = 2+3+2+4+3+11+3/7 = 28/7 = 4

Question 15.
The data set shows the scores of three players for a board game.

For numbers 15a–15d, choose Yes or No to indicate whether the statement is correct.
15a. The mean absolute deviation of Player B’s scores is 0.
15b. The mean absolute deviation of Player A’s scores is 0.
15c. The mean absolute deviation of Player B’s scores is greater than the mean absolute deviation of Player C’s scores.
15a. ___________
15b. ___________
15c. ___________

15b. Yes
15c.  Yes

Explanation:
Mean of player A = 90+90+90/3 = 90

Mean absolute deviation:

STEP 1 Label each observation with its distance from the mean.
Starting from left to right:
90: 90-90  = 0
90: 90-90  = 0
90: 90-90  = 0

STEP 2 Find the mean of the distances.
0+0+0/3 = 0
So, the mean absolute deviation of player A is 0

Mean of player B = 110+100+90/3 = 100

Mean absolute deviation:

STEP 1 Label each observation with its distance from the mean.
Starting from left to right:
100: 100-110  = -10
100: 100-100  = 0
100: 100-90    = 10

STEP 2 Find the mean of the distances.
10+0+10/3 = 20/3 = 6.67
So, the mean absolute deviation of player B is 6.67

Mean of player C = 95+100+95/3 = 96.67

Mean absolute deviation:

STEP 1 Label each observation with its distance from the mean.
Starting from left to right:
96.67: 96.67-95    = 1.67
96.67: 96.67-100  = -3.33
96.67: 96.67-95    = 1.67

STEP 2 Find the mean of the distances.
1.67+3.33+1.67/3 = 6.67/3 = 2.22
So, the mean absolute deviation of player C is 2.22

Conclusion:

Hope the solutions provided in this Go Math Grade 6 Answer Key Chapter 13 are helpful for all the students. Download the Answer Key of Go Math Grade 6 Chapter 13 Variability and Data Distributions and start your preparation now. Stay with us to get the solutions of all Grade 6 chapters.

## Go Math Grade 6 Answer Key Chapter 1 Divide Multi-Digit Numbers

Go Math Grade 6 Answer Key Chapter 1 Divide Multi-Digit Numbers contains the topics like Divide Multi-Digit Numbers, Prime Factorization, LCM, GCF, etc. So the students of Grade 6 can refer our Go Math Grade 6 Answer Key  and solve the problems. With the help of Go Math 6th Grade Chapter, 1 Answer Key the scholars will not find any difficulty in solving the questions. This HMH Go Math Grade 6 Chapter 1 answer key is very useful to students in solving assignments and puzzles. The solutions are explained in a simple way that students can grasp easily.

## Go Math Grade 6 Answer Key Chapter 1 Divide Multi-Digit Numbers

The Go Math Answer Key helps in finding solutions for Grade 6 students. As Go Math Grade 6 Answer Key Chapter 1 Divide Multi-Digit Numbers makes students, teachers to understand and learn quickly. Go Math Grade 6 Answer Key helps students to make solutions understand easily and gain knowledge. And every solution wast presented in a unique way and students will never face any difficulty in learning.

Lesson 1: Divide Multi-Digit Numbers

Lesson 2: Prime Factorization

Lesson 3: Least Common Multiple

Lesson 4: Greatest Common Factor

Lesson 5: Problem Solving • Apply the Greatest Common Factor

Mid-Chapter Checkpoint

Lesson 6: Add and Subtract Decimals

Lesson 7: Multiply Decimals

Lesson 8: Divide Decimals by Whole Numbers

Lesson 9: Divide with Decimals

Chapter 1 Review/Test

### Page No. 7

Estimate. Then find the quotient. Write the remainder, if any, as a fraction.

Question 3.
6,114 ÷ 63

Answer:  Quotient is 97 3/63= 97 1/21 and the remainder is 3

Explanation:

Question 4.
11050 ÷ 26

Answer: Quotient is 425 and the remainder is 0.

Explanation:

Estimate. Then find the quotient. Write the remainder, if any, as a fraction.

Question 5.
3150 ÷ 9

Answer: Quotient is 350 and the remainder is 0.

Explanation:

Question 6.
2115 ÷ 72

Answer: Quotient is 29 27/72= 29 3/8 and the remainder is 27.

Explanation:

Question 7.
20835 ÷ 180

Answer: Quotient is 115 135/180= 115 3/4 and the remainder is 135

Explanation:

Question 8.
Find the least whole number that can replace ? to make the statement true.
110 < ? ÷ 47

Answer: Least whole number is 5,171.

Explanation: 110×47= 5,170

Question 9.
Use Reasoning Name two whole numbers that can replace ? to make both statements true.
2 × ? < 1800 ÷ 12                         ? > 3744 ÷ 52

Explanation:

Question 10.
The 128 employees of a company volunteer 12,480 hours in 26 weeks. On average, how many hours do they all volunteer per week? On average, how many hours does each employee volunteer per week?

Explanation: In 26  weeks 128 employees volunteer 12,480 hours, so in 1 week they volunteer 12,480÷26= 480 hours.
And each employee volunteer per week is 480÷128= 3.75 hours.

Question 11.
A factory produces 30,480 bolts in 12 hours. If the same number of bolts are produced each hour, how many bolts does the factory produce in 5 hours?

Explanation: As the factory produces 30,480 bolts in 12 hours, so in a 1-hour company produces 30,480÷12= 2,450 boults and in 5 hours it produces 2,450×5= 12,700.

### Problem Solving + Applications – Page No. 8

Use the table for 12-15.

Question 12.
A Smooth Flight jet carried 6,045 passengers last week, and all of its flights were full. How many flights did the jet make last week?

Explanation: As there are 403 seats in Smooth flight and 6,045 passengers are carried in last week, so no.of flights did the jet make in last week are 6045÷403= 15

Question 13.
Last month an airline made 6,322 reservations for flights from Newark, New Jersey, to Frankfurt, Germany. If there were 21 full flights and 64 reservations cancelled, which airplane made the flights?

Explanation: Total reservations made by the airline are 6,322 and cancelled are 64, so completed reservations are 6,322-64= 6,258 and 21 flights are full so 6258÷21= 298 passengers in each flight and that airplane is Jet set

Question 14.
An airline carries about 750 passengers from Houston to Chicago each day. How many Blue Sky jets would be needed to carry this many passengers, and how many empty seats would there be?

Answer: 5 Sky jets would be needed and 50 empty seats would be there.

Explanation: Let’s round off 750 to 800, As there are 800 passengers each day so no. of Sky jets needed are 800÷160= 5. and 50 empty seats would be there.

Question 15.
Pose a Problem Refer back to Problem 12. Use the information in the table to write a similar problem involving airplane passenger seats.

Explanation:

Question 16.
For numbers 16a – 16d, choose Yes or No to indicate whether the equation is correct.
16a. 1,350 ÷ 5 = 270 O Yes O No
16b. 3,732 ÷ 4 = 933 O Yes O No
16c. 4,200 ÷ 35 = 12 O Yes O No
16d. 1,586 ÷ 13 = 122 O Yes O No

Explanation: 1,350÷5= 270.

Explanation: 3732÷4= 933

Explanation: 4200÷35= 120

Explanation: 1586÷13= 122.

### Divide Multi-Digit Numbers – Page No. 9

Estimate. Then find the quotient. Write the remainder, if any, with an r.

Question 1.
180)$$\overline { 20835 }$$

Answer: Quotient is 115 and remainder r135

Explanation:

Question 2.
19)$$\overline { 800 }$$

Answer: Quotient is 42 and remainder r2

Explanation:

Question 3.
68)$$\overline { 1025 }$$

Answer: Quotient is 15 and remainder r5

Explanation:

Estimate. Then find the quotient. Write the remainder, if any, as a fraction.

Question 4.
20)$$\overline { 1683 }$$

Answer: Quotient is 84 and remainder r3.

Explanation:

Question 5.
14124 ÷ 44

Answer: Quotient is 321 and remainder r0

Explanation:

Question 6.
11629 ÷ 29

Answer: Quotient is 401 and remainder r0

Explanation:

Find the least whole number that can replace ? to make the statement true.

Question 7.
? ÷ 7 > 800

Answer: The least whole number to makes the statement true is 5600

Explanation: 5600÷7> 800

Question 8.
? ÷ 21 > 13

Answer: The least whole number to makes the statement true is 273

Explanation:  273÷21>13

Question 9.
15 < ? ÷ 400

Answer: The least whole number to makes the statement true is 6000

Explanation: 15< 6000÷400

Problem Solving

Question 10.
A plane flew a total of 2,220 miles. Its average speed was 555 miles per hour. How many hours did the plane fly?

Explanation: Total miles does a plane flew is 2,220 miles and average speed is 555 miles per hour. So total hours did plane fly are 2,220÷555= 4 hours

Question 11.
A van is carrying 486 pounds. There are 27 boxes in the van. What is the average weight of each box in the van?

Explanation: No.of pounds did the van carry are 486 pounds and no.of boxes in a van are 27. So the average weight of each box is 486÷27= 18

Question 12.
Find 56,794 ÷ 338. Write the quotient twice, once with the remainder as a fraction and once with an r.

Answer: 56,794÷338= 168 10/338= 168 5/169, r=10.

Explanation: 56,794÷338= 168 10/338= 168 5/169 and reminder is 10

### Lesson Check – Page No. 10

Question 1.
A caterer’s fee is based on the number of meals she provides. How much is the price per meal if the total fee is $1,088 for 64 meals? Answer:$17.

Explanation: No.of meals are 64 and the total fee is $1,088. Therefore the price per meal is$1,088÷64= $17. Question 2. Amelia needs 24 grains of beads to make a bracelet. She has 320 grams of beads. How many bracelets can she make? Answer: 13 bracelets. Explanation: No.of grains of beads Amelia need are 24 and she has 320 grams of beads. So no.of bracelets can Amelia make are 320÷24= 13.33 will round off to 13. Spiral Review Question 3. Hank bought 2.4 pounds of apples. Each pound cost$1.95. How much did Hank spend on the apples?

Answer: $4.68 Explanation: No.of pounds of apples Hank bought is 2.4 pounds and each pound cost is$ 1.95, so total Hank spend on apples is 2.4×$1.95=$4.68

Question 4.
Gavin bought 4 packages of cheese. Each package weighed 1.08 kilograms. How many kilograms of cheese did Gavin buy?

Explanation: No.of cheese packages Gavin bought are 4 and each package weight is 1.08 kg. So total weight of cheese is 4×1.08= 4.32 kg

Question 5.
Mr. Thompson received a water bill for $85.98. The bill covered three months of service. He used the same amount of water each month. How much does Mr. Thompson pay for water each month? Answer:$28.66

Explanation: Water bill received to Mr. Thompson is $85.98 as he covered for 3 months the amount Mr.Thompson paid for each month is$85.98÷3= $28.66 Question 6. Layla used 0.482 gram of salt in her experiment. Maurice use 0.51 gram of salt. Who used the greater amount of salt? Answer: Maurice as 0.51 is greater than 0.482. Explanation: Salt used by Layla is 0.482 grams and salt used by Maurice is 0.51 grams, so the greatest amount of salt used is Maurice as 0.51 is greater than 0.482. ### Find the prime factorization – Page No. 13 Question 3. 75 Answer: 5×5×3. Explanation: 75 15 5 5×3 5 5×5×3 Question 4. 12 Answer: 3×2×2. Explanation: 12 6×2 3×2×2 Question 3. 65 Answer: 13×5 Explanation: 65 13×5 On Your Own Write the number whose prime factorization is given. Question 6. 2 × 2 × 2 × 7 Answer: 56 Question 7. 2 × 2 × 5 × 5 Answer: 100 Question 8. 2 × 2 × 2 × 2 × 3 × 3 Answer: 144 Practice: Copy and Solve Find the prime factorization. Question 9. 45 Answer: 5×3×3 Explanation: 45 5×9 5×3×3 Question 10. 50 Answer: 5×5×2 Explanation: 50 5×10 5×5×2 Question 11. 32 Answer: 2×2×2×2×2 Explanation: 32 2×16 2×2×8 2×2×2×4 2×2×2×2×2 Question 12. 76 Answer: 2×2×19 Explanation: 76 2×38 2×2×19 Question 13. 108 Answer: 2×2×3×3×3 Explanation: 108 2×54 2×2×27 2×2×3×9 2×2×3×3×3 Question 14. 126 Answer: 2×7×3×3 Explanation: 126 2×63 2×7×9 2×7×3×3 Question 15. The area of a rectangle is the product of its length and width. A rectangular poster has an area of 260 square inches. The width of the poster is greater than 10 inches and is a prime number. What is the width of the poster? Answer: Width is 13. Explanation: Area of a rectangular poster is 260 square inches i.e width×length= 260 sq inches. And the width of the poster is greater than 10 inches and it is a prime number, so the width will be 13 as 13 is a prime number and also 260 is divisible by 13, and length is 13×length= 260 in which length is 260÷13= 20. Question 16. Look for Structure Dani says she is thinking of a secret number. As a clue, she says the number is the least whole number that has three different prime factors. What is Dani’s secret number? What is its prime factorization? Answer: Dani’s secret number is 30 and the prime factorization is 2,3,5. Explanation: The least three prime numbers are 2,3,5, so the product of three prime numbers is 2×3×5= 30. ### Problem Solving + Applications – Page No. 14 Use the table for 17–19. Agent Sanchez must enter a code on a keypad to unlock the door to her office. Question 17. In August, the digits of the code number are the prime factors of 150. What is the code number for the office door in August? Answer: 2355. Explanation: Prime Factors of 150 are 2×3×5×5, so code number for office door in August is 2355 Question 18. In September, the fourth digit of the code number is 2 more than the fourth digit of the code number based on the prime factors of 225. The prime factors of what number were used for the code in September? Answer: 315. Explanation: Prime factors of 225 are 3×3×5×5 which is 3355 as the fourth digit of the code number is 2 more than the fourth digit, s0 5+2=7 and by replacing 7 in 3×3×5×5, then 3×3×5×7= 315. Question 19. One day in October, Agent Sanchez enters the code 3477. How do you know that this code is incorrect and will not open the door? Answer: 4 is not a prime number. Explanation: The code 3477 is incorrect as the code contains only a prime number and 4 is not a prime number. Question 20. Use the numbers to complete the factor tree. You may use a number more than once. 2 3 6 9 18 Answer: 36= 2×2×3×3 Explanation: ### Prime Factorization – Page No. 15 Find the prime factorization. Question 1. 44 Answer: 2×2×11 Explanation: 44 2×22 2×2×11 Question 2. 90 Answer: 2×3×3×5 Explanation: 90 2×45 2×3×15 2×3×3×5 Question 3. 48 Answer: Explanation: 48 2×24 2×2×12 2×2×2×6 2×2×2×2×3 Question 4. 204 Answer: 2×2×3×17 Explanation: 204 2×102 2×2×51 2×2×3×17 Question 5. 400 Answer: 2×2×2×2×5×5 Explanation: 400 2×200 2×2×100 2×2×2×50 2×2×2×2×25 2×2×2×2×5×5 Question 6. 112 Answer: 2×2×2×2×7 Explanation: 112 2×56 2×2×28 2×2×2×14 2×2×2×2×7 Problem Solving Question 7. A computer code is based on the prime factorization of 160. Find the prime factorization of 160. Answer: 2×2×2×2×2×5 Explanation: Prime factors of 160 is 2×2×2×2×2×5 Question 8. The combination for a lock is a 3-digit number. The digits are the prime factors of 42 listed from least to greatest. What is the combination for the lock? Answer: 237. Explanation: Prime factors of 42 is 2×3×7. Question 9. Describe two methods for finding the prime factorization of a number. Answer: 1. Divison Method. 2. Factor Tree Method. Explanation: 1. Division Method: In Division method first we will divide the number by smallest prime number, and repeat the process until the quotient became 1. 2. Factor Tree Method: In Factor Tree Method we will write a pair of factors as the branches of the tree and then we will factorize. ### Lesson Check – Page No. 16 Question 1. Maritza remembers her PIN because it is between 1,000 and 1,500 and it is the product of two consecutive prime numbers. What is her PIN? Answer: Two consecutive prime numbers are 31 and 37 and PIN is 1147. Explanation: As 31 and 37 are two consecutive prime numbers and their product is 1147 which is between 1,000 to 1,500. Question 2. Brent knows that the 6 -digit number he uses to open his computer is the prime factorization of 5005. If each digit of the code increases from left to right, what is his code? Answer: 111357. Explanation: Factors of 5005 are 5×7×11×13, as the increases from left to right so the code is 111357 Spiral Review Question 3. Piano lessons cost$15. What expressions could be used to find the cost in dollars of 5 lessons?

Answer: $15×5=$75

Explanation: We will use multiplication to find the cost in dollars of 5 lessons.

Question 4.
A jet plane costs an airline $69,500,000. What is the place value of the digit 5 in this number? Answer: Hundred thousand. Explanation: The place value of 5 in$69,500,000 is 500,000.

Question 5.
A museum has 13,486 butterflies, 1,856 ants, and 13,859 beetles. What is the order of the insects from least number to greatest number?

Answer: Ants, Butterflies, Beetles.

Explanation: The order of insects from least to greatest are Ants, Butterflies, Beetles.

Question 6.
Juan is reading a 312-page book for school. He reads 12 pages each day. How long will it take him to finish the book?

Explanation: As Juan reads 12 pages each day and the book has 312 pages, so he will finish in 312÷12= 26 days

### Find the LCM – Page No. 19

Question 2.
3, 5

Explanation:
Multiples of 3: 3,6,9,12,15
Multiples of 5: 5,10,15.
LCM is 15

Question 3.
3, 9

Explanation:
Multiples of 3: 3,6,9
Multiples of 9: 9
LCM is 9

Question 4.
9, 15

Explanation:
Multiples of 9: 9,18,27,36,45,54,63,72,81,90,99,108,117,126,135.
Multiples of 15: 15,30,45,60,75,90,105,120,135.
LCM is 135

Find the LCM.

Question 5.
5, 10

Explanation:
Multiples of 5: 5,10
Multiples of 10: 10
LCM is 10

Question 6.
3, 8

Explanation:
Multiples of 3: 3,6,92,15,18,21,24
Multiples of 8: 8,16,24
LCM is 24

Question 7.
9, 12

Explanation:
Multiples of 9: 9,18,27,36,45,54,63,72,81,90,99,108
Multiples of 12: 12,24,36,48,60,72,84,96,108
LCM is 108

Use Reasoning Algebra Write the unknown number for ?.

Question 8.
5, 8      LCM : ?
? =

Explanation:
Multiples of 5: 5,10,15,20,25,30,35,40
Multiples of 8: 8,16,24,32,40
LCM is 40

Question 9.
?, 6      LCM : 42
? =

Explanation: 6×7= 42

Question 10.
How can you tell when the LCM of two numbers will equal one of the numbers or equal the product of the numbers?

Answer: If the other number is 1 then the LCM of two numbers will equal one.

Question 11.
Verify the Reasoning of Others Mr. Haigwood is shopping for a school picnic. Veggie burgers come in packages of 15, and buns come in packages of 6. He wants to serve veggie burgers on buns and wants to have no items left over. Mr. Haigwood says that he will have to buy at least 90 of each item, since 6 × 15 = 90. Do you agree with his reasoning? Explain.

Answer: No. We must find the least number of burgers and buns, so we must find LCM of 15 and 6.

Explanation:
Multiples of 15: 15,30
Multiples of 6: 6,12,18,24,30
LCM is 30.

Question 12.
A deli has a special one -day event to celebrate its anniversary. On the day of the event, every eighth customer receives a free drink. Every twelfth customer receives a free sandwich. If 200 customers show up for the event, how many of the customers will receive both a free drink and a free sandwich?

Answer: 24,48,72,96,120,144,168,192 are the customers who get both free drink and free sandwich.

Explanation: To find how many customers have received both a free drink and a sandwich, first we have to find who got a free sandwich and a free drink separately, so
Multiples of 8 are 8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128, 136,144,152,160,168,176,184,192 and 200 and
Multiples of 12 are 12,24,36,48,60,72,84,96,108,120,132,144,156,168,180 and 192. So common customers are 24,48,72,96,120,144,168,192 are the customers who get both free drink and free sandwich.

### Unlock The Problem – Page No. 20

Question 13.
Katie is making hair clips to sell at the craft fair. To make each hair clip, she uses 1 barrette and 1 precut ribbon. The barrettes are sold in packs of 12, and the precut ribbons are sold in packs of 9. How many packs of each item does she need to buy to make the least number of hair clips with no supplies left over?
a. What information are you given?

Answer: 3 packs of barrettes and 4 packs of precut ribbons.

Explanation: As barrettes are sold in packs of 12 and precut ribbons are sold in packs of 9, so we need to find the number of packs of each item does she need to make the least number of hair clips with no supplies left over. So the LCM of 12 and 9.
Multiples of 12 are: 12,24,36
Multiples of 9 are: 9,18,27,36
LCM is 36
So Katie needs 36 barrettes and ribbons to make the least number of hair clips with no supplies left over, and she needs 3 packs of barrettes and 4 packs of precut ribbons.

Question 13.
b. What problem are you being asked to solve?

Answer: To find the number of packs of each item does she need to make the least number of hair clips with no supplies left over

Question 13.
c. Show the steps you use to solve the problem.

Multiples of 12 are: 12,24,36
Multiples of 9 are: 9,18,27,36
LCM is 36

Question 13.
d. Complete the sentences.
The least common multiple of 12 and 9 is _____ .
Katie can make _____ hair clips with no supplies left over.
To get 36 barrettes and 36 ribbons, she needs to buy _____ packs of barrettes and _____ packs of precut ribbons.

Answer: 36, 3, 4.

Explanation:
The least common multiple of 12 and 9 is 36.
Katie can make 36 hair clips with no supplies left over.
To get 36 barrettes and 36 ribbons, she needs to buy 3 packs of barrettes and 4 packs of precut ribbons.

Question 14.
Reptile stickers come in sheets of 6 and fish stickers come in sheets of 9. Antonio buys the same number of both types of stickers and he buys at least 100 of each type. What is the least number of sheets of each type he might buy?

Explanation: As Reptile stickers come in sheets of 6 and fish stickers come in sheets of 9, so we will find the LCM of 6 and 9 to get the least number of sheets,
Multiples of 6 are 6,12,18
Multiples of 9 are 9,18
LCM is 18
As Antonio buys at least 100 of each type, so multiples of 18 are 18,36,54,72,90,108 as 108 is the least number and more than 100 and nearest to 100, so the least number of sheets he might buy= 108

Question 15.
For numbers 15a -15d, choose Yes or No to indicate whether the LCM of the two numbers is 16.
15a. 2,8 O Yes O No
15b. 2,16 O Yes O No
15c. 4,8 O Yes O No
15d. 8,16 O Yes O No

15a. 2,8 O Yes O No

Explanation:
Multiples of 2 are 2,4,6,8
Multiples of 8 are 8
LCM is 8

15b. 2,16 O Yes O No

Explanation:
Multiples of 2 are 2,4,6,8,10,12,14,16
Multiples of 16 are 16
LCM is 16

15c. 4,8 O Yes O No

Explanation:
Multiples of 4 are 4,8
Multiples of 8 are 8
LCM is 8

15d. 8,16 O Yes O No

Explanation:
Multiples of 8 are 8,16
Multiples of 16 are 16
LCM is 16

### Least Common Multiple – Page No. 21

Find the LCM.

Question 1.
2, 7

Explanation:
Multiples of 2 are 2,4,6,8,10,12,14.
Multiples of 7 are 7,14.
LCM is 14.

Question 2.
4, 12

Explanation:
Multiples of 4 are 4,8,12
Multiples of 12 are 12
LCM is 12

Question 3.
6, 9

Explanation:
Multiples of 6 are 6,12,18,24,30,36,42,48,54
Multiples of 9 are 9,18,27,36,45,54
LCM is 54

Question 4.
5, 4

Explanation:
Multiples of 5 are 5,10,15
Multiples of 4 are 8
LCM is 8

Question 5.
5, 8, 4

Explanation:
Multiples of 5 are 5,10,15,20,25,30,35,40
Multiples of 8 are 8,16,24,32,40
Multiples of 4 are 4,8,12,16,20,24,28,32,36,40
LCM is 40

Question 6.
12, 8, 24

Explanation:
Multiples of 12 are 12,24
Multiples of 8 are 8,16,24
Multiples of 24 are 24
LCM is 24

Write the unknown number for the?

Question 7.
3, ?        LCM : 21
? =

Explanation: 3×7= 21

Question 8.
?, 7        LCM : 63
? =

Explanation: 9×7=63

Question 9.
10, 5     LCM : ?
? =

Explanation:
Multiples of 10 are 10
Multiples of 5 are 5,10
LCM is 10

Problem Solving

Question 10.
Juanita is making necklaces to give as presents. She plans to put 15 beads on each necklace. Beads are sold in packages of 20. What is the least number of packages she can buy to make necklaces and have no beads left over?

Explanation:
Multiples of 15: 15,30,45,60
Multiples of 20: 20,40,60
LCM is 60
As beads are sold in packages of 20 Juanita needs 3 least number of packages to make necklaces with no beads leftover.

Question 11.
Pencils are sold in packages of 10, and erasers are sold in packages of 6. What is the least number of pencils and erasers you can buy so that there is one pencil for each eraser with none left over?

Answer: 30 pencils and 30 erasers are the least numbers we can buy without any leftover.

Explanation:
Multiples of 10: 10,20,30.
Multiples of 6: 6,12,18,24,30.
LCM is 30.
So 30 pencils and 30 erasers are the least numbers we can buy without any leftover.

Question 12.
Explain when you would use each method (finding multiples or prime factorization) for finding the LCM and why.

Answer: When the numbers are smaller we can use finding multiples and when the numbers are larger then we can use prime factorization.

### Lesson Check – Page No. 22

Question 1.
Martha is buying hot dogs and buns for the class barbecue. The hot dogs come in packages of 10. The buns come in packages of 12. What is the least number she can buy of each so that she has exactly the same number of hot dogs and buns? How many packages of each should she buy?
_________ packages of hot dogs
_________ packages of buns

Answer: 6 packages of hot dogs and 5 packages of buns she can buy.

Explanation:
Multiples of 10: 10,20,30,40,50,60.
Multiples of 12: 12,24,36,48,60.
LCM is 60.
So 60 is the least number she can buy and 6 packages of hot dogs and 5 packages of buns she can buy.

Question 2.
Kevin makes snack bags that each contain a box of raisins and a granola bar. Each package of raisins contains 9 boxes. The granola bars come 12 to a package. What is the least number he can buy of each so that he has exactly the same number of granola bars and boxes of raisins? How many packages of each should he buy?
_________ packages of raisins
_________ packages of granola bars

Answer: 4 packages of raisins and 3 packages of granola bars he should buy.

Explanation: Kevin’s every package contains 9 raisins boxes and 12 granola bars in each package, so LCM of 9 and 12 are
Multiples of 9: 9,18,21,36
Multiples of 12: 12,24,36
LCM is 36.
So 4 packages of raisins and 3 packages of granola bars he should buy.

Spiral Review

Question 3.
John has 2,456 pennies in his coin collection. He has the same number of pennies in each of 3 boxes. Estimate to the nearest hundred the number of pennies in each box.

Explanation: Let’s round off 2,456 to 2400, as he has the same no. of pennies in each of 3 boxes, so in each box no.of pennies are 2400÷3= 800 pennies.

Question 4.
What is the distance around a triangle that has sides measuring 2 $$\frac{1}{8}$$ feet, 3 $$\frac{1}{2}$$ feet, and 2 $$\frac{1}{2}$$ feet?

Answer: 8 1/8 feet

Explanation: Distance around the triangle is 2 1/8+3 1/2+ 2 1/2= 8 1/8 feet

Question 5.
The 6th grade class collects $1,575. The class wants to give the same amount of money to each of 35 charities. How much will each charity receive? Answer:$45

Explanation: The 6th-grade class collects $1575 and wants to give the same amount to 35 charities each, so each charity receives$1575÷35= $45. Question 6. Jean needs $$\frac{1}{3}$$ cup of walnuts for each serving of salad she makes. She has 2 cups of walnuts. How many servings can she make? Answer: 6. Explanation: No.of servings made by 1/3 cup of walnuts is 1, so for 1 cup Jean serves 1/(1/3+1/3+1/3)= 3. So for 2 cups, no.of servings can she make are 3×2= 6. ### Share and Show – Page No. 25 Question 1. List the factors of 12 and 20. Circle the GCF. Factors of 12 : __________ Factors of 20 : __________ Answer: 4 Explanation: Factors of 12: 1,2,3,4,6,12 Factors of 20: 1,2,4,5,10,20 Common factors are 1,2,4 GCF is 4 Find the GCF. Question 2. 16, 18 Answer: 2 Explanation: Factors of 16: 1,2,4,8,16 Factors of 18: 1,2,3,6,9,18 Common factors are 1,2 GCF is 2 Question 3. 25, 40 Answer: 5 Explanation: Factors of 25: 1,2,5,25 Factors of 40: 1,2,4,5,8,10,20,40 Common factors are 1,2,5 GCF is 5 Question 4. 24, 40 Answer: 8 Explanation: Factors of 24: 1,2,3,4,6,8,12,24 Factors of 40: 1,2,4,5,8,10,20,40 Common factors are 1,2,4,8 GCF is 8 Question 5. 14, 35 Answer: 7 Explanation: Factors of 14: 1,2,7,14 Factors of 35: 1,2,5,7,35 Common factors are 1,2,7 GCF is 7 Use the GCF and the Distributive Property to express the sum as a product. Question 6. 21 + 28 Answer: 7×(3+4) Explanation: 21+28= (7×3)+(7×4) =7×(3+4) Question 7. 15 + 27 Answer: 3×(5+9) Explanation: 15+27= (3×5)+(3×9) =3×(5+9) Question 8. 40 + 15 Answer: 5×(8+3) Explanation: 40+15= (5×8)+(5×3) = 5×(8+3) Question 9. 32 + 20 Answer: 4×(8+5) Explanation: 32+20= (4×8)+(4×5) = 4×(8+5) On Your Own Find the GCF. Question 10. 8, 25 Answer: 1 Explanation: Factors of 8: 1,2,4,8 Factors of 25: 1,5,25 Common factors are 1 GCF is 1 Question 11. 31, 32 Answer: 1 Explanation: Factors of 31: 1,31 Factors of 32: 1,2,4,8,16,32 Common Factors are 1 GCF is 1 Question 12. 56, 64 Answer: 8 Explanation: Factors of 56: 1,2,4,7,8,14,28,56 Factors of 64: 1,2,4,8,16,32,64 Common Factors are 1,2,4,8 GCF is 8 Question 13. 150, 275 Answer: 25 Explanation: Factors of 150: 1,2,3,5,6,10,15,25,30,50,75,150 Factors of 275: 1,5,11,25,55,275 Common Factors are 1,5,25. GCF is 25. Use the GCF and the Distributive Property to express the sum as a product. Question 14. 24 + 30 Answer: 6×(4+5) Explanation: 24+30= (6×4)+(6×5) =6×(4+5) Question 15. 49 + 14 Answer: 7×(7+2) Explanation: 49+14= (7×7)+(7×2) =7×(7+2) Question 16. 63 + 81 Answer: 9×(7+9) Explanation: 63+81= (9×7)+(9×9) =9×(7+9) Question 17. 60 + 12 Answer: 12×(5+1) Explanation: 60+12= (12×5)+(12×1) =12×(5+1) Question 18. Describe the difference between the LCM and the GCF of two numbers. Answer: In LCM we will get the Least Common Multiples of two numbers, and in GCF we will get Greatest Common Factor. ### Problem Solving + Applications – Page No. 26 Use the table for 19-22. Teachers at the Scott School of Music teach only one instrument in each class. No students take classes for more than one instrument. Question 19. Francisco teaches group lessons to all of the violin and viola students at the Scott School of Music. All of his classes have the same number of students. What is the greatest number of students he can have in each class? Answer: 6 Explanation: No. of students for Viola instrument is 30 and 36 for Violin, Factors of 30: 1,2,3,5,6,10,15,30 Factors of 36: 1,2,3,4,6,9,12,18,36 GCF is 6 So the greatest number of students he can have in each class is 6 Question 20. Amanda teaches all of the bass and viola students. All her classes have the same number of students. Each class has the greatest possible number of students. How many of these classes does she teach? __________ bass classes __________ viola classes Answer: 2 bass classes and 3 viola classes. Explanation: Factors of 20: 1,2,4,5,10,20 Factors of 30: 1,2,3,5,6,10,15,30 GCF is 10 As the greatest number of possible students in each class is 10, So Amanda teaches 2 bass classes and 3 viola classes. Question 21. Mia teaches jazz classes. She has 9 students in each class, and she teaches all the classes for two of the instruments. Which two instruments does she teach, and how many students are in her classes? Answer: 63 students. Explanation: Factors of 27: 1,3,9,27 Factors of 36: 1,2,3,4,6,9,12,18,36 GCF is 9 As 9 is the GCF of 27 and 36, So Mia teaches Cello and Violin classes for a total of 63 students. Question 22. Explain how you could use the GCF and the Distributive Property to express the sum of the number of bass students and the number of violin students as a product. Answer: GCF is 4 Distributive property is 4×(5+9) Explanation: The no.of bass students are 20 and no.of violin students are 36, Factors of 20: 1,2,4,5,10,20 Factors of 36: 1,2,3,4,6,12,18,36 GCF is 4 And the Distributive property is 20+36 = (4×5)+(4×9) = 4×(5+9) Question 23. Answer: 6 Explanation: Factors of 6: 1,2,3,6 Factors of 12: 1,2,3,4,6 GCF is 6 ### Greatest Common Factor – Page No. 27 List the common factors. Circle the greatest common factor. Question 1. 25 and 10 Answer: 5 Explanation: Factors of 25: 1,5,25. Factors of 10: 1,2,5,10 Common factors are 1,5 GCF is 5 Question 2. 36 and 90 Answer: 18 Explanation: Factors of 36: 1,2,3,4,6,9,12,18,36 Factors of 90: 1,2,3,5,6,9,10,15,18,30,45,90 Common Factors are 1,2,3,6,9,18 GCF is 18 Question 3. 45 and 60 Answer: 15 Explanation: Factors of 45: 1,3,5,9,15,45 Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60 Common Factors are 1,3,5,15 GCF is 15 Find the GCF. Question 4. 14, 18 Answer: 2 Explanation: Factors of 14: 1,2,7,14 Factors of 18: 1,2,3,6,9,18 Common Factors are 1,2 GCF is 2 Question 5. 6, 48 Answer: 6 Explanation: Factors of 6: 1,2,3,6 Factors of 48: 1,2,3,4,6,8,12,24,48 Common Factors are 1,2,3,6 GCF is 6 Question 6. 16, 100 Answer: 4 Explanation: Factors of 16: 1,2,4,8,16 Factors of 100: 1,2,4,5,10,20,25,50,100 Common Factors are 1,2,4 GCF is 4 Use the GCF and the Distributive Property to express the sum as a product. Question 7. 20 + 35 Answer: 5×(4+7) Explanation: 20+35= (5×4)+(5×7) =5×(4+7) Question 8. 18 + 27 Answer: 9×(2+3) Explanation: 18+27= (9×2)+(9×3) =9×(2+3) Question 9. 64 + 40 Answer: 8×(8+5) Explanation: 64+40= (8×8)+(8×5) = 8×(8+5) Problem Solving Question 10. Jerome is making prizes for a game at the school fair. He has two bags of different pins, one with 15 square pins and one with 20 round pins. Every prize will have one kind of pin. Each prize will have the same number of pins. What is the greatest number of pins Jerome can put in each prize? Answer: 5 Explanation: Factors of 15: 1,3,5,15 Factors of 20: 1,2,4,5,10,20 Common factors are 1,5 So the greatest number of pins Jerome can put in each prize is 5 Question 11. There are 24 sixth graders and 40 seventh graders. Mr. Chan wants to divide both grades into groups of equal size, with the greatest possible number of students in each group. How many students should be in each group? Answer: 8. Explanation: Factors of 24: 1,2,3,4,6,8,12,24 Factors of 40: 1,2,4,5,8,10,20,40 Common Factors are 1,2,4,8 So the greatest possible number of students are 8 Question 12. Write a short paragraph to explain how to use prime factorization and the Distributive Property to express the sum of two whole numbers as a product. Answer: Prime Factorization is the product of prime numbers ### Lesson Check – Page No. 28 Question 1. There are 15 boys and 10 girls in Miss Li’s class. She wants to group all the students so that each group has the same number of boys and the same number of girls. What is the greatest number of groups she can have? Answer: 5 Explanation: Factors of 15: 1,3,5,15 Factors of 10: 1,2,5,10 Common Factors are 1,5 The greatest number of groups she can have is 5. Question 2. A pet shop manager wants the same number of birds in each cage. He wants to use as few cages as possible, but can only have one type of bird in each cage. If he has 42 parakeets and 18 canaries, how many birds will he put in each cage? Answer: 6 Explanation: Factors of 42: 1,2,3,6,7,14,21,42 Factors of 18: 1,2,3,6,9,18 Common Factors are 1,2,3,6 GCF is 6 So he will put 6 birds in each cage. Spiral Review Question 3. There are 147 people attending a dinner party. If each table can seat 7 people, how many tables are needed for the dinner party? Answer: 21 tables. Explanation: Total no.of people attending a dinner party are 147 and 7 people can seat in each table, so 147÷7= 21 tables are needed for a dinner party. Question 4. Sammy has 3 pancakes. He cuts each one in half. How many pancake halves are there? Answer: 6 Explanation: Sammy has 3 pancakes, as he cut each one into half so there are 3×2= 6 pancake halves. Question 5. The Cramer Company had a profit of$8,046,890 and the Coyle Company had a profit of $8,700,340 last year. Which company had the greater profit? Answer: Coyle company Explanation: Coyle company had a profit of$8,700,340 and Cramer Company had $8,046,890, So$8,700,340-$8,046,890=$653,450 Coyle company have greater profits.

Question 6.
There are 111 guests attending a party. There are 15 servers. Each server has the same number of guests to serve. Jess will serve any extra guests. How many guests will Jess be serving?

Explanation:
Total guests attending a party are 111 and no.of servers are 15, as each server has the same number of guests to serve so we will divide total guests by the number of servers 111÷15= 7.4 round off to 6. Therefore, no.of guests, will Jess be serving is 6.

### Share and Show – Page No. 31

Question 1.
Toby is packaging 21 baseball cards and 12 football cards to sell at a swap meet. Each packet will have the same number of cards. Each packet will have cards for only one sport. What is the greatest number of cards he can place in each packet? How many packets will there be for each sport?

Answer: 7 packets of baseball cards and 4 packets of football cards and each packet contains 3 cards.

Explanation: The GCF of 21 and 12 are
Factors of 21: 1,3,7,21
Factors of 12: 1,2,3,4,6,12
GCF is 3
By Distributive property 21+12
= (3×7)+(3×4)
= 3×(7+4)
So there will be 7 packets of baseball cards and 4 packets of football cards and each packet contains 3 cards.

Question 2.
What if Toby had decided to keep one baseball card for himself and sell the rest? How would your answers to the previous problem have changed?

Answer: 5 packets of baseball cards and 3 football and each packet contains 4 cards.

Explanation: If Toby had decided to keep one baseball card for himself, so he will have 20 baseball cards and 12 football cards
Factors of 20: 1,2,4,5,10,20
Factors of 12: 1,2,3,4,6,12
GCF is 4
By Distributive property 20+12
= (4×5)+(4×3)
=4×(5+3)
So there will be 5 packets of baseball cards and 3 football and each packet contains 4 cards.

Question 3.
Melissa bought 42 pine seedlings and 30 juniper seedlings to plant in rows on her tree farm. She wants each row to have the same number of seedlings. She wants only one type of seedling in each row. What is the greatest number of seedlings she can plant in each row? How many rows of each type of tree will there be?

Answer: 7 rows of pine seedlings and 5 rows of juniper seedling with 6 seedlings in each row.

Explanation:
Factors of 42: 1,2,3,6,7,14,21,42
Factors of 30: 1,2,3,6,10,15,30
GCF is 6
By Distributive 42+30
=(6×7)+(6×5)
=6×(7+5)
So there will be 7 rows of pine seedlings and 5 rows of juniper seedling with 6 seedlings in each row.

### On Your Own – Page No. 32

Question 4.
Make Sense of Problems A drum and bugle marching band has 45 members who play bugles and 27 members who play drums. When they march, each row has the same number of players. Each row has only bugle players or only drummers. What is the greatest number of players there can be in each row? How many rows of each type of player can there be?

Answer: 9 people in each row, And there will be 5 rows of bugle players and 3 rows of drummers.

Explanation:
Factors of 45: 1,3,5,9,15,45
Factors of 27: 1,3,9,27
GCF is 9
So there will be 9 people in each row and by the distributive law 45+27
= (9×5)+(9×3)
= 9×(5+3)
And there will be 5 rows of bugle players and 3 rows of drummers.

Question 5.
The “color guard” of a drum and bugle band consists of members who march with flags, hoops, and other props. How would your answers to Exercise 4 change if there were 21 color guard members marching along with the bugle players and drummers?

Answer: 15 rows of bugle players, 9 rows of drummers, and 7 rows color guard members with 3 marchers in each row.

Explanation:
Factors of 21: 1,3,7,21
Factors of 45: 1,3,5,9,15,45
Factors of 27: 1,3,9,27
GCF is 3
So there would be 15 rows of bugle players, 9 rows of drummers, and 7 rows color guard members with 3 marchers in each row.

Question 6.
If you continue the pattern below so that you write all of the numbers in the pattern less than 500, how many even numbers will you write?
4, 9, 14, 19, 24, 29…

Explanation: You can write 50 numbers.

Question 7.
Mr. Yaw’s bookcase holds 20 nonfiction books and 15 fiction books. Each shelf holds the same number of books and contains only one type of book. How many books will be on each shelf if each shelf has the greatest possible number of books? Show your work.

Explanation:
Factors of 15: 1,3,5,15
Factors of 20: 1,2,4,5,10,20.
GCF is 5
5 books will be on each self.

### Problem Solving Apply the Greatest Common Factor – Page No. 33

Read the problem and solve.

Question 1.
Ashley is bagging 32 pumpkin muffins and 28 banana muffins for some friends. Each bag will hold only one type of muffin. Each bag will hold the same number of muffins. What is the greatest number of muffins she can put in each bag? How many bags of each type of muffin will there be?

Answer: 8 pumpkin muffins and 7 banana muffins with 4 greatest number of muffins in each bag.

Explanation:
Factors of 32: 1,2,4,8,16,32
Factors of 28: 1,2,4,7,14,28
GCF is 4
By distributive property 32+28
= (4×8)+(4×7)
=4×(8+7)
So there will be 8 pumpkin muffins and 7 banana muffins with 4 greatest number of muffins in each bag.

Question 2.
Patricia is separating 16 soccer cards and 22 baseball cards into groups. Each group will have the same number of cards, and each group will have only one kind of sports card. What is the greatest number of cards she can put in each group? How many groups of each type will there be?

Answer: Patricia has 8 soccer cards and 11 baseball cards and 2 groups each.

Explanation:
Factors of 16: 1,2,4,8,16
Factors of 22: 1,2,11,22
GCF is 2
By distributive property 16+22
= (2×8)+(2×11)
=2×(8+11)
Patricia has 8 soccer cards and 11 baseball cards and 2 groups each.

Question 3.
Bryan is setting chairs in rows for a graduation ceremony. He has 50 black chairs and 60 white chairs. Each row will have the same number of chairs, and each row will have the same color chair. What is the greatest number of chairs that he can fit in each row? How many rows of each color chair will there be?

Answer: 10 chairs per row and 5 black chairs and 6 white chairs.

Explanation:
By distributive law 50+60
= (10×5)+(10×60)
= 10×(5+6)
So there will 10 chairs per row and 5 black chairs and 6 white chairs.

Question 4.
A store clerk is bagging spices. He has 18 teaspoons of cinnamon and 30 teaspoons of nutmeg. Each bag needs to contain the same number of teaspoons, and each bag can contain only one spice. What is the maximum number of teaspoons of spice the clerk can put in each bag? How many bags of each spice will there be?

Answer: 6 no. of teaspoons of spices and 3 teaspoons of cinnamon 5 teaspoons of nutmeg.

Explanation:
By distributive property (18+30)
= (6×3)+(6×5)
= 6×(3+5)
So there will be 6 no. of teaspoons of spices and 3 teaspoons of cinnamon 5 teaspoons of nutmeg.

Question 5.
Write a problem in which you need to put as many of two different types of objects as possible into equal groups. Then use the GCF, Distributive Property, and a diagram to solve your problem

Answer: Jack has a bag full of 20 red apples and 32 green apples. Each bag needs to contain same number of apples and each bag can contain only one type of apple. What is the maximum number of apples can Jack put in each bag? How many bags of each apple will be there?

Explanation: By distributive property (20+32)
= (4×5)+(4×8)
= 4×(5+8)
So there will be 4 bags and in that 5 red apples and 8 green apples.

### Lesson Check – Page No. 34

Question 1.
Fred has 36 strawberries and 42 blueberries. He wants to use them to garnish desserts so that each dessert has the same number of berries, but only one type of berry. He wants as much fruit as possible on each dessert. How many berries will he put on each dessert? How many desserts with each type of fruit will he have?

Answer: 6 berries on each dessert and 6 strawberries and 7 blueberries in each type of fruit.

Explanation:
By distributive property 36+42
= (6×6)+(6×7)
= 6×(6+7)
So he put 6 berries on each dessert and 6 strawberries and 7 blueberries in each type of fruit.

Question 2.
Dolores is arranging coffee mugs on shelves in her shop. She wants each shelf to have the same number of mugs. She only wants one color of mug on each shelf. If she has 49 blue mugs and 56 red mugs, what is the greatest number she can put on each shelf? How many shelves does she need for each color?
__________ shelves for blue mugs
__________ shelves for red mugs

Answer: 7 blue mugs and 8 red mugs.

Explanation:
By distributive property 49+56
= (7×7)+(7×8)
= 7×(7+8)
So the greatest number she can put on each shelf is 7, 7 blue mugs and 8 red mugs.

Spiral Review

Question 3.
A rectangle is 3 $$\frac{1}{3}$$ feet long and 2 $$\frac{1}{3}$$ feet wide. What is the distance around the rectangle?
_____ $$\frac{□}{□}$$

Answer: 11 1/3 feet

Explanation: Distance of a rectangle= 2(L+W)
= 2(3 1/3+ 2 1/3)
= 2(10/3+7/3)
= 2(17/3)
= 34/3
= 11 1/3 feet.

Question 4.
Lowell bought 4 $$\frac{1}{4}$$ pounds of apples and 3 $$\frac{3}{5}$$ pounds of oranges. How many pounds of fruit did Lowell buy?
_____ $$\frac{□}{□}$$

Answer: 7 17/20 pounds

Explanation: Lowell bought 4 1/4 pounds of apples and 3 3/5 pounds of oranges, so total pounds of fruits Lowell bought is 4 1/4+ 3 3/5=
= 17/4+ 18/5
= 157/20
= 7 17/20 pounds

Question 5.
How much heavier is a 9 $$\frac{1}{8}$$ pound box than a 2 $$\frac{5}{6}$$ pound box?
_____ $$\frac{□}{□}$$

Answer: 6 7/4 much heavier.

Explanation: 9 1/8 – 2 5/6
= 73/8 – 17/6
= 151/24
= 6 7/4

Question 6.
The combination of Clay’s locker is the prime factors of 102 in order from least to greatest. What is the combination of Clay’s locker?

Explanation:
Prime Factors of 102 are 2,3,17, so the combination of Clay’s locker is 2317

### Vocabulary – Page No. 35

Choose the best term from the box to complete the sentence.

Question 1.
The _____ of two numbers is greater than or equal to the numbers.

Question 2.
The _____ of two numbers is less than or equal to the numbers.

Concepts and Skills

Estimate. Then find the quotient. Write the remainder, if any, with an r.

Question 3.
2,800 ÷ 25

Answer: Quotient is 112 and remainder is 0

Explanation:

Question 4.
19,129 ÷ 37

Answer: Quotient is 517 and remainder is 0

Explanation:

Question 5.
32,111 ÷ 181

Answer: Quotient is 177 and the remainder is 74

Explanation:

Find the prime factorization.

Question 6.
44

Explanation:
44= 4×11
2×2×11

Question 7.
36

Explanation:
36= 2×18
=2×2×9
=2×2×3×3

Question 8.
90

Explanation:
90= 9×10
=3×3×10
=3×3×5×2

Find the LCM.

Question 9.
8, 10

Explanation:
Multiples of 8: 8,16,24,32,40
Multiples of 10: 10,20,30,40
LCM is 40

Question 10.
4, 14

Explanation:
Multiples of 4:  4,8,12,16,20,24,28
Multiples of 14: 14,28
LCM is 28

Question 11.
6, 9

Explanation:
Multiples of 6: 6,12,18
Multiples of 9: 9,18
LCM is 18

Find the GCF.

Question 12.
16, 20

Explanation:
Factors of 16: 1,2,4,8,16
Factors of 20: 1,2,4,5,10,20
Common Factors are 1,2,4
GCF is 4

Question 13.
8, 52

Explanation:
Factors of 8: 1,2,4,8
Factors of 52: 1,2,4,13,26,52
Common Factors are 1,2,4
GCF is 4

Question 14.
36, 54

Explanation:
Factors of 36: 1,2,3,4,6,9,12,18,36
Factors of 54:  1,2,3,6,9,18,27,54
Common Factors are 1,2,3,6,9,18
GCF is 18

### Page No. 36

Question 15.
A zookeeper divided 2,440 pounds of food equally among 8 elephants. How many pounds of food did each elephant receive?

Explanation: Zookeeper divides 2,440 pounds of food equally among 8 elephants, so no. of pounds is
2,440÷8= 305 pounds.

Question 16.
DVD cases are sold in packages of 20. Padded mailing envelopes are sold in packets of 12. What is the least number of cases and envelopes you could buy so that there is one case for each envelope with none left over?

Explanation:
Multiples of 20: 20,40,60
Multiples of 12: 12,24,36,48,60
LCM is 60
So the Least number of cases and envelopes without any leftover is 60.

Question 17.
Max bought two deli sandwich rolls measuring 18 inches and 30 inches. He wants them to be cut into equal sections that are as long as possible. Into what lengths should the rolls be cut? How many sections will there be in all?

Answer: 6 inches and 8 sections.

Explanation:
By distributive property 18+30
= (6×3)+(6×5)
= 6(3+5)
So Length of the rolls should cut at 6 inches and sections are (3+5)= 8 sections.

Question 18.
Susan is buying supplies for a party. If spoons only come in bags of 8 and forks only come in bags of 6, what is the least number of spoons and the least number of forks she can buy so that she has the same number of each?

Answer: So least no. of forks and spoons are 24.

Explanation:
Multiples of 8: 8,16,24
Multiples of 6: 6,2,18,24
LCM is 24
So least no. of forks and spoons are 24.

Question 19.
Tina is placing 30 roses and 42 tulips in vases for table decorations in her restaurant. Each vase will hold the same number of flowers. Each vase will have only one type of flower. What is the greatest number of flowers she can place in each vase? If Tina has 24 tables in her restaurant, how many flowers can she place in each vase?

Answer: Maximum flowers in a vase is 3.

Explanation: Tina is placing 30 roses and 42 tulips, so total flowers are 30+42= 72 flowers. The total number of tables are 24, as each vase hold same no. of flowers, Let the no. of flowers in each vase be X, so total no.of flowers to be decorate 24X,
24X = 72
X= 3.
So maximum flowers in a vase is 3.

### Share and Show – Page No. 39

Question 1.
Find 3.42 − 1.9.

Explanation: 3.42 − 1.9= 1.52.

Estimate. Then find the sum or difference.

Question 2.
2.3 + 5.68 + 21.047

Explanation: 2.3 + 5.68 + 21.047= 29.027

Question 3.
33.25 − 21.463

Explanation: 33.25 − 21.463= 11.787

Question 4.
Evaluate (8.54 + 3.46) − 6.749.

Explanation:
(8.54 + 3.46) − 6.749= (12)-6.749
= 5.251

Estimate. Then find the sum or difference.

Question 5.
57.08 + 34.71

Explanation:
57.08 + 34.71= 91.79

Question 6.
20.11 − 13.27

Explanation:
20.11−13.27= 33.38

Question 7.
62 − 9.817

Explanation:
62 − 9.817= 52.183

Question 8.
35.1 + 4.89

Explanation:
35.1 + 4.89= 39.99

Practice: Copy and Solve Evaluate using the order of operations.

Question 9.
8.01 − (2.2 + 4.67)

Explanation:
8.01 − (2.2 + 4.67)
= 8.01-(6.87)
= 1.14

Question 10.
54 + (9.2 − 1.413)

Explanation: 54 + (9.2 − 1.413)
= 54+(7.787)
=61.787

Question 11.
21.3 − (19.1 − 3.22)

Explanation: 21.3 − (19.1 − 3.22)
= 21.3-(15.88)
=5.42

Question 12.
Make Arguments A student evaluated 19.1 + (4.32 + 6.9) and got 69.2. How can you use estimation to convince the student that this answer is not reasonable?

Answer: The answer is not reasonable, because 19.1+4.32+6.9= 30.32

Explanation: 19.1 + (4.32 + 6.9)
= 19.1+(11.22)
= 30.32

Question 13.
Lynn paid $4.75 for cereal,$8.96 for chicken, and $3.25 for soup. Show how she can use properties and compatible numbers to evaluate (4.75 + 8.96) + 3.25 to find the total cost. Answer: 16.96 Explanation: Total cost is (4.75 + 8.96) + 3.25 = (13.71)+3.25 = 16.96 ### Page No. 40 Question 14. For numbers 14a–14d, select True or False for each equation. 14a. 3.76 + 2.7 = 6.46 True False 14b. 4.14 + 1.8 = 4.32 True False 14c. 2.01 – 1.33 = 0.68 True False 14d. 51 – 49.2 = 1.8 True False 14a. 3.76 + 2.7 = 6.46 Answer: True Explanation: 3.76 + 2.7 = 6.46 14b. 4.14 + 1.8 = 4.32 Answer: False Explanation: 4.14 + 1.8 = 5.94 14c. 2.01 – 1.33 = 0.68 Answer: True Explanation: 2.01 – 1.33 = 0.68 14d. 51 – 49.2 = 1.8 Answer: True Explanation: 51 – 49.2 = 1.8 Comparing Eggs Different types of birds lay eggs of different sizes. Small birds lay eggs that are smaller than those that are laid by larger birds. The table shows the average lengths and widths of five different birds’ eggs. Use the table for 15–17. Question 15. What is the difference in average length between the longest egg and the shortest egg? Answer: 0.073 Explanation: The length of the longest egg is 0.086 and the shortest egg is 0.013, so the difference is 0.086-0.013= 0.073 Question 16. Which egg has a width that is eight thousandths of a meter shorter than its length? Answer: Turtledove Explanation: The length of the turtledove egg is 0.031 and the width is 0.023, so 0.031-0.023= 0.08m shorter than length. Question 17. How many robin eggs, laid end to end, would be about equal in length to two raven eggs? Justify your answer Answer: 5 robin eggs should be laid. Explanation: The length of Two raven eggs is 0.049+0.049=0.098, so 5 robin eggs should be laid. ### Add and Subtract Decimals – Page No. 41 Estimate. Then find the sum or difference. Question 1. 43.53 + 27.67 Answer: 71.2 Explanation: 43.53 + 27.67=71.2 Question 2. 17 + 3.6 + 4.049 Answer: 24.649 Explanation: 17 + 3.6 + 4.049 =17+7.649 =24.649 Question 3. 3.49 − 2.75 Answer: 0.74 Explanation: 3.49-2.75= 0.74 Question 4. 5.07 − 2.148 Answer: 2.922 Explanation: 5.07-2.148= 2.922 Question 5. 3.92 + 16 + 0.085 Answer: 20.005 Explanation: 3.92 + 16 + 0.085 = 3.92+16.085 = 20.005 Question 6. 41.98 + 13.5 + 27.338 Answer: 82.818 Explanation: 41.98 + 13.5 + 27.338 = 41.98+ 40.838 Evaluate using the order of operations. Question 7. 8.4 + (13.1 − 0.6) Answer: 20.9 Explanation: 8.4 + (13.1 − 0.6) = 8.4+(12.5) = 20.9 Question 8. 34.7 − (12.07 + 4.9) Answer: 17.73 Explanation: 34.7 − (12.07 + 4.9) = 34.7-(16.97) = 17.73 Question 9. (32.45 − 4.8) − 2.06 Answer: 25.59 Explanation: (32.45 − 4.8) − 2.06 = 27.65- 2.06 = 25.59 Problem Solving Question 10. The average annual rainfall in Clearview is 38 inches. This year, 29.777 inches fell. How much less rain fell this year than falls in an average year? Answer: 8.23 Explanation: Average annual rainfall in last year is 38 inches and this year is 29.777 inches, so 38-29.77= 8.23 inches less rainfall Question 11. At the theater, the Worth family spent$18.00 on adult tickets, $16.50 on children’s tickets, and$11.75 on refreshments. How much did they spend in all?

Answer: $46.25 Explanation: As the family spent$18.00 on adult tickets, $16.50 on children’s tickets, and$11.75 on refreshments,
So the total spent by the family is $18.00+$16.50+$11.75=$46.25

Question 12.
Write a word problem that involves adding or subtracting decimals. Include the solution.

Answer: Mark and Jack went to the park and cost of ticket is $6.50. Mark has$20. How much remaining did mark has left?

Explanation: As MArk and jack went to the park where ticket price is $6.50, so for both it will be$6.50+$6.50=$13.00. As Mark has $20, remaining amount left with Mark is$20-$13=$7

### Lesson Check – Page No. 42

Question 1.
Alden fills his backpack with 0.45 kg of apples, 0.18 kg of cheese, and a water bottle that weighs 1.4 kg. How heavy are the contents of his backpack?

Explanation: The total weight of a backpack is 0.45+0.18+1.4= 2.03kg

Question 2.
Gabby plans to hike 6.3 kilometers to see a waterfall. She stops to rest after hiking 4.75 kilometers. How far does she have left to hike?

Explanation: Gobby hikes 6.3kms and stops at 4.75kms, so she left at 6.3-4.75= 1.55kms
Spiral Review

Question 3.
A 6-car monorail train can carry 78 people. If one train makes 99 trips during the day, what is the greatest number of people the train can carry in one day?

Explanation: The greatest number of people the train can carry in one day is 78×99= 7,722.

Question 4.
An airport parking lot has 2,800 spaces. If each row has 25 spaces, how many rows are there?

Explanation: As parking lot has 2,800 spaces and each row has 25 spaces, no. of rows is 2800÷25= 112 rows

Question 5.
Evan brought 6 batteries that cost $10 each and 6 batteries that cost$4 each. The total cost was the same as he would have spent buying 6 batteries that cost $14 each. So, 6 ×$14 = (6 × 10) + (6 × 4). What property does the equation illustrate?

Explanation: By distributive property (a×b)+(a×c)= a×(b+c), here a= 6, b=10, c=4.

Question 6.
Cups come in packages of 12 and lids come in packages of 15. What is the least number of cups and lids that Corrine can buy if she wants to have the same number of cups and lids?

Answer: 60 cups and 60 lids.

Explanation:
Multiples of 12: 12,24,36,48,60
Multiples of 15: 15,30,45,60
LCM is 60
So the least number of cups and lids she can buy is 60 cups and 60 lids.

### Share and Show – Page No. 45

Estimate. Then find the product.

Question 1.
12.42 × 28.6

Explanation: 12.42 × 28.6
= 355.212

Question 2.
32.5 × 7.4

Explanation: 32.5 × 7.4
=240.5

Attend to Precision Algebra Evaluate using the order of operations.

Question 3.
0.24 × (7.3 + 2.1)

Explanation: 0.24 × (7.3 + 2.1)
= 0.24×9.4
= 2.256

Question 4.
0.075 × (9.2 − 0.8)

Explanation: 0.075 × (9.2 − 0.8)
= 0.075×(8.4)
= 0.63

Question 5.
2.83 + (0.3 × 2.16)

Explanation: 2.83 + (0.3 × 2.16)
= 2.83+0.648
= 3.478

Estimate. Then find the product.

Question 6.
29.14 × 5.2

Explanation: 29.14 × 5.2

= 151.528

Question 7.
6.95 × 12

Explanation: 6.95 × 12
= 83.4

Question 8.
0.055 × 1.82

Explanation: 0.055 × 1.82
= 0.1001

Attend to Precision Algebra Evaluate using the order of operations.

Question 9.
(3.62 × 2.1) − 0.749

Explanation: (3.62 × 2.1) − 0.749
= 7.602- 0.749
= 6.853

Question 10.
5.8 − (0.25 × 1.5)

Explanation: 5.8 − (0.25 × 1.5)
= 5.8- (0.375)
= 5.425

Question 11.
(0.83 + 1.27) × 6.4

Explanation: (0.83 + 1.27) × 6.4
= (2.1)×6.4
= 13.44

Question 12.
Jamal is buying ingredients to make a large batch of granola to sell at a school fair. He buys 3.2 pounds of walnuts for $4.40 per pound and 2.4 pounds of cashews for$6.25 per pound. How much change will he receive if he pays with two $20 bills? Answer:$40-$29.08=$10.92.

Explanation: Jamal bought 3.2 pounds of walnuts for $4.40 per pound, so for 3.2 pounds it will be 3.2×4.40= 14.08, and 2.4 pounds of cashew for$6.25 per pound, so for 2.4 pounds it will be 2.4×6.25= 15. Total Jamal spend is 14.08+15= 29.08. As he have two $20 so he will receive$40-$29.08=$10.92.

### Unlock the Problem – Page No. 46

The table shows some currency exchange rates for 2009.

Question 13.
When Cameron went to Canada in 2007, he exchanged 40 U.S. dollars for 46.52 Canadian dollars. If Cameron exchanged 40 U.S. dollars in 2009, did he receive more or less than he received in 2007? How much more or less?
a. What do you need to find?

Answer: We need how much or less 40 US dollars are worth in Canadian dollars in 2009 compared to 2007.

Question 13.
b. How will you use the table to solve the problem?

Answer: The table provides exchange rates for 2009, will multiply to find the value of 40 US dollars in Canadian dollars in 2009.

Question 13.
c. Complete the sentences.
40 U.S. dollars were worth _____ Canadian dollars in 2009.
So, Cameron would receive _____ Canadian dollars in 2009.

4.44 Canadian dollars in 2009

Explanation: In 2009 1 US dollar is 1.052, so 40 US dollars is 40×1.052= 42.08 and in 2007 Cameron received 46.52, so in 2009 Cameron would receive 46.52-42.08= 4.44 Canadian dollars in 2009.

Question 14.
At a convenience store, the Jensen family puts 12.4 gallons of gasoline in their van at a cost of $3.80 per gallon. They also buy 4 water bottles for$1.99 each, and 2 snacks for $1.55 each. Complete the table to find the cost for each item. Mrs. Jensen says the total cost for everything before tax is$56.66. Do you agree with her? Explain why or why not.

Answer: No, the answer is not reasonable.

Explanation: As the total cost is 58.18
12.4×3.80= 47.12
4×1.99= 7.96
2×1.55= 3.1
So 47.12+7.96+3.1= $58.18 ### Multiply Decimals – Page No. 47 Estimate. Then find the product. Question 1. 5.69 × 7.8 Answer: 44.382 Explanation: 5.69 × 7.8 = 44.382 Question 2. 3.92 × 0.051 Answer: 0.19992 Explanation: 3.92 × 0.051 = 0.19992 Question 3. 2.365 × 12.4 Answer: 29.326 Explanation: 2.365 × 12.4 = 29.326 Question 4. 305.08 × 1.5 Answer: 457.62 Explanation: 305.08 × 1.5 = 457.62 Evaluate the expression using the order of operations. Question 5. (61.8 × 1.7) + 9.5 Answer: 114.56 Explanation: (61.8 × 1.7) + 9.5 = 105.06+ 9.5 = 114.56 Question 6. 205 − (35.80 × 5.6) Answer: 4.52 Explanation: 205 − (35.80 × 5.6) = 205- 200.48 = 4.52 Question 7. 1.9 × (10.6 − 2.17) Answer: 16.017 Explanation: 1.9 × (10.6 − 2.17) = 1.9×( 8.43) = 16.017 Problem Solving Question 8. Blaine exchanges$100 for yen before going to Japan. If each U.S. dollar is worth 88.353 yen, how many yen should Blaine receive?

Explanation: As 1 US dollar is 88.353 yen, so when Blaine exchanges $100 to yen it will be$100×88.353=8835.3 yen

Question 9.
A camera costs 115 Canadian dollars. If each Canadian dollar is worth 0.952 U.S. dollars, how much will the camera cost in U.S. dollars?

Explanation: As 1 Canadian dollar is 0.952 US dollars, so camers cost is 115×0.952= 109.48.

Question 10.
Explain how to mentally multiply a decimal number by 100.

Answer: Move the decimal point two places right.

### Lesson Check – Page No. 48

Question 1.
A gallon of water at room temperature weighs about 8.35 pounds. Lena puts 4.5 gallons in a bucket. How much does the water weigh?

Explanation: As 1 gallon= 8.35 pounds, Lena put 4.5 gallons in a bucket. So water weight is 4.5×8.35= 37.575

Question 2.
Shawn’s rectangular mobile home is 7.2 meters wide and 19.5 meters long. What is its area?

Explanation: Area= Length×wide, so 7.2×19.5= 140.4

Spiral Review

Question 3.
Last week, a store sold laptops worth a total of $3,885. Each laptop cost$555. How many laptops did the store sell last week?

Explanation: Total Laptops sold is $3885 and each laptop cost is$555, so 3885÷555= 7 laptops were sold by the store.

Question 4.
Kyle drives his truck 429 miles on 33 gallons of gas. How many miles can Kyle drive on 1 gallon of gas?

Explanation: As Kyle drives 429 miles on 33 gallons gas, so 429÷33= 13 miles he can drive on 1 gallon of gas.

Question 5.
Seven busloads each carrying 35 students arrived at the game, joining 23 students who were already there. Evaluate the expression 23 + (7 × 35) to find the total number of students at the game.

Explanation: 23+(7×35)
=23+(245)
=268.
Total students are 268.

Question 6.
A store is giving away a $10 coupon to every 7th person to enter the store and a$25 coupon to every 18th person to enter the store. Which person will be the first to get both coupons?

Answer: 126th person will get both coupons.

Explanation: LCM of 7 and 18 is 18×7= 126. So 126th person will get both coupons.

### Estimate. Then find the quotient – Page No. 51

Question 2.
7)$$\overline { 17.15 }$$

Explanation: $17.15÷7= 2.45 Question 3. 4)$$\overline { 1.068 }$$ Answer: 0.267 Explanation: 1.068÷4= 0.267 Question 4. 12)$$\overline { 60.84 }$$ Answer: 5.07 Explanation: 60.84÷12= 5.07 Question 5. 18.042 ÷ 6 Answer: 3.007 Explanation: 18.042÷6= 3.007 On Your Own Estimate. Then find the quotient. Question 6.$21.24 ÷ 6

Explanation: $21.24 ÷ 6= 3.54 Question 7. 28.63 ÷ 7 Answer: 4.09 Explanation: 28.63 ÷ 7= 4.09 Question 8. 1.505 ÷ 35 Answer: 0.043 Explanation: 1.505 ÷ 35= 0.043 Question 9. 0.108 ÷ 18 Answer: 0.006 Explanation: 0.108 ÷ 18= 0.006 Attend to Precision Algebra Evaluate using the order of operations. Question 10. (3.11 + 4.0) ÷ 9 Answer: 0.79 Explanation: (3.11 + 4.0) ÷ 9 = (7.11)+9 = 0.79 Question 11. (6.18 − 1.32) ÷ 3 Answer: 1.62 Explanation: (6.18 − 1.32) ÷ 3 = (4.86)÷3 = 1.62 Question 12. (18 − 5.76) ÷ 6 Answer: 2.04 Explanation: (18 − 5.76) ÷ 6 = (12.24)÷6 = 2.04 Question 13. Use Appropriate Tools Find the length of a dollar bill to the nearest tenth of a centimeter. Then show how to use division to find the length of the bill when it is folded in half along the portrait of George Washington Answer: 3.07 inches or 7.8 centimeter. Explanation: As the length of a dollar bill to the nearest tenth of a centimeter is 15.6 cm, and length of the bill when it is folded in half along the portrait of George Washington is 3.07 inches or 7.8 centimeter. Question 14. Emilio bought 5.65 pounds of green grapes and 3.07 pounds of red grapes. He divided the grapes equally into 16 bags. If each bag of grapes has the same weight, how much does each bag weigh? Answer: 0.545 pounds. Explanation: Total weight of grapes is 5.65+3.07= 8.72 pounds, so each bag weight is 8.72÷16= 0.545 pounds. ### Problem Solving + Applications – Page No. 52 Pose a Problem Question 15. This table shows the average height in inches for girls and boys at ages 8, 10, 12, and 14 years. To find the average growth per year for girls from age 8 to age 12, Emma knew she had to find the amount of growth between age 8 and age 12, then divide that number by the number of years between age 8 and age 12. Emma used this expression: (60.50−50.75)÷4 She evaluated the expression using the order of operations. Write the expression. (60.50−50.75)÷4 Perform operations in parentheses. 9.75÷4 Divide. 2.4375 So, the average annual growth for girls ages 8 to 12 is 2.4375 inches. Write a new problem using the information in the table for the average height for boys. Use division in your problem. Answer: Find the average growth per year for girls 8 to 14. Explanation: As (62.50-50.75)÷6 = (11.75)÷6 = 1.96 So the average annual growth for girls age 8 to age 14 is 1.96 inches. Question 16. The table shows the number of books each of three friends bought and the cost. On average, which friend spent the most per book? Use numbers and words to explain your answer Answer: Nabil spent the most per book. Explanation: Joyce purchased 1 book which costs$10.95
Nabil purchased 2 books which costs $40.50, so 1 book cost is 40.50÷2=$20.26
Kenneth purchased 3 books for $51.15 , so 1 book cost is 51.15÷3=$17.05
So, Nabil spent the most per book.

### Divide Decimals by Whole Numbers – Page No. 53

Estimate. Then find the quotient.

Question 1.
1.284 ÷ 12

Explanation: 1.284÷12= 0.107

Question 2.
9)$$\overline { 2.43 }$$

Explanation: 2.43÷9 = 0.27

Question 3.
25.65 ÷ 15

Explanation: 25.65÷15= 1.71

Question 4.
12)$$\overline { 2.436 }$$

Explanation: 2.436÷12 = 0.203

Evaluate using the order of operations.

Question 5.
(8 − 2.96) ÷ 3

Explanation: (8 − 2.96) ÷ 3
= (5.04)÷3
= 1.68

Question 6.
(7.772 − 2.38) ÷ 8

Explanation: (7.772 − 2.38) ÷ 8
= (5.392)÷8
= 0.674

Question 7.
(53.2 + 35.7) ÷ 7

Explanation: (53.2 + 35.7) ÷ 7
= (88.9)÷7
= 12.7

Problem Solving

Question 8.
Jake earned $10.44 interest on his savings account for an 18-month period. What was the average amount of interest Jake earned on his savings account per month? Answer:$0.58.

Explanation: Jake earned $10.44 interest on his savings account for an 18 month period, so average amount interest is 10.44÷18=$0.58.

Question 9.
Gloria worked for 6 hours a day for 2 days at the bank and earned $114.24. How much did she earn per hour? Answer:$9.52.

Explanation: As gloria worked for 6 hours for 2 days, so total hours is 6×2= 12 hours earned $114.24. So per hour she earns$114.24÷12= $9.52. Question 10. Explain the importance of correctly placing the decimal point in the quotient of a division problem. Answer: If you don’t have the decimals in right spot your answer could be differ. ### Lesson Check – Page No. 54 Estimate each quotient. Then find the exact quotient for each question. Question 1. Ron divided 67.6 fluid ounces of orange juice evenly among 16 glasses. How much did he pour into each glass? Answer: 4.225 ounces. Explanation: As there are 16 glasses, he pours into each glass 67.6÷16= 4.225 ounces. Question 2. The cost of a$12.95 pizza was shared evenly by 5 friends. How much did each person pay?

Answer: $2.59. Explanation: The cost of pizza is$12.95 which was shared by 5 friends, so each person pays $12.95÷5=$2.59

Spiral Review

Question 3.
What is the value of the digit 6 in 968,743,220?

Explanation: The place value of 6 is 60,00,000.

Question 4.
The Tama, Japan, monorail carries 92,700 riders each day. If the monorail runs 18 hours each day, what is the average number of passengers riding each hour?

Explanation: No. of riders each day is 92,700 and he runs for 18 hours in each day, so average no. of passengers riding each hour is 92,700÷18= 5150 passengers.

Question 5.
Ray paid $812 to rent music equipment that costs$28 per hour. How many hours did he have the equipment?

Explanation: As Ray paid $812 which costs$28 per hour, so no.of hours did he have the equipment is
$812÷$28= 29 hours.

Question 6.
Jan has 35 teaspoons of chocolate cocoa mix and 45 teaspoons of french vanilla cocoa mix. She wants to put the same amount of mix into each jar, and she only wants one flavor of mix in each jar. She wants to fill as many jars as possible. How many jars of french vanilla cocoa mix will Jan fill?

Explanation: By distributive property (35+45)
= (5×7)+(5×9)
= 5(7+9)
So she will fill 9 jars.

### Share and Show – Page No. 57

Question 1.
Find the quotient.
14.8)$$\overline { 99.456 }$$

Explanation: 99.456÷14.8= 6.72

Estimate. Then find the quotient.

Question 2.
$10.80 ÷$1.35

Explanation:
$10.80 ÷$1.35
= 8

Question 3.
26.4 ÷ 1.76

Explanation:
26.4 ÷ 1.76
= 15.113

Question 4.
8.7)$$\overline { 53.07 }$$

Explanation: 53.07÷8.7= 6.1

Estimate. Then find the quotient.

Question 5.
75 ÷ 12.5

Explanation:

Question 6.
544.6 ÷ 1.75

Explanation:

Question 7.
0.78)$$\overline { 0.234 }$$

Explanation: 0.234÷0.78= 0.3.

Attend to Precision Algebra Evaluate using the order of operations.

Question 8.
36.4 + (9.2 − 4.9 ÷ 7)

Explanation: By BODMAS rule
36.4+(9.2−4.9÷ 7)
= 36.4+(9.2−(4.9÷7))
= 36.4+(9.2-(0.7))
= 36.4+(8.5)
= 44.9

Question 9.
16 ÷ 2.5 − 3.2 × 0.043

Explanation: 16 ÷ 2.5 − 3.2 × 0.043
= (16÷2.5) − (3.2 × 0.043)
= (6.4)-(3.2 × 0.043)
= 6.4 – 0.1376
= 6.2624

Question 10.
142 ÷ (42 − 6.5) × 3.9

Explanation: 142 ÷ (42 − 6.5) × 3.9
= (142÷ 35.5) × 3.9
= 4×3.9
= 15.6

Question 11.
Marcus can buy 0.3 pound of sliced meat from a deli for $3.15. How much will 0.7 pound of sliced meat cost? Answer:$7.35

Explanation: As 0.3 pound of sliced meat is $3.15, so cost of 1 pound of sliced meat is 3.15÷0.3=$10.5. And for 0.7 pound of sliced meat cost is 10.5×0.7= $7.35 ### Page No. 58 Question 12. The table shows the earnings and the number of hours worked for three employees. Complete the table by finding the missing values. Which employee earned the least per hour? Explain. Answer: Employee 2 has earned least per hour. Explanation: 1. No. of hours worked is 34.02÷ 9.72= 3.5 hours. 2. Earnings per hour is 42.75÷4.5=$9.5
3. No.of hours worked is 52.65÷9.75= 5.4 hours
Employee 2 has earned least per hour.

Amoebas

Amoebas are tiny one-celled organisms. Amoebas can range in size from 0.01 mm to 5 mm in length. You can study amoebas by using a microscope or by studying photographic enlargements of them.

Jacob has a photograph of an amoeba that has been enlarged 1,000 times. The length of the amoeba in the photo is 60 mm. What is the actual length of the amoeba?
Divide 60 ÷ 1,000 by looking for a pattern.
60 ÷ 1 = 60
60 ÷ 10 = 6.0 The decimal point moves _____ place to the left.
60 ÷ 100 = ____ The decimal point moves _____ place to the left.
60 ÷ 1000 =____ The decimal point moves _____ place to the left.
So, the actual length of the amoeba is _____ mm.

Explanation:
60 ÷ 10 = 6.0 The decimal point moves one place to the left.
60 ÷ 100 =0.6  The decimal point moves two place to the left.
60 ÷ 1000 =0.06 The decimal point moves three place to the left.
Actual length of amoeba is 0.06mm

Question 13.
Explain the pattern.

Explanation: 60÷1000= 0.06mm.

Question 14.
Pelomyxa palustris is an amoeba with a length of 4.9 mm. Amoeba proteus has a length of 0.7 mm. How many Amoeba proteus would you have to line up to equal the length of three Pelomyxa palustris? Explain.

Explanation:
Let N be the number, then
N×(proteus length)= 3× (palustris length)
N× 0.7= 3× 4.9
N×0.7= 14.7
N= 14.7÷0.7
N= 21

### Divide with Decimals – Page No. 59

Estimate. Then find the quotient.

Question 1.
43.18 ÷ 3.4

Explanation: 43.18 ÷ 3.4= 12.7

Question 2.
4.185 ÷ 0.93

Explanation: 4.185 ÷ 0.93= 4.5

Question 3.
6.3)$$\overline { 25.83 }$$

Explanation: 6.3÷25.83= 0.244

Question 4.
0.143 ÷ 0.55

Explanation: 0.143 ÷ 0.55= 0.26

Evaluate using the order of operations.

Question 5.
4.92 ÷ (0.8 – 0.12 ÷ 0.3)

Explanation: 4.92 ÷ (0.8 – 0.12 ÷ 0.3)
= 4.92÷(0.8-(0.12÷0.3))
= 4.92÷(0.8-(0.4))
= 4.92÷(0.4)
= 12.3

Question 6.
0.86 ÷ 5 – 0.3 × 0.5

Explanation: 0.86 ÷ 5 – 0.3 × 0.5
= (0.86÷5) – (0.3 × 0.5)
= (0.172)-(0.3 × 0.5)
= 0.172 – (0.15)
= 0.022

Question 7.
17.28 ÷ (1.32 – 0.24) × 0.6

Explanation: 17.28 ÷ (1.32 – 0.24) × 0.6
= (17.28 ÷ (1.32 – 0.24))× 0.6
= (17.28 ÷( 1.08))×0.6
= (16)×0.6
= 9.6

Problem Solving

Question 8.
If Amanda walks at an average speed of 2.72 miles per hour, how long will it take her to walk 6.8 miles?

Explanation: Amanda walks at an average speed of 2.72 miles per hour, so for 6.8 miles it will be
6.8÷2.72= 2.5 hours.

Question 9.
Chad cycled 62.3 miles in 3.5 hours. If he cycled at a constant speed, how far did he cycle in 1 hour?

Explanation: Chad cycled 62.3 miles in 3.5 hours, so in 1 hour 62.3÷3.5= 17.8 miles.

Question 10.
Explain how dividing by a decimal is different from dividing by a whole number and how it is similar.

Answer: By moving the decimals first the dividing will be different, and after that it will be same.

### Lesson Check – Page No. 60

Question 1.
Elliot drove 202.8 miles and used 6.5 gallons of gasoline. How many miles did he travel per gallon of gasoline?

Explanation: Elliot drove 202.8 miles and used 6.5 gallons of gasoline, so per gallon of gasoline he will travel 202.8÷6.5= 31.2 miles.

Question 2.
A package of crackers weighing 8.2 ounces costs $2.87. What is the cost per ounce of crackers? Answer: 0.35 per ounce. Explanation: As 8.2 ounces costs$2.87, so per ounce of crackers it will be 2.87÷8.2= 0.35 per ounce.

Spiral Review

Question 3.
Four bags of pretzels were divided equally among 5 people. How much of a bag did each person get?
$$\frac{□}{□}$$

Explanation: As 4 bags were divided equally among 5 people, so each person gets 4÷5= 0.8 of a bag

Question 4.
A zebra ran at a speed of 20 feet per second. What operation should you use to find the distance the zebra ran in 10 seconds?

Explanation: Per second zebra ran at a speed of 20 feet, so for 10 seconds 20×10= 200 feet.

Question 5.
Nira has $13.50. She receives a paycheck for$55. She spends $29.40. How much money does she have now? Answer:$39.10.

Explanation: As Nira has $13.50 and she receives paycheck of$55, so total she had is $13.50+$55= $68.5. As she spent$29.40, so she has now $68.5-$29.40= $39.10. Question 6. A piece of cardboard is 24 centimeters long and 15 centimeters wide. What is its area? _____ cm2 Answer: 360 cm2 Explanation: Area= Length×wide = 24×15 = 360 cm2 ### Chapter 1 Review/Test – Page No. 61 Question 1. Use the numbers to complete the factor tree. You may use a number more than once. Write the prime factorization of 54 Answer: 54=2×3×3×3 Explanation: Question 2. For numbers 2a–2d, choose Yes or No to indicate whether the LCM of the two numbers is 15. 2a. 5, 3 Yes No 2b. 5, 10 Yes No 2c. 5, 15 Yes No 2d. 5, 20 Yes No 2a. 5, 3 Answer: Yes Explanation: Multiples of 5: 5,10,15 Multiples of 3: 53,6,9,12,15 LCM of 5,3 is 15 2b. 5, 10 Answer: No Explanation: Multiples of 5: 5,10 Multiples of 10: 10 LCM of 5,10 is 10 2c. 5, 15 Answer: Yes Explanation: Multiples of 5: 5,10,15 Multiples of 15: 15 LCM is 15 2d. 5, 20 Answer: No Explanation: Multiples of 5: 5,10,15,20 Multiples of 20: 20 LCM is 20 Question 3. Select two numbers that have 9 as their greatest common factor. Mark all that apply. Options: a. 3, 9 b. 3, 18 c. 9, 18 d. 9, 36 e. 18, 27 Answer: c,d,e Explanation: a. 3,9 Factors of 3: 1,3. Factors of 9: 1,3,9. GCF is 3 b. 3,18 Factors of 3: 1,3 Factors of 18: 1,2,3,6,9,18 GCF is 3 c. 9,18 Factors of 9: 1,3,9 Factors of 18: 1,2,3,6,9,18. GCF is 9 d. 9,36 Factors of 9: 1,3,9 Factors of 36: 1,2,3,4,6,9,18,36 GCF is 9 e. 18,27 Factors of 18: 1,2,3,6,9,18 Factors of 27: 1,3,9,27 GCF is 9 ### Page No. 62 Question 4. The prime factorization of each number is shown. 15 = 3 × 5 18 = 2 × 3 × 3 Part A Using the prime factorization, complete the Venn diagram Answer: Prime factors of 15: 3×5 Prime factors of 18: 2×3×3 Common factors are: 3 Explanation: Question 4. Part B Find the GCF of 15 and 18. Answer: 3 Explanation: Factors of 15: 1,3,5 Factors of 18: 1,2,3,6,9,18 GCF is 3 Question 5. For numbers 5a–5d, choose Yes or No to indicate whether each equation is correct. 5a. 222.2 ÷ 11 = 22.2 Yes No 5b. 400 ÷ 50 = 8 Yes No 5c. 1,440 ÷ 36 = 40 Yes No 5d. 7,236 ÷ 9 = 804 Yes No 5a. 222.2 ÷ 11 = 22.2 Answer: No Explanation: 222.2 ÷ 11 = 20.2 5b. 400 ÷ 50 = 8 Answer: Yes Explanation: 400 ÷ 50 = 8 5c. 1,440 ÷ 36 = 40 Answer: Yes Explanation: 1,440 ÷ 36 = 40 5d. 7,236 ÷ 9 = 804 Answer: Yes Explanation: 7,236 ÷ 9 = 804 ### Page No. 63 Question 6. For numbers 6a–6d, select True or False for each equation. 6a. 1.7 + 4.03 = 6 True False 6b. 2.58 + 3.5 = 6.08 True False 6c. 3.21 − 0.98 = 2.23 True False 6d. 14 − 1.3 = 0.01 True False 6a. 1.7 + 4.03 = 6 Answer: False Explanation: 1.7 + 4.03 = 5.73 6b. 2.58 + 3.5 = 6.08 Answer: True Explanation: 2.58 + 3.5 = 6.08 6c. 3.21 − 0.98 = 2.23 Answer: True Explanation: 3.21 − 0.98 = 2.23 6d. 14 − 1.3 = 0.01 Answer: False Explanation: 6d. 14 − 1.3 = 12.7 Question 7. Four friends went shopping at a music store. The table shows the number of CDs each friend bought and the total cost. Complete the table to show the average cost of the CDs each friend bought. What is the average cost of all the CDs that the four friends bought? Show your work. Answer:$8.94.

Explanation:
Lana purchased 4 CDs and total cost is $36.68, so cost of 1 CD is$36.68÷4= $9.17 Troy purchased 5 CDs and total cost is$40.55, so cost of 1 CD is $40.55÷5=$8.11
Juanita purchased 5 CDs and total cost is $47.15, so cost of 1 CD is$47.15÷5= $9.43 Alex purchased 6 CDs and total cost is$54.42, so cost of 1 CD is $54.42÷6=$9.07
Average cost of all CD’s i= (cost of all CD’s)÷(No.of CD’S)
=($36.68+$40.55+$47.15+$54.42)÷20
= (178.8) ÷20
= $8.94 Question 8. The table shows the earnings and the number of hours worked for five employees. Complete the table by finding the missing values. Answer: 1. No. of hours worked is 2.5 hours. 2. Earnings per hour is$93.654.
3. No. of hours worked is 4.4 hours.
4. Earnings per hour is $302.5. 5. Earnings per hour is$150.

Explanation:
1. No. of hours worked is $23.75÷$9.50= 2.5 hours.
2. Earnings per hour is $28.38×3.3=$93.654.
3. No. of hours worked is $38.50÷8.75= 4.4 hours. 4. Earnings per hour is$55×5.5= $302.5. 5. Earnings per hour is$60×2.5= $150. ### Page No. 64 Question 9. The distance around the outside of Cedar Park is 0.8 mile. Joanie ran 0.25 of the distance during her lunch break. How far did she run? Show your work. Answer: 0.2 miles. Explanation: Joanie ran 0.25 miles and the distance around the outside of cedar park is 0.8 mile, so she ran 0.25×0.8= 0.2 miles. Question 10. A one-celled organism measures 32 millimeters in length in a photograph. If the photo has been enlarged by a factor of 100, what is the actual length of the organism? Show your work. Answer: 3200 millimeters. Explanation: Length of one celled organism is 32 millimeters, as the photo was enlarged by a factor of 100, it’s actual length is 32×100= 3200 millimeters. Question 11. You can buy 5 T-shirts at Baxter’s for the same price that you can buy 4 T-shirts at Bixby’s. If one T-shirt costs$11.80 at Bixby’s, how much does one T-shirt cost at Baxter’s? Use numbers and words to explain your answer.

Answer: $9.44. Explanation: As one T-shirt costs$11.80, so 4 T-shirts cost is 4×$11.80= 47.2. So 5 T-shirts at Baxter’s is 47.2 and one T-shirt cost is 47.2÷5=$9.44.

### Page No. 65

Question 12.
Crackers come in packages of 24. Cheese slices come in packages of 18. Andy wants one cheese slice for each cracker. Patrick made the statement shown.
If Andy doesn’t want any crackers or cheese slices left over, he needs to buy at least 432 of each.
Is Patrick’s statement correct? Use numbers and words to explain why or why not. If Patrick’s statement is incorrect, what should he do to correct it?

Answer: Patrick’s statement is wrong.

Explanation:
Multiples of 18: 18,36,54,72
Multiples of 24: 24,48,72
LCM is 72
So the least packages he need to buy is 72.

Question 13.
There are 16 sixth graders and 20 seventh graders in the Robotics Club. For the first project, the club sponsor wants to organize the club members into equal-size groups. Each group will have only sixth graders or only seventh graders.
Part A
How many students will be in each group if each group has the greatest possible number of club members? Show your work.

Answer: Each group will have 4 members, and 4 groups of sixth grade and 5 groups of seventh grade.

Explanation: By distributive property 16+20
=(4×4)+(4×5)
=4×(4+5)
So each group will have 4 members, and 4 groups of sixth grade and 5 groups of seventh grade.

Question 13.
Part B
If each group has the greatest possible number of club members, how many groups of sixth graders and how many groups of seventh graders will there be? Use numbers and words to explain your answer
__________ groups of sixth graders
__________ groups of seventh graders

Answer: Each group will have 4 members, and 4 groups of sixth grade and 5 groups of seventh grade.

Explanation: By distributive property 16+20
=(4×4)+(4×5)
=4×(4+5)
So each group will have 4 members, and 4 groups of sixth grade and 5 groups of seventh grade.

### Page No. 66

Question 14.
The Hernandez family is going to the beach. They buy sun block for $9.99, 5 snacks for$1.89 each, and 3 beach toys for $1.49 each. Before they leave, they fill up the car with 13.1 gallons of gasoline at a cost of$3.70 per gallon.
Part A
Complete the table by calculating the total cost for each item.

Answer: Total cost is $48.47+$9.45++$4.47+$9.99= $72.38 Explanation: Gasoline 13.1×$3.70= $48.47 Snacks 5×$1.89= $9.45 Beach toys 3×$1.49= $4.47 Sun block 1×$9.99= $9.99 Total cost is$48.47+$9.45++$4.47+$9.99=$72.38

Question 14.
Part B
What is the total cost for everything before tax? Show your work.

Answer: $72.38. Explanation: Total cost is$48.47+$9.45++$4.47+$9.99=$72.38.

Question 14.
Part C
Mr. Hernandez calculates the total cost for everything before tax using this equation.
Total cost = 13.1 + 3.70 × 5 + 1.89 × 3 + 1.49 × 9.99
Do you agree with his equation? Use numbers and words to explain why or why not. If the equation is not correct, write a correct equation.

Explanation: Mr. Hernandez calculated in a wrong way.
Total cost is (13.1×$3.70)+(5×$1.89)+(3×$1.49)+(1×$9.99)= $72.38. Conclusion: Refer our Go Math Grade 6 Answer Chapter 1 and score the highest marks in the exams. Students who are lagging in maths can click on the links and learn the concepts. The students who are unable to understand the concept can post your comments in the below section. ## Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume contains 6th Standard Go Math solutions which will make students understand the concepts easily help the students to score well in the exams. This Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume. And in this, each and every question was explained intimately. The answers in this chapter are explained in a simple way that anyone can understand easily. ## Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume This chapter 11 contains Three-Dimensional Figures and Nets, Explore Surface Area Using Nets, Surface Area of Prisms, etc. are explained clearly which makes the scholars learn quickly. Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume. questions are explained in a basic way that students will never feel any difficulty in learning. By this, students can gain good knowledge and this is helpful in finish student’s assignments also. Lesson 1: Three-Dimensional Figures and Nets Lesson 2: Investigate • Explore Surface Area Using Nets Lesson 3: Algebra • Surface Area of Prisms Lesson 4: Algebra • Surface Area of Pyramids Mid-Chapter Checkpoint Lesson 5: Investigate • Fractions and Volume Lesson 6: Algebra • Volume of Rectangular Prisms Lesson 7: Problem Solving • Geometric Measurements Chapter 11 Review/Test ### Share and Show – Page No. 599 Identify and draw a net for the solid figure. Question 1. Answer: The base Square or Rectangle, and lateral faces are Triangle and the figure is a Square pyramid or Rectangular pyramid. Explanation: Question 2. Answer: Cube or Rectangular prism. Explanation: The base is a square or rectangle and lateral faces are squares are rectangle. The figure is a Cube or Rectangular prism. Identify and sketch the solid figure that could be formed by the net. Question 3. Answer: Triangular pyramid. Explanation: The net has four triangles, so it is a triangular pyramid. Question 4. Answer: Cube Explanation: The net has six squares. On Your Own Identify and draw a net for the solid figure. Question 5. Answer: Triangular prism. Explanation: The base is a rectangle and the lateral faces are triangle and rectangles, so it is a triangular prism. Question 6. Answer: Rectangular Prism. Explanation: The base is a rectangle and the lateral faces are squares and rectangles. And it is a Rectangular prism. ### Problem Solving + Applications – Page No. 600 Solve. Question 7. The lateral faces and bases of crystals of the mineral galena are congruent squares. Identify the shape of a galena crystal. Answer: Cube Explanation: The shape of the galena is Cube. Question 8. Rhianon draws the net below and labels each square. Can Rhianon fold her net into a cube that has letters A through G on its faces? Explain. Answer: No, she cannot fold her net into a cube. Rhianon’s net has seven squares but there are only six squares in a net of a cube. Question 9. Describe A diamond crystal is shown. Describe the figure in terms of the solid figures you have seen in this lesson. Answer: We can see that Diamond crystal consists of two square pyramids with congruent bases and the pyramids are reversed and placed base to base. Question 10. Sasha makes a triangular prism from paper. The bases are _____. The lateral faces are _____. Answer: The bases are Triangle The lateral faces are Rectangle ### Three-Dimensional Figures and Nets – Page No. 601 Identify and draw a net for the solid figure. Question 1. Answer: Rectangular Prism Explanation: Question 2. Answer: Cube, Rectangular prism Explanation: Question 3. Answer: Square Pyramid Explanation: Question 4. Answer: Triangular Prism Explanation: Problem Solving Question 5. Hobie’s Candies are sold in triangular-pyramidshaped boxes. How many triangles are needed to make one box? Answer: 4 Explanation: As triangled pyramids have four faces. Question 6. Nina used plastic rectangles to make 6 rectangular prisms. How many rectangles did she use? Answer: 36 Explanation: Question 7. Describe how you could draw more than one net to represent the same three-dimensional figure. Give examples. Answer: Explanation: ### Lesson Check – Page No. 602 Question 1. How many vertices does a square pyramid have? Answer: 5 Explanation: Question 2. Each box of Fred’s Fudge is constructed from 2 triangles and 3 rectangles. What is the shape of each box? Answer: Triangular Prism Explanation: Spiral Review Question 3. Bryan jogged the same distance each day for 7 days. He ran a total of 22.4 miles. The equation 7d = 22.4 can be used to find the distance d in miles he jogged each day. How far did Bryan jog each day? Answer: 3.2 miles Explanation: As given equation 7d= 22.4, d= 22.4÷7 = 3.2 miles. Question 4. A hot-air balloon is at an altitude of 240 feet. The balloon descends 30 feet per minute. What equation gives the altitude y, in feet, of the hot-air balloon after x minutes? Answer: Y= 240- 30X. Explanation: Given altitude Y, and the ballon was descended 30 feet per minute. So the equation is Y= 240- 30X. Question 5. A regular heptagon has sides measuring 26 mm and is divided into 7 congruent triangles. Each triangle has a height of 27 mm. What is the area of the heptagon? Answer: 351 mm2 Explanation: Area of heptagon= 1/2 b×h = 1/2 (26)×(27) = 13×27 = 351 mm2 Question 6. Alexis draws quadrilateral STUV with vertices S(1, 3), T(2, 2), U(2, –3), and V(1, –2). What name best classifies the quadrilateral? Answer: Parallelogram Explanation: ### Share and Show – Page No. 605 Use the net to find the surface area of the prism. Question 1. Answer: Explanation: First we must find the area of each face A= 4×3= 12 B= 4×3= 12 C= 5×4= 20 D= 5×4= 20 E= 5×3= 15 F= 5×3= 15 So, the surface area is 12+12+20+20+15+15= 94 cm2 Find the surface area of the rectangular prism. Question 2. Answer: 222 cm2 Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(7×9+ 3×9+ 3×7) = 2(63+27+21) = 2(111) = 222 cm2 Question 3. Answer: Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(10×10+ 10×10+ 10×10) = 2(100+100+100) = 2(300) = 600 cm2 Question 4. Answer: 350 cm2 Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(15×5+ 5×5+ 15×5) = 2(75+25+75) = 2(175) = 350 cm2 Problem Solving + Applications Question 5. A cereal box is shaped like a rectangular prism. The box is 20 cm long by 5 cm wide by 30 cm high. What is the surface area of the cereal box? Answer: 1700 cm2 Explanation: The length of the box is 20 cm, the wide is 5 cm and the height is 30 cm. So surface area of the cereal box is 2(wl+hl+hw)= 2(20×5+30×20+30×5) = 2(100+600+150) = 2(850) = 1700 cm2 Question 6. Darren is painting a wooden block as part of his art project. The block is a rectangular prism that is 12 cm long by 9 cm wide by 5 cm high. Describe the rectangles that make up the net for the prism. Answer: Question 7. In Exercise 6, what is the surface area, in square meters, that Darren has to paint? Answer: 416 cm2 Explanation: Surface area = 2(wl+hl+hw) = 2(9×12+5×12+ 5×9) = 2(108+60+45) = 2(213) = 416 cm2 ### What’s the Error? – Page No. 606 Question 8. Emilio is designing the packaging for a new MP3 player. The box for the MP3 player is 5 cm by 3 cm by 2 cm. Emilio needs to find the surface area of the box. Look at how Emilio solved the problem. Find his error. STEP 1: Draw a net. STEP 2: Find the areas of all the faces and add them. Face A: 3 × 2 = 6 cm2. Face B: 3 × 5 = 15 cm2. Face C: 3 × 2 = 6 cm2. Face D: 3 × 5 = 15 cm2. Face E: 3 × 5 = 15 cm2. Face F: 3 × 5 = 15 cm2. The surface area is 6 + 15 + 6 + 15 + 15 + 15 = 72 cm2. Correct the error. Find the surface area of the prism. Answer: Emilio drew the net incorrectly Face D and F should have been 2 cm by 5 cm, not 3 cm by 5 cm Explanation: Face A: 3×2= 6 cm2 Face B: 3×5= 15 cm2 Face C: 3×2= 6 cm2 Face D: 2×5= 10 cm2 Face E: 3×5= 15 cm2 Face F: 2×5= 10 cm2 So, the surface area of the prism area is 6+15+6+10+15+10= 62 cm2. Question 9. For numbers 9a–9d, select True or False for each statement. 9a. The area of face A is 10 cm2. 9b. The area of face B is 10 cm2. 9c. The area of face C is 40 cm2. 9d. The surface area of the prism is 66 cm2. 9a. The area of face A is 10 cm2. Answer: True Explanation: The area of face A is 2×5= 10 cm2. 9b. The area of face B is 10 cm2. Answer: False Explanation: The area of face B is 2×8= 16 cm2. 9c. The area of face C is 40 cm2. Answer: The area of face C is 8×5= 40 cm2. 9d. The surface area of the prism is 66 cm2. Answer: 160 cm2. Explanation: The surface area of the prism is = 2×10+2×10+2×40 = 20+20+80 = 160 cm2. ### Explore Surface Area Using Nets – Page No. 607 Use the net to find the surface area of the rectangular prism. Question 1. _______ square units Answer: 52 square units. Explanation: The area of face A is 6 squares. The area of face B is 8 squares. The area of face C is 6 squares. The area of face D is 12 squares. The area of face E is 8 squares. The area of face F is 12 squares. The surface area is 6+8+6+12+8+12= 52 square units. Question 2. _______ square units Answer: 112 square units. Explanation: The area of face A is 16 squares. The area of face B is 8 squares. The area of face C is 32 squares. The area of face D is 16 squares. The area of face E is 32 squares. The area of face F is 8 squares. The surface area is 112 square units. Question 3. Answer: 102 mm2 Explanation: Area= 2(wl+hl+hw) = 2(3×7+3×7+3×3) = 2(21+21+9) = 2(51) = 102 mm2 Question 4. _______ in.2 Answer: 58 in.2 Explanation: Area= 2(wl+hl+hw) = 2(5×1+ 4×1+ 4×5) = 2(5+4+20) = 2(29) = 58 in.2 Question 5. _______ ft2 Answer: 77 ft2 Explanation: Area= 2(wl+hl+hw) = 2(6.5×2+3×2+3×6.5) = 2(13+6+19.5) = 2(38.5) = 77 ft2 Problem Solving Question 6. Jeremiah is covering a cereal box with fabric for a school project. If the box is 6 inches long by 2 inches wide by 14 inches high, how much surface area does Jeremiah have to cover? _______ in.2 Answer: 248 in.2 Explanation: Surface area of a cereal box is 2(wl+hl+hw) = 2(2×6+14×6+14×2) = 2(12+84+28) = 2(124) = 248 in.2 Question 7. Tia is making a case for her calculator. It is a rectangular prism that will be 3.5 inches long by 1 inch wide by 10 inches high. How much material (surface area) will she need to make the case? _______ in.2 Answer: 97 in.2 Explanation: Surface Area= 2(wl+hl+hw) = 2(1×3.5+ 10×3.5+ 10×1) = 2(3.5+35+10) = 2(48.5) = 97 in.2 Question 8. Explain in your own words how to find the surface area of a rectangular prism. Answer: To find the surface area we must know the width, length, and height of the prism and then we can apply the formula which is Surface area= 2(width ×length)+ 2(length×height)+ 2(height×width) = 2(width ×length+ length×height+ 2(height×width) ### Lesson Check – Page No. 608 Question 1. Gabriela drew a net of a rectangular prism on centimeter grid paper. If the prism is 7 cm long by 10 cm wide by 8 cm high, how many grid squares does the net cover? _______ cm2 Answer: 412 cm2. Explanation: Surface area is 2(wl+hl+hw) = 2(10×7+8×7+8×10) = 2(70+56+80) = 2(206) = 412 cm2. Question 2. Ben bought a cell phone that came in a box shaped like a rectangular prism. The box is 5 inches long by 3 inches wide by 2 inches high. What is the surface area of the box? _______ in.2 Answer: 62 in.2 Explanation: Surface area is 2(wl+hl+hw) = 2(3×5+2×5+2×3) = 2(15+10+6) = 2(31) = 62 in.2 Spiral Review Question 3. Katrin wrote the inequality x + 56 < 533. What is the solution of the inequality? Answer: X<477. Explanation: X+56<533 = X<533-56 = X<477. Question 4. The table shows the number of mixed CDs y that Jason makes in x hours. Which equation describes the pattern in the table? Answer: y= 5x Explanation: y/x = 10/2= 15/4= 3 y= 5x The pattern is y is x multipled by 5. Question 5. A square measuring 9 inches by 9 inches is cut from a corner of a square measuring 15 inches by 15 inches. What is the area of the L-shaped figure that is formed? _______ in.2 Answer: 144 in.2 Explanation: The area of a square A= a2, so we will find the area of each square. Area= 92 = 9×9 = 81 in.2 And the area of another square is A= 152 = 15×15 = 225 in.2 So the area of L shaped figure is 225-81= 144 in.2 Question 6. Boxes of Clancy’s Energy Bars are rectangular prisms. How many lateral faces does each box have? Answer: 4 Explanation: As Lateral faces are not included in the bases, so rectangular prism has 4. ### Share and Show – Page No. 611 Use a net to find the surface area. Question 1. _______ ft2 Answer: 24 ft2 Explanation: The area of each face is 2 ft×2 ft= 4 ft and the number of faces is 6, so surface area is 6×4= 24 ft2 Question 2. Answer: 432 cm2 Explanation: The area of face A is 16×6= 96 cm2 The area of face B is 16×8= 128 cm2 The area of face C and D is 1/2 × 6×8= 24 cm2 The area of face E is 16×10= 160 cm2 The surface 96+128+2×24+160= 432 cm2 Question 3. _______ in.2 Answer: 155.5 in.2 Explanation: The area of face A and E is 8 ½ × 3½ = 17/2 × 7/2 = 119/4 = 29.75 in.2 The area of face B and F is 8 ½×4 = 17 ½ × 4 = 34 in.2 The area of face C and D is 3 ½×4 7/2 × 4= 14 in.2 The surface area is 2×29.75+2×34+2×14 = 59.5+68+28 = 155.5 in.2 On Your Own Use a net to find the surface area. Question 4. _______ m2 Answer: Explanation: The area of face A and E is 8×3= 24 m2 The area of face B and F is 8×5= 40 m2 The area of face C and D is 3×5= 15 m2 The surface area is 2×24+2×40+2×15 = 48+80+30 = 158 m2 Question 5. _______ $$\frac{□}{□}$$ in.2 Answer: Explanation: The area of each face is 7 1/2 × 7 1/2 = 15/2 × 15/2 = 225/4 in.2 The no.of faces are 6 and the surface area is 6× 225/4 = 675/4 = 337 1/2 in.2 Question 6. Attend to Precision Calculate the surface area of the cube in Exercise 5 using the formula S = 6s2. Show your work. Answer: 337 1/2 in.2 Explanation: As S= s2 = 6(7 1/2)2 = 6(15/2)2 = 6(225/4) = 675/2 = 337 1/2 in.2 ### Unlock the Problem – Page No. 612 Question 7. The Vehicle Assembly Building at Kennedy Space Center is a rectangular prism. It is 218 m long, 158 m wide, and 160 m tall. There are four 139 m tall doors in the building, averaging 29 m in width. What is the building’s outside surface area when the doors are open? a. Draw each face of the building, not including the floor. Answer: Question 7. b. What are the dimensions of the 4 walls? Answer: The 2 walls measure 218 m ×160 m and 2 walls measure by 158 m×160 m. Question 7. c. What are the dimensions of the roof? Answer: The dimensions of the roof are 218 m×158 m. Question 7. d. Find the building’s surface area (not including the floor) when the doors are closed. _______ m2 Answer: 1,54,764 m2 Explanation: The area of two walls is 218×160= 34,880 m2 The area of the other two walls is 158×160= 25,280 m2 The area of the roof 158×218= 34,444 m2 The surface area is 2× 34,880+ 2× 25,280+ 34,444 = 69,760+ 50,560+ 34,444 = 1,54,764 m2 Question 7. e. Find the area of the four doors. _______ m2 Answer: 16,124 m2 Explanation: Area of a door is 139×29 = 4031 m2 And the area of 4 doors is 4×4031= 16,124 m2 Question 7. f. Find the building’s surface area (not including the floor) when the doors are open. _______ m2 Answer: 1,38,640 m2 Explanation: The building’s surface area (not including the floor) when the doors are open is 1,54,764 – 16,124= 1,38,640 m2 Question 8. A rectangular prism is 1 $$\frac{1}{2}$$ ft long, $$\frac{2}{3}$$ ft wide, and $$\frac{5}{6}$$ ft high. What is the surface area of the prism in square inches? _______ in.2 Answer: 808 in.2 Explanation: The area of two faces is 1 1/2× 5/6 = 3/2 × 5/6 = 5/4 cm2 The area of two faces is 2/3 × 5/6 = 5/9 ft2 The area of two faces is 1 1/2× 2/3 = 3/2 × 2/3 = 1 ft2 The surface area of the prism is 2(wl+hl+hw) = 2(5/4 + 5/9 + 1) = 2( 1.25+0.55+1) = 2.5+1.1+2 = 5.61 ft2 As 1 square foot = 144 square inches so 5.61×144 = 807.84 = 808 in.2 Question 9. A gift box is a rectangular prism. The box measures 8 inches by 10 inches by 3 inches. What is its surface area? _______ in.2 Answer: 268 in.2 Explanation: The area of face A and Face E is 8×10= 80 in.2 The area of face B and Face F is 8×3= 24 in.2 The area of face C and Face D is 10×3= 30 in.2 The surface area is 2×80+2×24+2×30 = 160+48+60 = 268 in.2 ### Surface Area of Prisms – Page No. 613 Use a net to find the surface area. Question 1. _______ cm2 Answer: 104 cm2 Explanation: Surface area= 2(wl+hl+hw) = 2(6×5+2×5+2×6) = 2(30+10+12) = 2(52) = 104 cm2 Question 2. _______ in.2 Answer: 118 in.2 Explanation: Surface area= 2(wl+hl+hw) = 2(3.5×4+6×4+6×3.5) = 2(59) = 118 in.2 Question 3. _______ ft2 Answer: 486 ft2 Explanation: Surface area= 2(wl+hl+hw) = 2(9×9+9×9+9×9) = 2(81+81+81) = 2(243) = 486 ft2 Question 4. _______ cm2 Answer: 336 cm2. Explanation: Area = 1/2 bh = 1/2 (6)(8) = 3×8 = 24. As there are 2 triangles, so 2×24= 48. Surface Area= (wl+hl+hw) = (6×12+8×12+12×10) = 228 Total Surface area = 228+48 = 336 cm2 Problem Solving Question 5. A shoe box measures 15 in. by 7 in. by 4 $$\frac{1}{2}$$ in. What is the surface area of the box? _______ in.2 Answer: 408 in.2 Explanation: The area of two faces is 15×7= 105 in.2 The area of two faces is 15× 4 1/2 = 15 × 9/2 = 15 × 4.5 = 67.5 in.2 The area of two faces is 7× 4 1/2 = 7× 9/2 = 7× 4.5 = 31.5 in.2 The surface area is 2×105+ 2×67.5+ 2×31.5 = 210+ 135+ 63 = 408 in.2 Question 6. Vivian is working with a styrofoam cube for art class. The length of one side is 5 inches. How much surface area does Vivian have to work with? _______ in.2 Answer: 150 in.2 Explanation: The area of each face is 5×5= 25 in.2 The number of faces that styrofoam cube has is 6 So the surface area is 6×25= 150 in.2 Question 7. Explain why a two-dimensional net is useful for finding the surface area of a three-dimensional figure. Answer: Two-dimensional net is useful because by using a two-dimensional net you can calculate the surface area of each face and add them up to find the surface area of the three-dimensional figure. ### Lesson Check – Page No. 614 Question 1. What is the surface area of a cubic box that contains a baseball that has a diameter of 3 inches? _______ in.2 Answer: 54 in.2 Explanation: The area of each face is 3×3= 9 in.2 The number of faces for a cubic box is 6 in.2 The surface area of box that contains a baseball is 6×9= 54 in.2 Question 2. A piece of wood used for construction is 2 inches by 4 inches by 24 inches. What is the surface area of the wood? _______ in.2 Answer: 304 in.2 Explanation: The area of two faces is 4×2= 8 in.2 The area of two faces is 2×24= 48 in.2 The area of two faces is 24×4= 96 in.2 So the surface area is 2×8+ 2×48+ 2×96 = 16+96+192 = 304 in.2 Spiral Review Question 3. Detergent costs$4 per box. Kendra graphs the equation that gives the cost y of buying x boxes of detergent. What is the equation?

Explanation: The total price Y and the price is equal to 4 × X, and X is the number of boxes that Kendra buys. So the equation is Y=4X.

Question 4.
A trapezoid with bases that measure 8 inches and 11 inches has a height of 3 inches. What is the area of the trapezoid?
_______ in.2

Explanation:
Area of a trapezoid is 1/2(b1+b2)h
= 1/2(8+11)3
= 1/2(19)3
= 1/2 (57)
= 28.5 in.2

Question 5.
City Park is a right triangle with a base of 40 yd and a height of 25 yd. On a map, the park has a base of 40 in. and a height of 25 in. What is the ratio of the area of the triangle on the map to the area of City Park?

Explanation:
Area= 1/2 bh
= 1/2 (40)(25)
= (20)(25)
= 500 yd2
So area of city park is 500 yd2
Area= 1/2 bh
= 1/2 (40)(25)
= (20)(25)
= 500 in2
So area on the map is 500 in
as 1 yd2= 1296 in2
So 500 in2 = 500×1296
= 648,000
So, the ratio of the area of the triangle on the map to the area of City Park is 648,000:500
= 1296:1.

Question 6.
What is the surface area of the prism shown by the net?

Answer: 72 square units.

Explanation:
The area of two faces is 18 squares
The area of two faces is 6 squares
The area of two faces is 12 squares
So the surface area is 2×18+ 2×6+ 2×12
= 72 square units.

### Share and Show – Page No. 617

Question 1.
Use a net to find the surface area of the square pyramid.

_______ cm2

Explanation:

Area of the base 5×5= 25 ,
and area of one face is 1/2 × 5 × 8
= 5× 4
= 20 cm2
The surface area of a pyramid is 25+ 4×20
= 25+80
= 105 cm2

Question 2.
A triangular pyramid has a base with an area of 43 cm2 and lateral faces with bases of 10 cm and heights of 8.6 cm. What is the surface area of the pyramid?
_______ cm2

Explanation:
The area of one face is 1/2×10×8.6
= 5×8.6
= 43 cm2
The surface area of the pyramid is 43+3×43
= 43+ 129
= 172 cm2

Question 3.
A square pyramid has a base with a side length of 3 ft and lateral faces with heights of 2 ft. What is the lateral area of the pyramid?
_______ ft2

Explanation:
The area of one face is 1/2×3×2= 3 ft2
The lateral area of the pyramid is 4×3= 12 ft2

Use a net to find the surface area of the square pyramid.

Question 4.

_______ ft2

Explanation:

The area of the base is 8×8= 64
The area of one face is 1/2 ×8×9
= 36 ft2
The surface area of the pyramid is 64+4×36
= 64+144
= 208 ft2

Question 5.

_______ cm2

Explanation:

The area of base is 10×10= 100
The area of one place is 1/2×10×6
= 10×3
= 30
The surface area of the pyramid is 100+4×30
= 100+120
= 220 cm2

Question 6.

_______ in.2

Explanation:

The area of the base is 8×8= 64
The area of one face is 1/2×8×12.5
= 4×12.5
= 50 in.2
The surface area of the pyramid is 64+ 4×50
= 64+200
= 264 in.2

Question 7.
The Pyramid Arena is located in Memphis, Tennessee. It is in the shape of a square pyramid, and the lateral faces are made almost completely of glass. The base has a side length of about 600 ft and the lateral faces have a height of about 440 ft. What is the total area of the glass in the Pyramid Arena?
_______ ft2

Explanation:
The area of one face is 1/2×600×440= 1,32,000 ft2
The surface of tha lateral faces is 4× 1,32,000= 5,28,000 ft2
So, the total area of the glass in the arena is 5,28,000 ft2

### Problem Solving + Applications – Page No. 618

Use the table for 8–9.

Question 8.
The Great Pyramids are located near Cairo, Egypt. They are all square pyramids, and their dimensions are shown in the table. What is the lateral area of the Pyramid of Cheops?
_______ m2

Explanation:
The area of one face is 1/2×230×180
= 230×90
= 20,700 m2
The lateral area of the pyramid of Cheops is 4×20,700= 82,800 m2

Question 9.
What is the difference between the surface areas of the Pyramid of Khafre and the Pyramid of Menkaure?
_______ m2

Explanation:
The area of the base is 215×215= 46,225
The area of one face is 1/2×215×174
= 215× 87
18,705 m2
The surface area of Pyramid Khafre is= 46,225+4×18,705
= 46,225+ 74820
= 121,045 m2
The area of the base 103×103= 10,609
The area of one face is 1/2×103×83
= 8549÷2
= 4274.4 m2
The surface area of the Pyramid of Menkaure is 10,609+4×4274.5
= 10,609+ 17,098
= 27,707 m2

The difference between the surface areas of the Pyramid of Khafre and the Pyramid of Menkaure
= 121,405-27,707
= 93,338 m2

Question 10.
Write an expression for the surface area of the square pyramid shown.

Explanation: The expression for the surface area of the square pyramid is 6x+9 ft2.

Question 11.
Make Arguments A square pyramid has a base with a side length of 4 cm and triangular faces with a height of 7 cm. Esther calculated the surface area as (4 × 4) + 4(4 × 7) = 128 cm2. Explain Esther’s error and find the correct surface area

Explanation: Esther didn’t apply the formula correctly, she forgot to include 1/2 in the calculated surface area.
The correct surface area is (4×4)+4(1/2 ×4×7)
= 16+4(14)
= 16+56
= 72 cm2.

Question 12.
Jose says the lateral area of the square pyramid is 260 in.2. Do you agree or disagree with Jose? Use numbers and words to support your answer.

Explanation: No, I disagree with Jose as he found surface area instead of the lateral area, so the lateral area is
4×1/2×10×8
= 2×10×8
= 160 in.2

### Surface Area of Pyramids – Page No. 619

Use a net to find the surface area of the square pyramid.

Question 1.

_______ mm2

Explanation:

The area of the base is 5×5= 25 mm2
The area of one face is 1/2×5×7
= 35/2
= 17.5 mm2
The surface area is 25+4×17.5
= 25+4×17.5
= 25+70
= 95 mm2

Question 2.

_______ cm2

Explanation:

The area of the base is 18×18= 324 cm2
The area of one face is 1/2×18×8
= 18×4
=  72 cm2
The surface area is 324+4×72
= 25+4×17.5
= 25+70
= 612 cm2

Question 3.

_______ yd2

Explanation:

The area of the base is 2.5×2.5= 6.25  mm2
The area of one face is 1/2×2.5×9
= 22.5/2
= 11.25 yd2
The surface area is 25+4×17.5
= 6.25+4×11.25
= 6.25+45
= 51.25 yd2

Question 4.

_______ in.2

Explanation:

The area of the base is 10×10= 100 in2
The area of one face is 1/2×4×10
= 2×10
= 20 in2
The surface area is 100+4×20
= 100+4×20
= 100+80
= 180 in2

Problem Solving

Question 5.
Cho is building a sandcastle in the shape of a triangular pyramid. The area of the base is 7 square feet. Each side of the base has a length of 4 feet and the height of each face is 2 feet. What is the surface area of the pyramid?
_______ ft2

Explanation:
The area of one face is 1/2×4×2= 4 ft2
The surface area of the triangular pyramid is 7+3×4
= 7+12
= 19 ft2

Question 6.
The top of a skyscraper is shaped like a square pyramid. Each side of the base has a length of 60 meters and the height of each triangle is 20 meters. What is the lateral area of the pyramid?
_______ m2

Explanation:
The area of the one face is 1/2×60×20
= 600 m2
The lateral area of the pyramid is 4×600= 2400 m2

Question 7.
Write and solve a problem finding the lateral area of an object shaped like a square pyramid.

Answer: Mary has a triangular pyramid with a base of 10cm and a height of 15cm. What is the lateral area of the pyramid?

Explanation:
The area of one face is 1/2×10×15
= 5×15
= 75 cm2
The lateral area of the triangular pyramid is 3×75
= 225 cm2

### Lesson Check – Page No. 620

Question 1.
A square pyramid has a base with a side length of 12 in. Each face has a height of 7 in. What is the surface area of the pyramid?
_______ in.2

Explanation:
The area of the base is 12×12= 144 in.2
The area of one face is 1/2×12×7
= 6×7
= 42 in.2
The surface area of the square pyramid is 144+4×42
= 144+ 168
= 312 in.2

Question 2.
The faces of a triangular pyramid have a base of 5 cm and a height of 11 cm. What is the lateral area of the pyramid?
_______ cm2

Explanation:
The area of one face is 1/2×5×11
= 55/2
= 27.5 cm2
The lateral area of the triangular pyramid is 3×27.5= 82.5 cm2

Spiral Review

Question 3.
What is the linear equation represented by the graph?

Explanation: As the figure represents that every y value is 1 more than the corresponding x value, so the linear equation is y=x+1.

Question 4.
A regular octagon has sides measuring about 4 cm. If the octagon is divided into 8 congruent triangles, each has a height of 5 cm. What is the area of the octagon?
_______ cm2

Explanation:
Area is 1/2bh
= 1/2× 4×5
= 2×5
= 10 cm2
So the area of each triangle is 10 cm2
and the area of the octagon is 8×10= 80 cm2

Question 5.
Carly draws quadrilateral JKLM with vertices J(−3, 3), K(3, 3), L(2, −1), and M(−2, −1). What is the best way to classify the quadrilateral?

Answer: It is a Trapezoid.

Explanation: It is a Trapezoid.

Question 6.
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
_______ ft2

Explanation:
The area of the two faces of the rectangular prism is 8×3= 24 ft2
The area of the two faces of the rectangular prism is 8×5= 40 ft2
The area of the two faces of the rectangular prism is 3×5= 15 ft2
The surface area of the rectangular prism is 2×24+2×40+2×15
= 48+80+30
= 158 ft2

### Mid-Chapter Checkpoint – Vocabulary – Page No. 621

Choose the best term from the box to complete the sentence.

Question 1.
_____ is the sum of the areas of all the faces, or surfaces, of a solid figure.

Answer: Surface area is the sum of the areas of all the faces, or surfaces, of a solid figure.

Question 2.
A three-dimensional figure having length, width, and height is called a(n) _____.

Answer: A three-dimensional figure having length, width, and height is called a(n) solid figure.

Question 3.
The _____ of a solid figure is the sum of the areas of its lateral faces.

Answer: The lateral area of a solid figure is the sum of the areas of its lateral faces.

Concepts and Skills

Question 4.
Identify and draw a net for the solid figure.

Explanation:

Question 5.
Use a net to find the lateral area of the square pyramid.

_______ in.2

Explanation:

The area of one face is 1/2×9×12
= 9×6
= 54 in.2
The lateral area of the square pyramid is 4×54= 216 in.2

Question 6.
Use a net to find the surface area of the prism.

_______ cm2

Explanation:

The area of face A and E is 10×5= 50 cm2
The area of face B and F is 10×7= 70 cm2
The area of face C and D is 7×5= 35 cm2
The surface area of the prism is 2×50+2×70+2×35
= 100+140+70
= 310 cm2

### Page No. 622

Question 7.
A machine cuts nets from flat pieces of cardboard. The nets can be folded into triangular pyramids used as pieces in a board game. What shapes appear in the net? How many of each shape are there?

Explanation: There are 4 triangles.

Question 8.
Fran’s filing cabinet is 6 feet tall, 1 $$\frac{1}{3}$$ feet wide, and 3 feet deep. She plans to paint all sides except the bottom of the cabinet. Find the area of the sides she intends to paint.
_______ ft2

Explanation:
The two lateral face area is 6×1 1/3
= 6× 4/3
= 2×4
= 8 ft2
The area of the other two lateral faces is 6×3= 18
The area of the top and bottom is 3× 1 1/3
= 3× 4/3
= 4 ft2
The area of the sides she intends to paint is 2×8+2×18+4
= 16+36+4
= 56 ft2

Question 9.
A triangular pyramid has lateral faces with bases of 6 meters and heights of 9 meters. The area of the base of the pyramid is 15.6 square meters. What is the surface area of the pyramid?

Explanation:
The area of one face is 1/2× 6× 9
= 3×9
= 27 m2
The surface area of the triangular pyramid is 15.6+3×27
= 15.6+ 81
= 96.6 m2

Question 10.
What is the surface area of a storage box that measures 15 centimeters by 12 centimeters by 10 centimeters?
_______ cm2

Explanation:
The area of two faces is 15×12= 180 cm2
The area of another two faces is 15×10= 150 cm2
The area of the other two faces is 10×12= 120 cm2
So surface area of the storage box is 2×180+2×150+2×120 cm2
= 360+300+240
= 900 cm2

Question 11.
A small refrigerator is a cube with a side length of 16 inches. Use the formula S = 6s2 to find the surface area of the cube.
_______ in.2

Explanation:
Area = s2
= 6×(16)2
= 6× 256
= 1,536 in.2

### Share and Show – Page No. 625

Question 1.
A prism is filled with 38 cubes with a side length of $$\frac{1}{2}$$ unit. What is the volume of the prism in cubic units?
_______ $$\frac{□}{□}$$ cubic units

Answer: 4.75 cubic units

Explanation:
The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 38 cubes so 38×0.125= 4.75 cubic units.

Question 2.
A prism is filled with 58 cubes with a side length of $$\frac{1}{2}$$ unit. What is the volume of the prism in cubic units?
_______ $$\frac{□}{□}$$ cubic units

Answer: 7.25 cubic units.

Explanation:
The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 58 cubes so 58×0.125= 7.25 cubic units.

Find the volume of the rectangular prism.

Question 3.

_______ cubic units

Answer: 33 cubic units.

Explanation:
The volume of the rectangular prism is= Width×Height×Length
= 5 1/2 ×3×2
= 11/2 ×3×2
= 33 cubic units.

Question 4.

_______ $$\frac{□}{□}$$ cubic units

Answer: 91 1/8 cubic units.

Explanation:
The volume of the rectangular prism is= Width×Height×Length
= 4 1/2 ×4 1/2×4 1/2
= 9/2 ×9/2×9/2
= 729/8
= 91 1/8 cubic units.

Question 5.
Theodore wants to put three flowering plants in his window box. The window box is shaped like a rectangular prism that is 30.5 in. long, 6 in. wide, and 6 in. deep. The three plants need a total of 1,200 in.3 of potting soil to grow well. Is the box large enough? Explain.

Answer: No, the box is not large enough as the three plants need a total of 1,200 in.3 and here volume is 1,098 in.3

Explanation:
Volume= Width×Height×Length
= 30.5×6×6
= 1,098 in.3

Question 6.
Explain how use the formula V = l × w × h to verify that a cube with a side length of $$\frac{1}{2}$$ unit has a volume of $$\frac{1}{8}$$ of a cubic unit.

Answer: 1/8 cubic units

Explanation:
As length, width and height is 1/2′ so
Volume = Width×Height×Length
= 1/2 × 1/2 × 1/2
= 1/8 cubic units

### Problem Solving + Applications – Page No. 626

Use the diagram for 7–10.

Question 7.
Karyn is using a set of building blocks shaped like rectangular prisms to make a model. The three types of blocks she has are shown at right. What is the volume of an A block? (Do not include the pegs on top.)
$$\frac{□}{□}$$ cubic units

Answer: 1/2 cubic units

Explanation: Volume = Width×Height×Length
= 1× 1/2 ×1
= 1/2 cubic units

Question 8.
How many A blocks would you need to take up the same amount of space as a C block?
_______ A blocks

Answer: No of blocks required to take up the same amount of space as a C block is 4 A blocks.

Explanation: Volume = Width×Height×Length
= 1×2×1
= 2 cubic unit
No of blocks required to take up the same amount of space as a C block is 1/2 ÷2
= 2×2
= 4 A blocks

Question 9.
Karyn puts a B block, two C blocks, and three A blocks together. What is the total volume of these blocks?
_______ $$\frac{□}{□}$$ cubic units

Answer: 6 1/2 cubic units

Explanation: The volume of A block is
Volume = Width×Height×Length
= 1×1 ×1/2
= 1/2 cubic units.
As Karyn puts three A blocks together, so 3× 1/2= 3/2 cubic units.
The volume of B block is
Volume = Width×Height×Length
= 1×1 × 1
= 1 cubic units.
As Karyn puts only one B, so 1 cubic unit.
The volume of C block is
Volume = Width×Height×Length
= 2×1×1
= 2 cubic units.
As Karyn puts two C blocks together, so 2× 2= 4 cubic units.
So, the total volume of these blocks is 3/2 + 1+ 4
= 3/2+5
= 13/2
= 6 1/2 cubic units

Question 10.
Karyn uses the blocks to make a prism that is 2 units long, 3 units wide, and 1 $$\frac{1}{2}$$ units high. The prism is made of two C blocks, two B blocks, and some A blocks. What is the total volume of A blocks used?
_______ cubic units

Answer: 3 cubic units.

Explanation:
Volume = Width×Height×Length
= 2×3×1 1/2
= 2×3× 3/2
= 9 cubic units.
The total volume of A block used is 9-(2×2)-(2×1)
= 9- 4- 2
= 9-6
= 3 cubic units.

Question 11.
Verify the Reasoning of Others Jo says that you can use V = l × w × h or V = h × w × l to find the volume of a rectangular prism. Does Jo’s statement make sense? Explain.

Explanation: Yes, Jo’s statement makes sense because by the commutative property we can change the order of the variables of length, width, height and both will produce the same result.

Question 12.
A box measures 5 units by 3 units by 2 $$\frac{1}{2}$$ units. For numbers 12a–12b, select True or False for the statement.
12a. The greatest number of cubes with a side length of $$\frac{1}{2}$$ unit that can be packed inside the box is 300.
12b. The volume of the box is 37 $$\frac{1}{2}$$ cubic units.
12a. __________
12b. __________

12a True.
12b True.

Explanation: The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8 cubic units
As there are 300 cubes so 300× 1/8= 75/2
= 37 1/2 cubic units.

### Fractions and Volume – Page No. 627

Find the volume of the rectangular prism.

Question 1.

_______ $$\frac{□}{□}$$ cubic units

Answer: 6 3/4 cubic units

Explanation: Volume = Width×Height×Length
= 3× 1 1/2× 1 1/2
= 3× 3/2 × 3/2
= 27/4
= 6 3/4 cubic units

Question 2.

_______ $$\frac{□}{□}$$ cubic units

Answer: 22 1/2 cubic units

Explanation: Volume = Width×Height×Length
= 5×1× 4 1/2
= 5× 9/2
= 45/2
= 22 1/2 cubic units

Question 3.

_______ $$\frac{□}{□}$$ cubic units

Answer: 16 1/2 cubic units.

Explanation: Volume = Width×Height×Length
= 5 1/2× 1 1/2× 2
= 11/2×3/2×2
= 33/2
= 16 1/2 cubic units.

Question 4.

_______ $$\frac{□}{□}$$ cubic units

Answer: 28 1/8 cubic units.

Explanation: Volume = Width×Height×Length
= 2 1/2× 2 1/2 × 4 1/2
= 5/2 × 5/2 × 9/2
= 225/8
= 28 1/8 cubic units.

Problem Solving

Question 5.
Miguel is pouring liquid into a container that is 4 $$\frac{1}{2}$$ inches long by 3 $$\frac{1}{2}$$ inches wide by 2 inches high. How many cubic inches of liquid will fit in the container?
_______ $$\frac{□}{□}$$ in.3

Answer: 31 1/2 cubic units

Explanation: Volume = Width×Height×Length
= 4 1/2 × 3 1/2 ×2
= 9/2 × 7/2 × 2
= 63/2
= 31 1/2 cubic units

Question 6.
A shipping crate is shaped like a rectangular prism. It is 5 $$\frac{1}{2}$$ feet long by 3 feet wide by 3 feet high. What is the volume of the crate?
_______ $$\frac{□}{□}$$ ft3

Answer: 49 1/2 ft3

Explanation: Volume = Width×Height×Length
= 5 1/2 × 3 × 3
= 11/2 ×9
= 99/2
= 49 1/2 ft3

Question 7.
How many cubes with a side length of $$\frac{1}{4}$$ unit would it take to make a unit cube? Explain how you determined your answer.

Answer: There will be 4×4×4= 64 cubes and 1/4 unit in the unit cube.

Explanation:
As the unit cube has a 1 unit length, 1 unit wide, and 1 unit height
So length 4 cubes = 4× 1/4= 1 unit
width 4 cubes = 4× 1/4= 1 unit
height 4 cubes = 4× 1/4= 1 unit
So there will be 4×4×4= 64 cubes and 1/4 unit in the unit cube.

### Lesson Check – Page No. 628

Question 1.
A rectangular prism is 4 units by 2 $$\frac{1}{2}$$ units by 1 $$\frac{1}{2}$$ units. How many cubes with a side length of $$\frac{1}{2}$$ unit will completely fill the prism?

Explanation:
No of cubes with a side length of 1/2 unit is
Length 8 cubes= 8× 1/2= 4 units
Width 5 cubes= 5× 1/2= 5/2= 2 1/2 units
Height 3 cubes= 3× 1/2= 3/2= 1 1/2 units
So there are 8×5×3= 120 cubes in the prism.

Question 2.
A rectangular prism is filled with 196 cubes with $$\frac{1}{2}$$-unit side lengths. What is the volume of the prism in cubic units?
_______ $$\frac{□}{□}$$ cubic units

Answer: 24 1/2 cubic units.

Explanation: As it takes 8 cubes with a side length of 1/2 to form a unit cube, so the volume of the prism in the cubic units is 196÷8= 24 1/2 cubic units.

Spiral Review

Question 3.
A parallelogram-shaped piece of stained glass has a base measuring 2 $$\frac{1}{2}$$ inches and a height of 1 $$\frac{1}{4}$$ inches. What is the area of the piece of stained glass?
_______ $$\frac{□}{□}$$ in.2

Answer: 3 1/8 in.2

Explanation: Area of a parallelogram = base×height
= 2 1/2 × 1 1/4
= 5/2 × 5/4
= 25/8
= 3 1/8 in.2

Question 4.
A flag for the sports club is a rectangle measuring 20 inches by 32 inches. Within the rectangle is a yellow square with a side length of 6 inches. What is the area of the flag that is not part of the yellow square?
_______ in.2

Explanation: Area of a flag= Length×width
= 20×32
= 640 in.2
Area of the yellow square= S2
= 6
= 36 in.2
So the area of the flag that is not a part of the yellow square is 640-36= 604 in.2

Question 5.
What is the surface area of the rectangular prism shown by the net?

_______ square units

Answer: 80 square units

Explanation:
Area of two faces is 12 squares
Area of other two faces is 16 squares
Area of another two faces is 12 squares
So the surface area is 2×12+2×16+2×12
= 24+32+24
= 80 square units

Question 6.
What is the surface area of the square pyramid?

_______ cm2

Explanation: The area of the base is 7×7= 49 cm2
And the area of one face is 1/2 × 7× 8
= 7×4
= 28 cm2
The surface area of the square pyramid is 49+4×28
= 49+112
= 161 cm2

### Share and Show – Page No. 631

Find the volume.

Question 1.

_______ $$\frac{□}{□}$$ in.3

Answer: 3,937 1/2 in.3

Explanation: Volume= Length× wide× heght
= 10 1/2 ×15 × 25
= 11/2 × 15 × 25
= 4,125/2
= 3,937 1/2 in.3

Question 2.

_______ $$\frac{□}{□}$$ in.3

Explanation: Volume= Length× wide× height
=3/8 ×3/8 × 3/8
= 27/512 in.3

Find the volume of the prism.

Question 3.

_______ $$\frac{□}{□}$$ in.3

Explanation: Volume= Length× wide× height
= 8 1/2 × 6 1/2 × 12 1/2
= 17/2 × 13/2× 25/2
= 5525/2
= 690 5/8in.3

Question 4.

_______ $$\frac{□}{□}$$ in.3

Explanation: Volume= Length× wide× height
= 5/16 ×5/16 × 5/16
= 125/4096 in.3

Question 5.

_______ yd3

Explanation:
Area= 3 1/3 yd2
So Area= wide×height
3 1/3= w × 1 1/3
10/3= w× 4/3
w= 10/3 × 3/4
w= 5/2
w= 2.5 yd
Volume= Length×width×height
= 6× 2.5× 1 1/3
= 6×2.5× 4/3
= 2×2.5×4
= 20 yd3

Question 6.
Wayne’s gym locker is a rectangular prism with a width and height of 14 $$\frac{1}{2}$$ inches. The length is 8 inches greater than the width. What is the volume of the locker?
_______ $$\frac{□}{□}$$ in.3

Answer: 4,730 5/8 in.3

Explanation: As length is 8 inches greater than width, so 14 1/2+ 8
= 29/2+8
= 45/2
= 22 1/2 in
Then volume= Length×width×height
= 22 1/2 × 14 1/2 × 14 1/2
= 45/2× 29/2× 29/2
= 37845/8
= 4,730 5/8 in.3

Question 7.
Abraham has a toy box that is in the shape of a rectangular prism.

The volume is _____.
_______ $$\frac{□}{□}$$ ft3

Answer: 33 3/4 ft3

Explanation: Volume of rectangular prism is= Length×width×height
= 4 1/2× 2 1/2× 3
= 9/2 × 5/2× 3
= 135/3
= 33 3/4 ft3

### Aquariums – Page No. 632

Large public aquariums like the Tennessee Aquarium in Chattanooga have a wide variety of freshwater and saltwater fish species from around the world. The fish are kept in tanks of various sizes.
The table shows information about several tanks in the aquarium. Each tank is a rectangular prism.

Find the length of Tank 1.
V = l w h
52,500 = l × 30 × 35
$$\frac{52,500}{1,050}$$ = l
50 = l
So, the length of Tank 1 is 50 cm.

Solve.

Question 8.
Find the width of Tank 2 and the height of Tank 3.

Answer: Width of Tank 2= 8m, Height of the Tank 3= 10 m

Explanation:
The volume of Tank 2= 384 m3
so V= LWH
384=  12×W×4
W= 384/48
W= 8 m
So the width of Tank 2= 8m
The volume of Tank 3= 2160 m
So V= LWH
2160= 18×12×H
H= 2160/216
H= 10 m
So the height of the Tank 3= 10 m

Question 9.
To keep the fish healthy, there should be the correct ratio of water to fish in the tank. One recommended ratio is 9 L of water for every 2 fish. Find the volume of Tank 4. Then use the equivalencies 1 cm3 = 1 mL and 1,000 mL = 1 L to find how many fish can be safely kept in Tank 4.

Explanation:
Volume of Tank 4 = LWH
= 72×55×40
= 1,58,400 cm3
As 1 cm3 = 1 mL and 1,000 mL = 1 L
1,58,400 cm3 = 1,58,400 mL and 1,58,400 mL = 158.4 L
So tank can keep safely (158.4÷ 9)×2
= (17.6)× 2 = 35.2
= 35 Fishes

Question 10.
Use Reasoning Give another set of dimensions for a tank that would have the same volume as Tank 2. Explain how you found your answer.

Answer: Another set of dimensions for a tank that would have the same volume as Tank 2 is 8m by 8m by 6m.
So when we multiply the product will be 384

### Volume of Rectangular Prisms – Page No. 633

Find the volume.

Question 1.

_______ $$\frac{□}{□}$$ m3

Answer: 150 5/16 m3

Explanation: Volume= Length×width×height
= 5× 3 1/4× 9 1/4
= 5× 13/4 × 37/4
= 2405/16
= 150 5/16 m3

Question 2.

_______ $$\frac{□}{□}$$ in.3

Answer: 27 1/2 in.3

Explanation: Volume= Length×width×height
= 5 1/2 × 2 1/2 × 2
= 11/2 × 5/2 × 2
= 55/2
= 27 1/2 in.3

Question 3.

_______ $$\frac{□}{□}$$ mm3

Answer: 91 1/8 mm3

Explanation: Volume= Length×width×height
= 4 1/2 × 4 1/2 × 4 1/2
= 9/2 × 9/2 × 9/2
= 729/8
= 91 1/8 mm3

Question 4.

_______ $$\frac{□}{□}$$ ft3

Answer: 112 1/2 ft3

Explanation: Volume= Length×width×height
= 7 1/2 × 2 1/2 × 6
= 15/2 × 5/2 × 6
= 225/2
= 112 1/2 ft3

Question 5.

_______ m3

Explanation:
The area of shaded face is Length × width= 8 m2
Volume of the prism= Length×width×height
= 8 × 4 1/2
= 8 × 9/2
= 4 × 9
= 36 m3

Question 6.

_______ $$\frac{□}{□}$$ ft3

Answer: 30 3/8 ft3

Explanation: Volume of the prism= Length×width×height
= 2 1/4 × 6 × 2 1/4
= 9/4 × 6 × 9/4
= 243/8
= 30 3/8 ft3

Problem Solving

Question 7.
A cereal box is a rectangular prism that is 8 inches long and 2 $$\frac{1}{2}$$ inches wide. The volume of the box is 200 in.3. What is the height of the box?
_______ in.

Answer: H= 10 in

Explanation: As volume = 200 in.3. So
V= LWH
200= 8 × 2 1/2 × H
200= 8 × 5/2 × H
200= 20 × H
H= 10 in

Question 8.
A stack of paper is 8 $$\frac{1}{2}$$ in. long by 11 in. wide by 4 in. high. What is the volume of the stack of paper?
_______ in.3

Explanation: The volume of the stack of paper= LWH
= 8 1/2 × 11 × 4
= 17/2 × 11 × 4
= 374 in.3

Question 9.
Explain how you can find the side length of a rectangular prism if you are given the volume and the two other measurements. Does this process change if one of the measurements includes a fraction?

Answer: We can find the side length of a rectangular prism if you are given the volume and the two other measurements by dividing the value of the volume by the product of the values of width and height of the prism. And the process doesn’t change if one of the measurements include a fraction.

### Lesson Check – Page No. 634

Question 1.
A kitchen sink is a rectangular prism with a length of 19 $$\frac{7}{8}$$ inches, a width of 14 $$\frac{3}{4}$$ inches, and height of 10 inches. Estimate the volume of the sink.

Explanation: Length = 19 7/8 as the number was close to 20 and width 14 3/4 which is close to 15 and height is 10
So Volume= LBH
= 20 × 15 × 10
= 3,000 in.3

Question 2.
A storage container is a rectangular prism that is 65 centimeters long and 40 centimeters wide. The volume of the container is 62,400 cubic centimeters. What is the height of the container?

Answer: H= 24 cm

Explanation: Volume of container= LBH
Volume= 62,400 cubic centimeters
62,400 = 65× 40 × H
62,400 = 2600 × H
H= 62,400/ 2600
H= 24 cm

Spiral Review

Question 3.
Carrie started at the southeast corner of Franklin Park, walked north 240 yards, turned and walked west 80 yards, and then turned and walked diagonally back to where she started. What is the area of the triangle enclosed by the path she walked?
_______ yd2

Explanation:
Area of triangle= 1/2 bh
= 1/2 × 240 × 80
= 240 × 40
= 9,600 yd2

Question 4.
The dimensions of a rectangular garage are 100 times the dimensions of a floor plan of the garage. The area of the floor plan is 8 square inches. What is the area of the garage?

Explanation: As 1 in2= 10,000 in2, so area of the floor plan 8 in
= 8×10000
= 80,000 in2

Question 5.
Shiloh wants to create a paper-mâché box shaped like a rectangular prism. If the box will be 4 inches by 5 inches by 8 inches, how much paper does she need to cover the box?

Explanation: Area of the rectangular prism= 2(wl+hl+hw)
= 2(4×5 + 5×8 + 8×4)
= 2(20+40+32)
= 2(92)
= 184 in2

Question 6.
A box is filled with 220 cubes with a side length of $$\frac{1}{2}$$ unit. What is the volume of the box in cubic units?
_______ $$\frac{□}{□}$$ cubic units

Answer: 27.5 cubic units.

Explanation: The volume of a cube side is (1/2)3 = 1/8
So 220 cubes= 220× 1/8
= 27.5 cubic units.

### Share and Show – Page No. 637

Question 1.
An aquarium tank in the shape of a rectangular prism is 60 cm long, 30 cm wide, and 24 cm high. The top of the tank is open, and the glass used to make the tank is 1 cm thick. How much water can the tank hold?
_______ cm3

Answer: So tank can hold 37,352 cm3

Explanation: As Volume= LBH
Let’s find the inner dimensions of the tank, so 60-2 × 30-2 × 24-1
= 58×28×23
= 37,352 cm3

Question 2.
What if, to provide greater strength, the glass bottom were increased to a thickness of 4 cm? How much less water would the tank hold?
_______ cm3

Explanation: As the glass bottom was increased to a thickness of 4 cm, 60-2 × 30-2 × 24-4
= 58×28×20
= 32,480 cm3
So the tank can hold 37,352- 32,480= 4,872 cm3

Question 3.
An aquarium tank in the shape of a rectangular prism is 40 cm long, 26 cm wide, and 24 cm high. If the top of the tank is open, how much tinting is needed to cover the glass on the tank? Identify the measure you used to solve the problem.
_______ cm3

Answer: 4,208 cm3  tinting needed to cover the glass on the tank.

Explanation:
The lateral area of the two faces is 26×24= 624 cm2
The lateral area of the other two faces is 40×24= 960 cm2
And the area of the top and bottom is 40×26= 1040 cm2
So the surface area of the tank without the top is 2×624 + 2×960 + 1040
= 1,248+1,920+1,040
= 4,208 cm3

Question 4.
The Louvre Museum in Paris, France, has a square pyramid made of glass in its central courtyard. The four triangular faces of the pyramid have bases of 35 meters and heights of 27.8 meters. What is the area of glass used for the four triangular faces of the pyramid?

Explanation: The area of one face is 1/2 × 35 × 27.8= 486.5 m2
And the area of glass used for the four triangular faces of the pyramid is 4×486.5= 1946 m2

### On Your Own – Page No. 638

Question 5.
A rectangular prism-shaped block of wood measures 3 m by 1 $$\frac{1}{2}$$ m by 1 $$\frac{1}{2}$$ m. How much of the block must a carpenter carve away to obtain a prism that measures 2 m by $$\frac{1}{2}$$ m by $$\frac{1}{2}$$ m?
_______ $$\frac{□}{□}$$ m3

Answer: 6 1/4 m3

Explanation: The volume of the original block= LWH
= 3 × 1 1/2 × 1 1/2
= 3× 3/2 × 3/2
= 27/4
= 6 3/4 m2
And volume of carpenter carve is 2× 1/2 × 1/2
= 1/2 m2
So, the carpenter must carve 27/4 – 1/2
= 25/2
= 6 1/4 m3

Question 6.
The carpenter (Problem 5) varnished the outside of the smaller piece of wood, all except for the bottom, which measures $$\frac{1}{2}$$ m by $$\frac{1}{2}$$ m. Varnish costs $2.00 per square meter. What was the cost of varnishing the wood?$ _______

Answer: $8.50 Explanation: The area of two lateral faces are 2×1/2= 1 m2 The area of the other two lateral faces are 2×1/2= 1 m2 The area of the top and bottom is 1/2×1/2= 1/4 m2 And the surface area is 2×1 + 2×1 + 1/4 = 2+2+1/4 = 17/4 = 4.25 m2 And the cost of vanishing the wood is$2.00× 4.25= $8.50 Question 7. A wax candle is in the shape of a cube with a side length of 2 $$\frac{1}{2}$$ in. What volume of wax is needed to make the candle? _______ $$\frac{□}{□}$$ in.3 Answer: Explanation: The Volume of wax is needed to make the candle is= LWH = 2 1/2 × 2 1/2 × 2 1/2 = 5/2 × 5/2 × 5/2 = 125/8 = 15 5/8 in.3 Question 8. Describe A rectangular prism-shaped box measures 6 cm by 5 cm by 4 cm. A cube-shaped box has a side length of 2 cm. How many of the cube-shaped boxes will fit into the rectangular prismshaped box? Describe how you found your answer. Answer: 12 cube-shaped boxes Explanation: As 6 small boxes can fit on the base i.e 6 cm by 5 cm, as height is 4cm there can be a second layer of 6 small boxes. So, there will be a total of 12 cube-shaped boxes and will fit into a rectangular prism-shaped box Question 9. Justin is covering the outside of an open shoe box with colorful paper for a class project. The shoe box is 30 cm long, 20 cm wide, and 13 cm high. How many square centimeters of paper are needed to cover the outside of the open shoe box? Explain your strategy _______ cm2 Answer: 1,900 cm2 Explanation: The area of the two lateral faces of the shoebox is 20×13= 260 cm2 The area of another two lateral faces of the shoebox is 30×13= 390 cm2 The area of the top and bottom is 30×20= 600 cm2 So, the surface area of the shoebox without the top is 2×260 + 2× 390 + 600 = 520+780+600 = 1,900 cm2 ### Problem Solving Geometric Measurements – Page No. 639 Read each problem and solve. Question 1. The outside of an aquarium tank is 50 cm long, 50 cm wide, and 30 cm high. It is open at the top. The glass used to make the tank is 1 cm thick. How much water can the tank hold? _______ cm3 Answer: So water tank can hold 66,816 cm3 Explanation: The volume of inner dimensions of the aquarium is 50-2 × 50-2 × 30-1 = 48×48×29 = 66,816 cm3 So water tank can hold 66,816 cm3 Question 2. Arnie keeps his pet snake in an open-topped glass cage. The outside of the cage is 73 cm long, 60 cm wide, and 38 cm high. The glass used to make the cage is 0.5 cm thick. What is the inside volume of the cage? _______ cm3 Answer: The volume of the cage is 1,59,300 cm3 Explanation: The volume of inner dimensions is 73-1 × 60-1 × 38-0.5 = 72×59×37.5 = 1,59,300 cm3 So, the volume of the cage is 1,59,300 cm3 Question 3. A display number cube measures 20 in. on a side. The sides are numbered 1–6. The odd-numbered sides are covered in blue fabric and the even-numbered sides are covered in red fabric. How much red fabric was used? _______ in.2 Answer: 1200 in.2 Explanation: The area of each side of a cube is 20×20= 400 in.2, as there are 3 even-numbered sides on the cube. So there will be 3×400= 1200 in.2 Question 4. The caps on the tops of staircase posts are shaped like square pyramids. The side length of the base of each cap is 4 inches. The height of the face of each cap is 5 inches. What is the surface area of the caps for two posts? _______ in.2 Answer: 112 in.2 Explanation: The area of the base is 4×4= 16 in.2 The area of one face is 1/2×5×4= 10 in.2 The surface area of one cap is 16+4×10 = 16+40 = 56 in.2 And the surface area of the caps for two posts is 2×56= 112 in.2 Question 5. A water irrigation tank is shaped like a cube and has a side length of 2 $$\frac{1}{2}$$ feet. How many cubic feet of water are needed to completely fill the tank? _______ $$\frac{□}{□}$$ ft3 Answer: 15 5/8 ft3 Explanation: Volume= LWH = 2 1/2 × 2 1/2 × 2 1/2 = 5/2 × 5/2 × 5/2 = 125/8 = 15 5/8 ft3 Question 6. Write and solve a problem for which you use part of the formula for the surface area of a triangular prism. Answer: In a triangular prism, the triangular end has a base of 5cm and the height is 8 cm. The length of each side is 4 cm and the height of the prism is 10 cm. What is the lateral area of this triangular prism? Explanation: The area of two triangular faces is 1/2 × 5 × 8 = 5×4 = 20 cm2 The area of two rectangular faces is 4×10= 40 cm2 The lateral area is 2×20+2×40 = 40+80 = 120 cm2 ### Lesson Check – Page No. 640 Question 1. Maria wants to know how much wax she will need to fill a candle mold shaped like a rectangular prism. What measure should she find? Answer: Maria needs to find the volume of the mold. Question 2. The outside of a closed glass display case measures 22 inches by 15 inches by $$\frac{1}{2}$$ inches. The glass is 12 inch thick. How much air is contained in the case? _______ in.3 Answer: 3381 in.3 Explanation: The inner dimensions are 22-1× 15-1 × 12- 1/2 = 21 ×14×23/2 = 3381 in.3 Spiral Review Question 3. A trapezoid with bases that measure 5 centimeters and 7 centimeters has a height of 4.5 centimeters. What is the area of the trapezoid? _______ cm2 Answer: 27 cm2 Explanation: Area of trapezoid= 1/2 ×(7+5)×4.5 = 6×4.5 = 27 cm2 Question 4. Sierra has plotted two vertices of a rectangle at (3, 2) and (8, 2). What is the length of the side of the rectangle? _______ units Answer: 5 units. Explanation: The length of the side of the rectangle is 8-3= 5 units. Question 5. What is the surface area of the square pyramid? _______ m2 Answer: 104 m2 Explanation: The area of the base 4×4= 16 The area of the one face is 1/2 × 4 × 11 = 2×11 = 22 m2 The surface area of the square pyramid is 16+4×22 = 16+88 = 104 m2 Question 6. A shipping company has a rule that all packages must be rectangular prisms with a volume of no more than 9 cubic feet. What is the maximum measure for the height of a box that has a width of 1.5 feet and a length of 3 feet? _______ feet Answer: 2 feet. Explanation: As given volume = 9 cubic feet So 1.5×3×H < 9 4.5×H < 9 H< 9/4.5 and H<2 So maximum measure for the height of the box is 2 feet. ### Chapter 11 Review/Test – Page No. 641 Question 1. Elaine makes a rectangular pyramid from paper. The base is a _____. The lateral faces are _____. The base is a ___________ . The lateral faces are ___________ . Answer: The base is a rectangle. The lateral faces are triangles. Question 2. Darrell paints all sides except the bottom of the box shown below. Select the expressions that show how to find the surface area that Darrell painted. Mark all that apply. Options: a. 240 + 240 + 180 + 180 + 300 + 300 b. 2(20 × 12) + 2(15 × 12) + (20 × 15) c. (20 × 12) + (20 × 12) + (15 × 12) + (15 × 12) + (20 × 15) d. 20 × 15 × 12 Answer: b,c Explanation: The expressions that show how to find the surface area is 2(20 × 12) + 2(15 × 12) + (20 × 15), (20 × 12) + (20 × 12) + (15 × 12) + (15 × 12) + (20 × 15) Question 3. A prism is filled with 44 cubes with $$\frac{1}{2}$$-unit side lengths. What is the volume of the prism in cubic units? _______ $$\frac{□}{□}$$ cubic unit Answer: Explanation: The volume of a cube with S= (1/2)3 = 1/2×1/2×1/2 = 1/8 = 0.125 cubic units As there are 44 cubes so 44×0.125=5.5 cubic units. Question 4. A triangular pyramid has a base with an area of 11.3 square meters, and lateral faces with bases of 5.1 meters and heights of 9 meters. Write an expression that can be used to find the surface area of the triangular pyramid. Answer: 11.3+ 3 × 1/2+ 5.1×9 Explanation: The expression that can be used to find the surface area of the triangular pyramid is 11.3+ 3 × 1/2+ 5.1×9 ### Page No. 642 Question 5. Jeremy makes a paperweight for his mother in the shape of a square pyramid. The base of the pyramid has a side length of 4 centimeters, and the lateral faces have heights of 5 centimeters. After he finishes, he realizes that the paperweight is too small and decides to make another one. To make the second pyramid, he doubles the length of the base in the first pyramid. For numbers 5a–5c, choose Yes or No to indicate whether the statement is correct. 5a. The surface area of the second pyramid is 144 cm2. 5b. The surface area doubled from the first pyramid to the second pyramid. 5c. The lateral area doubled from the first pyramid to the second pyramid. 5a. ___________ 5b. ___________ 5c. ___________ Answer: 5a. True. 5b. False 5c. True. Explanation: The area of the base is 4×4= 16 cm2. The area of one face is 1/2×4×5 = 2×5 = 10 cm2. The surface area of the First pyramid is 16+ 4×10 = 16+40 = 56 cm2. The area of the base is 8×8= 64 The area of one face is 1/2×8×5 = 4×5 = 20 cm2. The surface area od the second pyramid is 64+ 4×20 = 64+80 = 144 cm2. Question 6. Identify the figure shown and find its surface area. Explain how you found your answer. Answer: 369 in2 Explanation: The area of the base is 9×9= 81 in2 The area of one face is 1//2 × 16× 9 = 8×9 = 72 in2 The surface area of a square pyramid is 81+ 4× 72 = 81+ 288 = 369 in2 Question 7. Dominique has a box of sewing buttons that is in the shape of a rectangular prism. The volume of the box is 2 $$\frac{1}{2}$$ in. × 3 $$\frac{1}{2}$$ in. × _____ = _____. Answer: 17.5 in3 Explanation: The volume of the box is 2 1/2 × 3 1/2 × 2 = 5/2 × 7/2 × 2 = 5/2 × 7 = 35/2 = 17.5 in3 ### Page No. 643 Question 8. Emily has a decorative box that is shaped like a cube with a height of 5 inches. What is the surface area of the box? _______ in.2 Answer: 150 in.2 Explanation: Surface area of the box is 6 a2 So 6 × 52 = 6×5×52 = 150 in.2 Question 9. Albert recently purchased a fish tank for his home. Match each question with the geometric measure that would be most appropriate for each scenario. Answer: Question 10. Select the expressions that show the volume of the rectangular prism. Mark all that apply. Options: a. 2(2 units × 2 $$\frac{1}{2 }$$ units) + 2(2 units × $$\frac{1}{2}$$ unit) + 2($$\frac{1}{2}$$ unit × 2 $$\frac{1}{2}$$ units) b. 2(2 units × $$\frac{1}{2}$$ unit) + 4(2 units × 2 $$\frac{1}{2}$$ units) c. 2 units × $$\frac{1}{2}$$ unit × 2 $$\frac{1}{2}$$ units d. 2.5 cubic units Answer: c, d Explanation: 2 units ×1/2 unit × 2 1/2 units and 2.5 cubic units ### Page No. 644 Question 11. For numbers 11a–11d, select True or False for the statement. 11a. The area of face A is 8 square units. 11b. The area of face B is 10 square units. 11c. The area of face C is 8 square units. 11d. The surface area of the prism is 56 square units. 11a. ___________ 11b. ___________ 11c. ___________ 11d. ___________ Answer: 11a. True. 11b. True. 11c. False. 11d. False. Explanation: The area of the face A is 4×2= 8 square units The area of the face B is 5×2= 10 square units The area of the face C is 5×4= 20 square units So the surface area is 2×8+2×10+2×20 = 16+20+40 = 76 square units Question 12. Stella received a package in the shape of a rectangular prism. The box has a length of 2 $$\frac{1}{2}$$ feet, a width of 1 $$\frac{1}{2}$$ feet, and a height of 4 feet. Part A Stella wants to cover the box with wrapping paper. How much paper will she need? Explain how you found your answer Answer: 39.5 ft2 Explanation: The area of two lateral faces is 4 × 2 1/2 = 4 × 5/2 = 2×5 = 10 ft2 The area of another two lateral faces is 4 × 1 1/2 = 4 × 3/2 = 2×3 = 6 ft2 The area of the top and bottom is 2 1/2 × 1 1/2 = 5/2 × 3/2 = 15/4 = 3 3/4 ft2 So Stella need 2×10+ 2×6 + 2 × 15/4 = 20+ 12+15/2 = 20+12+7.5 = 39.5 ft2 Question 12. Part B Can the box hold 16 cubic feet of packing peanuts? Explain how you know Answer: The box cannot hold 16 cubic feet of the packing peanuts Explanation: Volume = LWH = 2 1/2 ×1 1/2 × 4 = 5/2 × 3/2 ×4 = 5×3 = 15 ft3 So the box cannot hold 16 cubic feet of the packing peanuts. ### Page No. 645 Question 13. A box measures 6 units by $$\frac{1}{2}$$ unit by 2 $$\frac{1}{2}$$ units. For numbers 13a–13b, select True or False for the statement. 13a. The greatest number of cubes with a side length of $$\frac{1}{2}$$ unit that can be packed inside the box is 60. 13b. The volume of the box is 7 $$\frac{1}{2}$$ cubic units. 13a. ___________ 13b. ___________ Answer: 13a. True 13b. True. Explanation: Length is 12 × 1/2= 6 units Width is 1× 1/2= 1/2 units Height is 5× 1/2= 5/2 units So, the greatest number of cubes with a side length of 1/2 unit that can be packed inside the box is 12×1×5= 60 The volume of the cube is S3 The volume of a cube with S= (1/2)3 = 1/2×1/2×1/2 = 1/8 = 0.125 cubic units As there are 60 cubes so 60×0.125= 7.5cubic units. Question 14. Bella says the lateral area of the square pyramid is 1,224 in.2. Do you agree or disagree with Bella? Use numbers and words to support your answer. If you disagree with Bella, find the correct answer. Answer: 900 in2 Explanation: Area= 4× 1/2 bh = 4× 1/2 × 18 × 25 = 2× 18 × 25 = 900 in2 So lateral area is 900 in2, so I disagree Question 15. Lourdes is decorating a toy box for her sister. She will use self-adhesive paper to cover all of the exterior sides except for the bottom of the box. The toy box is 4 feet long, 3 feet wide, and 2 feet high. How many square feet of adhesive paper will Lourdes use to cover the box? _______ ft2 Answer: 40 ft2 Explanation: The area of two lateral faces is 4×2= 8 ft2 The area of another two lateral faces is 3×2= 6 ft2 The area of the top and bottom is 4×3= 12 ft2 So Lourdes uses to cover the box is 2×8 + 2×6 + 12 = 16+12+12 = 40 ft2 Question 16. Gary wants to build a shed shaped like a rectangular prism in his backyard. He goes to the store and looks at several different options. The table shows the dimensions and volumes of four different sheds. Use the formula V = l × w × h to complete the table. 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Get the solutions with step by step explanation from our Go Math Answer Key for Grade 7 Chapter 11 Analyzing and Comparing Data. So, before you start your preparation go through the topics given below. Chapter 11 – Lesson: 1 Chapter 11 – Lesson: 2 Chapter 11 – Lesson: 3 Chapter 11 – Comparing Data Displayed in Dot Plots ### Guided Practice – Page No. 338 The dot plots show the number of miles run per week for two different classes. For 1–5, use the dot plots shown. Question 1. Compare the shapes of the dot plots. Answer: In Class A the dot plot is clustered around two areas and in Class B the dot plot is clustered in the middle. Question 2. Compare the centers of the dot plots. Answer: In Class A the data is centered around 4 miles and 13 miles and in Class B the data is centered around 7 miles. Question 3. Compare the spreads of the dot plots. Answer: In class A the spread of the dot plot is 4 miles to 14 miles and in Class B the spread is 3 miles to 9 miles. Question 4. Calculate the medians of the dot plots. Answer: The median or the dot plots for Class A and Class B is 6. Explanation: For Class A median is 4,4,4,4,4,5,5,5,6,6,12,13,13,13,13,14,14 = 6. For Class B median is 3,4,4,4,5,5,5,5,6,6,7,7,7,7,7,8,8,9 = (6+6)/2 = 12/2 = 6. Question 5. Calculate the ranges of the dot plots. Answer: The range of the dot plot For Class A is 10 and Class B is 6. Explanation: For Class A the range is 14-4= 10. For Class B the range is 9-3= 6. Essential Question Check-In Question 6. What do the medians and ranges of two dot plots tell you about the data? Answer: The median of dot plots tells that the values of each dot plot are centered and we can get to know which dot plot has greater values. The range of the dot plot tells about the spread of each value in each plot. The smaller the range, the closer will be the values. ### Independent Practice – Page No. 339 The dot plot shows the number of letters in the spellings of the 12 months. Use the dot plot for 7–10. Question 7. Describe the shape of the dot plot. Answer: There is a slight increase in the number 8. Question 8. Describe the center of the dot plot. Answer: The center of the dot plot is 6. Question 9. Describe the spread of the dot plot. Answer: The spread of the dot plot is from 3 to 9 Question 10. Calculate the mean, median, and range of the data in the dot plot. Answer: The mean of the dot plot is 6.17. The median of the dot plot is 6.5. The range of the dot plot is 6. Explanation: 3,4,4,5,5,6,7,7,8,8,8,9 The mean of the dot plot is $$\frac{3+4+4+5+5+6+7+7+8+8+8+9}{12} = \frac{74}{12}$$ = 6.17. The medain of the dot plot is $$\frac{6+7}{2} = \frac{13}{2}$$ = 6.5. The range of the dot plot is 9-3= 6. The dot plots show the mean number of days with rain per month for two cities. Question 11. Compare the shapes of the dot plots. Answer: The most number of days with rain for Montgomery is greater than 8 days and in Lynchburg, the number of days of rain is 12 days or less. Question 12. Compare the centers of the dot plots. Answer: In Montgomery, the center of the dot plot is around 9 days. And in Lynchburg, the center of the dot plot is around 10 days. Question 13. Compare the spreads of the dot plots. Answer: In Montgomery, the spread of the dot plot is from 1 to 12 days and the outlier is 1. And in Lynchburg, the spread of the data plot is from 8 to 12 days. Question 14. What do the dot plots tell you about the two cities with respect to their average monthly rainfall? Answer: As the center of Lynchburg is greater than the center of Montgomery, so average monthly rainfall for Lynchburg is greater than the average monthly rainfall of Montgomery. ### Page No. 340 The dot plots show the shoe sizes of two different groups of people. Question 15. Compare the shapes of the dot plots. Answer: In Group A the shoe sizes are mostly less than 9. And in group B all the shoe sizes are 11.5 or less. Question 16. Compare the medians of the dot plots. Answer: The median of Group A is 8. The median of Group A is 9.5. Explanation: 6.5,7,7,7.5,7.5,7.5,8,8,8,8,8,8.5,8.5,9,13 The median of Group A is 8. 8.5,9,9,9,9,9.5,9.5,9.5,9.5,10,10,10.5,10.5,10.5,11.5 The median of Group B is 9.5. Question 17. Compare the ranges of the dot plots (with and without the outliers). Answer: The range with the outlier is 13-6.5= 6.5. The range without the outlier is 9-6.5= 2.5. The range is 11.5-8.5= 3. Explanation: The outlier in Group A is 13 The range with the outlier is 13-6.5= 6.5. The range without the outlier is 9-6.5= 2.5. There is no outlier in Group B, so the range is 11.5-8.5= 3. Question 18. Make A Conjecture Provide a possible explanation for the results of the dot plots. Answer: Group A is Girls and Group B is boys. Because boys have large feet than girls. H.O.T. Focus on Higher Order Thinking Question 19. Analyze Relationships Can two dot plots have the same median and range but have completely different shapes? Justify your answer using examples. Answer: Yes, it is possible to have the same median and range with different shapes. Explanation: Yes, it is possible to have the same median and range with different shapes. The median and the range of the below image is image 1 data – 1,2,2,3,3,3,4,4,5. The median of image 1 is 3. image 2 data is – 2,2,2,2,3,3,4,4,5,5,6. The median of image 2 is 3. The range of image 1 is 5-1= 4. The range of image 2 is 6-2= 4. Question 20. Draw Conclusions What value is most affected by an outlier, the median or the range? Explain. Can you see these effects in a dot plot? Answer: The most affected by an outlier is range. The outlier increases the range as median values are in the middle, so the outlier will not mostly affect the median. Yes, in a dot plot we can see both range and median. ### Guided Practice – Page No. 344 For 1–3, use the box plot Terrence created for his math test scores. Find each value. Question 1. Minimum = _____ ; Maximum = _____ Answer: Minimum = 72. Maximum = 88. Explanation: The minimum value is the smallest value in the box plot, so the minimum value is 72, and the maximum value is the largest value in the box plot which is 88 Question 2. Median = _____ Answer: The Median is 79. Explanation: The data is 72,75,79,85,88 The Median is 79. Question 3. Range = _____ ; IQR = _____ Answer: The range is 16. The IQR is 10. Explanation: The range is 88-72= 16 IQR is the difference between upper quartiles and lower quartiles, so 85-75= 10. For 4–7, use the box plots showing the distribution of the heights of hockey and volleyball players. Question 4. Which group has a greater median height? _____ Answer: The greater median height is Volleyball players with 74 in. Explanation: Hockey players data is 64,66,70,76,78. The median height of hockey players is 70 in. Volleyball players data is 67,68,74,78,85 The median height of the Volleyball player is 74 in. Question 5. Which group has the shortest player? _____ Answer: Hockey players have the shortest player with 64 in. Explanation: The minimum height of the hockey players is 64 in. The minimum height of the Volleyball players is 67 in. Question 6. Which group has an interquartile range of about 10? _____ Answer: The IQR for Hockey players and Volleyball players is 10. Explanation: The IQR for Hockey players is 76-66= 10. The IQR for Volleyball players is 78-68= 10. Essential Question Check-In Question 7. What information can you use to compare two box plots? Answer: To compare two box plots we can use minimum, maximum values, ////////the median, the range, and the IQR. ### Independent Practice – Page No. 345 For 8–11, use the box plots of the distances traveled by two toy cars that were jumped from a ramp. Question 8. Compare the minimum, maximum, and median of the box plots. Answer: The data of Car A is 165,170,180,195,210. The data of Car B is 160,175,185,200,205. The minimum value of Car A is 165. The minimum value of Car B is 165. The maximum value of Car A is 210. The maximum value of Car B is 205. The median of Car A is 180. The median of Car B is 185. Explanation: The data of Car A is 165,170,180,195,210. The data of Car B is 160,175,185,200,205. The minimum value of Car A is 165. The minimum value of Car B is 165. The maximum value of Car A is 210. The maximum value of Car B is 205. The median of Car A is 180. The median of Car B is 185. Question 9. Compare the ranges and interquartile ranges of the data in box plots. Answer: The range of Car A is 45. The range of Car B is 45. The IQR of Car A is 25. The IQR of Car B is 25. Explanation: The range of Car A is 210-165= 45. The range of Car B is 205-160= 45. The IQR of Car A is 195-170= 25. The IQR of Car B is 200-175= 25. Question 10. What do the box plots tell you about the jump distances of two cars? Answer: The box plot tells about the minimum and the maximum jump distance, the median jump distance, and the spread of the jump distance. Question 11. Critical Thinking What do the whiskers tell you about the two data sets? Answer: The whiskers tells about the spread of maximum and minimum values of the bottom and top 25% of data. For 12–14, use the box plots to compare the costs of leasing cars in two different cities. Question 12. In which city could you spend the least amount of money to lease a car? The greatest? ______ Answer: The least and the greatest amount is spent by City B. Explanation: The data set of City A is$425,$450,$475,$550,$600.
The data set of City B is $400,$425,$450,$475,$625. The minimum cost of City A is$425 and the maximum is $600. The minimum cost of City B is$400 and the maximum is $625. The least and the greatest amount is spent by City B. Question 13. Which city has a higher median price? How much higher is it? ______ Answer: The higher median price is City A with$475 and $50 higher. Explanation: The median of City A is$475 and the median of City B is $450. So the difference is$475-$425=$50.

Question 14.
Make a Conjecture
In which city is it more likely to choose a car at random that leases for less than $450? Why? ______ Answer: 450 corresponds to the first quartile of City A, which means 25% of the cars cost less than$450. 450 corresponds to the median for City B  which means 50% of the cars cost less than $450. So City B is more likely to have a car chosen randomly that costs less than$450.

### Page No. 346

Question 15.
Summarize
Look back at the box plots for 12–14 on the previous page. What do the box plots tell you about the costs of leasing cars in those two cities?

Answer: City A has a smaller range than City B, but it has greater IQR. And City B has 4 key values of City A which means leasing a car is cheaper in City B.

H.O.T.

Focus on Higher Order Thinking

Question 16.
Draw Conclusions
Two box plots have the same median and equally long whiskers. If one box plot has a longer box than the other box plot, what does this tell you about the difference between the data sets?

Answer: If two box plots have the same median and equally long whiskers and one box is longer than the other, that means the box plot with the larger box has a greater range and IQR.

Question 17.
Communicate Mathematical Ideas
What you can learn about a data set from a box plot? How is this information different from a dot plot?

Answer: We can learn about the minimum and the maximum values, the median, the range, the IQR, and the range of 25% of the data.
and a data plot contains all data values. which a box plot doesn’t have.

Question 18.
Analyze Relationships
In mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? Explain.

Answer: If the range and IQR are small, the values are clustering around some central values.

### Guided Practice – Page No. 350

The tables show the numbers of miles run by the students in two classes. Use the tables in 1–2.

Question 1.
For each class, what is the mean? What is the mean absolute deviation?
Class 1 mean: __________
Class 2 mean: __________
Class 1 MAD: __________
Class 2 MAD: __________

Class 1 mean: 6
Class 2 mean: 11
Class 1 MAD: 3.067
Class 2 MAD: 3.067

Explanation:
The mean of Class 1 is $$\frac{12+6+1+10+1+2+3+10+3+8+3+9+8+6+8}{6} = \frac{90}{15}$$
= 6
The mean of Class 2 is $$\frac{11+14+11+13+6+7+8+6+8+13+8+15+13+17+15}{15} = \frac{165}{15}$$
= 11
The mean absolute deviation of Class 1 is
|12-6| = 6
|6-6| = 0
|1-6| = 5
|10-6| = 4
|1-6| = 5
|2-6| = 4
|3-6| = 3
|10-6| = 4
|3-6| = 3
|8-6| = 2
|3-6| = 3
|9-6| = 3
|8-6| = 2
|6-6| = 0
|8-6| = 2
The mean absolute deviation of Class 1 is $$\frac{6+0+5+4+5+4+3+4+3+2+3+3+2+0+2}{15} = \frac{46}{15}$$
= 3.067

The mean absolute deviation of Class 2 is
|11-11| = 0
|14-11| = 3
|11-11| = 0
|13-11| = 2
|6-11| = 5
|7-11| = 4
|8-11| = 3
|6-11| = 5
|8-11| = 3
|13-11| = 2
|8-11| = 3
|15-11| = 4
|13-11| = 2
|17-11| = 6
|15-11| = 4
The mean absolute deviation of Class 2 is $$\frac{0+3+0+2+5+4+3+5+3+2+3+4+2+6+4}{15} = \frac{46}{15}$$
= 3.067

Question 2.
The difference of the means is about _____ times the mean absolute deviations.
_____

Explanation: The difference of the mean is 11-6=5, and the difference of the means is about 3 times the mean absolute deviations, so
5/3= 1.67.

Question 3.
Mark took 10 random samples of 10 students from two schools. He asked how many minutes they spend per day going to and from school. The tables show the medians and the means of the samples. Compare the travel times using distributions of the medians and means.

Essential Question Check-In

Question 4.
Why is it a good idea to use multiple random samples when making comparative inferences about two populations?

Answer: It’s important to use multiple random samples, so you can draw more interferences about the populations. The more samples we use the more convincing arguments you can make about the distributions.

### Independent Practice – Page No. 351

Josie recorded the average monthly temperatures for two cities in the state where she lives. Use the data for 5–7.

Question 5.
For City 1, what is the mean of the average monthly temperatures? What is the mean absolute deviation of the average monthly temperatures?
Mean: __________

Mean: 50 °F.

Explanation:
The mean of city 1 is $$\frac{23+38+39+48+55+56+71+86+57+53+43+31}{12} = \frac{600}{12}$$
= 50 °F.
|23-50|= 27
|38-50|= 12
|39-50|= 11
|48-50|= 2
|55-50|= 5
|56-50|= 6
|71-50|= 21
|86-50|= 36
|57-50|= 7
|53-50|= 3
|43-50|= 7
|31-50|= 19
The mean absolute deviation is $$\frac{27+12+11+2+5+6+21+36+7+3+7+19}{12} = \frac{156}{12}$$
= 13 °F.

Question 6.
What is the difference between each average monthly temperature for City 1 and the corresponding temperature for City 2?
_______ °F

Answer: The difference between each average monthly temperature for City 1 and the corresponding temperature for City 2 is 15 °F

Explanation:
|23-8|= 15
|38-23|= 15
|39-24|= 15
|48-33|= 15
|55-40|= 15
|56-41|= 15
|71-56|= 15
|86-71|= 15
|57-42|= 15
|53-38|= 15
|43-28|= 15
|31-16|=  15
The difference between each average monthly temperature for City 1 and the corresponding temperature for City 2 is 15 °F

Question 7.
Draw Conclusions
Based on your answers to Exercises 5 and 6, what do you think the mean of the average monthly temperatures for City 2 is? What do you think the mean absolute deviation of the average monthly temperatures for City 2 is? Give your answers without actually calculating the mean and the mean absolute deviation. Explain your reasoning.
Mean = __________ °F

Mean =35 °F

Explanation: As all the values of City 2 are 15 below the values of City 1, so the mean of the City 2 will be 50 less than the mean of City 1. Which means 50-15= 35. All of City 2’s values deviate from the mean the same way City 1’s values do which means that the mean absolute deviation is 13

Question 8.
What is the difference in the means as a multiple of the mean absolute deviations?

Explanation:
(50-35)/13
= 15/13
= 1.15.
The difference in the means as a multiple of the mean absolute deviations 1.15.

Question 9.
Make a Conjecture
The box plots show the distributions of mean weights of 10 samples of 10 football players from each of two leagues, A and B. What can you say about any comparison of the weights of the two populations? Explain.

Answer: As both leagues have a lot of variability since the ranges and IQR’s are both very large. The middle halves overlap entirely. The variation and overlap in the distributions make it hard to make any convincing comparison.

### Page No. 352

Question 10.
Justify Reasoning
Statistical measures are shown for the ages of middle school and high school teachers in two states.
State A: Mean age of middle school teachers = 38, mean age of high school teachers = 48, mean absolute deviation for both = 6
State B: Mean age of middle school teachers = 42, mean age of high school teachers = 50, mean absolute deviation for both = 4
In which state is the difference in ages between members of the two groups more significant? Support your answer.
_____________

Answer: State B has a difference in ages between members of the two groups more significant.

Explanation:
For State A the difference in the mean as a multiple of the mean absolute deviation is (48-38)/6
= 10/6
= 1.67.
So for State B, (50-42)/4
= 8/4
= 2.
As State B has a larger multiple, the differences in ages between members of the two groups are more significant.

Question 11.
Analyze Relationships
The tables show the heights in inches of all the adult grandchildren of two sets of grandparents, the Smiths and the Thompsons. What is the difference in the medians as a multiple of the ranges?

______ x range

Answer: The difference in the median is 1.75.

Explanation:
Smith: 64,65,65,66,66,67,68,68,69,70.
The Median is (66+67)/2
= 133/2
= 66.5.
The range is 70-64= 6.
Thompsons: 74,75,75,76,77,77,78,79,79,80.
The Median is (77+77)/2
= (154)/2
= 77.
The range is 80-74= 6.
The difference in the median is (77-66.5)/6
= 10.5/6
= 1.75.

H.O.T.

Focus on Higher Order Thinking

Question 12.
Critical Thinking
Jill took many samples of 10 tosses of a standard number cube. What might she reasonably expect the median of the medians of the samples to be? Why?
Median of the medians: ______

Median of the medians: 3.5.

Explanation: The possible outcome of a number cube is 1,2,3,4,5,6. So median is
= (3+4)/2
= 7/2
= 3.5
The median of the medians should be close to the median of the populations, so it will also be about 3.5.

Question 13.
Analyze Relationships
Elly and Ramon are both conducting surveys to compare the average numbers of hours per month that men and women spend shopping. Elly plans to take many samples of size 10 from both populations and compare the distributions of both the medians and the means. Ramon will do the same, but will use a sample size of 100. Whose results will probably produce more reliable inferences? Explain.
_____________

Answer: The larger the sample size, the less variability there should be in the distributions of the medians and means. And Ramon will most likely produce more reliable inferences since he will be using a much larger sample size.

Question 14.
Counterexamples
Seth believes that it is always possible to compare two populations of numerical values by finding the difference in the means of the populations as a multiple of the mean absolute deviations. Describe a situation that explains why Seth is incorrect.

Answer: In order to compare two populations by finding the difference in the means of the populations as a multiple of the mean absolute deviations, so the mean absolute deviations of both populations need to be about the same. So if the mean absolute deviations are significantly different, like 5 and 10 and we cannot compare the populations this way.

### 11.1 Comparing Data Displayed in Dot Plots – Page No. 353

The two dot plots show the number of miles run by 14 students at the start and at the end of the school year. Compare each measure for the two dot plots. Use the data for 1–3.

Question 1.
Means
Start: _________
End: _________

Mean
Start: 7.5 miles.
End: 8.2 miles.

Explanation:
The data for the start of the school year is 5,6,6,7,7,7,7,8,8,8,8,9,9,10.
The mean is $$\frac{5+6+6+7+7+7+7+8+8+8+8+9+9+10}{14} = \frac{105}{14}$$
= 7.5 miles.
The data for the end of the school year is 6,6,7,7,8,8,8,8,9,9,9,10,10,10.
The mean is $$\frac{6+6+7+7+8+8+8+8+9+9+9+10+10+10}{14} = \frac{115}{14}$$
= 8.2 miles.

Question 2.
Medians
Start: _________
End: _________

Median
Start: 7.5 miles.
End: 8 miles.

Explanation:
The median for the start of the school year is
= (7+8)/2
= 15/2
= 7.5 miles.
The median for the end of the school year is
= (8+8)/2
= 16/2
= 8 miles.

Question 3.
Ranges
Start: _________
End: _________

Ranges
Start: 5 miles.
End: 4 miles.

Explanation:
The range for the Start of the school year is 10-5= 5 miles.
The range for the end of the school year is 10-6= 4 miles.

11.2 Comparing Data Displayed in Box Plots

The box plots show lengths of flights in inches flown by two model airplanes. Use the data for 4–5.

Question 4.
Which has a greater median flight length?
_____________

The greater median flight length is Airplane A which is 210 in.

Explanation:
The median of Airplane A is 210 in and the median of Airplane B is 204 in. So greater median flight length is Airplane A which is 210 in.

Question 5.
Which has a greater interquartile range?
_____________

Answer: The greater IQR is Airplane B with 35 in.

Explanation:
The IQR for Airplane A is 225-208= 17 in and The IQR for Airplane B is 230-195= 35 in. So the greater IQR is Airplane B.

11.3 Using Statistical Measures to Compare Populations

Question 6.
Roberta grows pea plants, some in shade and some in sun. She picks 8 plants of each type at random and records the heights.

Express the difference in the means as a multiple of their ranges.
______

Answer: The difference in the means as a multiple of their ranges is 2.4 in.

Explanation:
The mean of Shade plant heights is $$\frac{7+11+11+12+9+12+8+10}{8} = \frac{80}{8}$$
= 10 in.
The range of Shade plant heights is 12-7= 5 in.
The mean of Sun plant heights is $$\frac{21+24+19+19+22+23+24+24}{8} = \frac{176}{8}$$
= 22 in.
The range of Sun plant heights is 24-19= 5 in.
The difference in the means as a multiple of their ranges is  (22-10)/5
= 12/5
= 2.4 in.

Essential Question

Question 7.
How can you use and compare data to solve real-world problems?

Answer: We can use and compare data to solve real-world problems by determining if one set is larger than the other set in terms of values, means, and medians.

### Selected Response – Page No. 354

Question 1.
Which statement about the data is true?

Options:
a. The difference between the medians is about 4 times the range.
b. The difference between the medians is about 4 times the IQR.
c. The difference between the medians is about 2 times the range.
d. The difference between the medians is about 2 times the IQR.

Answer: b is true.

Explanation:
Set 1 median is 60 and Set 2 median is 76
The range of Set 1 is 68-55= 13
The range of Set 2 is 80-65= 15
The IQR of Set 1 is 63-59= 4
The IQR of Set 2 is 77-73= 4
The difference in medians is 76-60= 16, So the difference between the medians is about 4 times the IQR.

Question 2.
Which is a true statement based on the box plots below?

Options:
a. The data for City A has a greater range.
b. The data for City B is more symmetric.
c. The data for City A has a greater interquartile range.
d. The data for City B has a greater median.

Answer: C is true.

Explanation: The length of the box for City A is much larger than for City B, so IQR for City A is greater.

Question 3.
What is −3 $$\frac{1}{2}$$ written as a decimal?
Options:
a. -3.5
b. -3.05
c. -0.35
d. -0.035

Explanation: −3 $$\frac{1}{2}$$
=  $$\frac{-7}{2}$$
= -3.5.

Question 4.
Which is a true statement based on the dot plots below?

Options:
a. Set A has the lesser range
b. Set B has a greater median.
c. Set A has the greater mean.
d. Set B is less symmetric than Set A.

Answer: c is a true statement.

Explanation:
The median of Set A is 30 and the median of Set B is 40, so Set A has the greater mean.

Question 5.
The dot plots show the lengths of a random sample of words in a fourth-grade book and a seventh-grade book.

a. Compare the shapes of the plots.

For Fourth grade, most of the words have a length of 6 or less and with two outliers 9 and 10.
For Seventh grade, most of the words have a length of 8 or less with 5 exceptions.

Question 5.
b. Compare the ranges of the plots. Explain what your answer means in terms of the situation.

The Seventh grade has a larger range, so it has more variability.

Explanation:
The range for the fourth grade is 10-1=9.
The range for the seventh grade 14-2= 12.
As the Seventh grade has a larger range it has more variability.

### EXERCISES – Page No. 356

Question 1.
Molly uses the school directory to select, at random, 25 students from her school for a survey on which sports people like to watch on television. She calls the students and asks them, “Do you think basketball is the best sport to watch on television?”
a. Did Molly survey a random sample or a biased sample of the students at her school?
_____________

Answer: Yes, Molly surveyed a random sample. As she selected 25 students from a school directory of the entire student’s population in her school.

Question 1.
b. Was the question she asked an unbiased question? Explain your answer.
_____________

Answer: No, the question is not unbiased. The question is biased because it assumes the person watches basketball on television.

Question 2.
There are 2,300 licensed dogs in Clarkson. A random sample of 50 of the dogs in Clarkson shows that 8 have ID microchips implanted. How many dogs in Clarkson are likely to have ID microchips implanted?
______ dogs

Explanation: Let the dogs in Clarkson to have ID microchips be X, so
X/2300 = 8/50
X= (8×2300)/50
X= 18,400/50
X= 368.

Question 3.
A store gets a shipment of 500 MP3 players. Twenty-five of the players are defective, and the rest are working. A graphing calculator is used to generate 20 random numbers to simulate a random sample of the players.
A list of 20 randomly generated numbers representing MP3 players is :

a. Let numbers 1 to 25 represent players that are _____
_____________

Answer: As there are twenty-five defective players, let the numbers 1 to 25 represent players that are defective.

Question 3.
b. Let numbers 26 to 500 represent players that are _____
_____________

Answer: Let the numbers 26 to 500 represent players that are working.

Question 3.
c. How many players in this sample are expected to be defective?
______ players

Answer: As there are 2 numbers in from 1 and 25 which are 5 and 9 are the players in the sample are expected to be defective.

Question 3.
d. If 300 players are chosen at random from the shipment, how many are expected to be defective based on the sample? Does the sample provide a reasonable inference? Explain.
______ players

Explanation:
X/300 = 2/20
X = (2×300)/20
X = 600/20
X = 30.
We may expect 25 out of 500 or 5% of the 300 players to be defective, which is only 15 players because the sample doesn’t provide a reasonable inference.

### EXERCISES – Page No. 357

The dot plots show the number of hours a group of students spends online each week, and how many hours they spend reading. Compare the dot plots visually.

Question 1.
Compare the shapes, centers, and spreads of the dot plots.

Shape:
Time spent online- Most of the students spend 4 hours are more.
Time spent reading- The students spent a maximum of 6 hours.
Centers:,6
The no.of hours spent online is centered around 6 hours.
The no.of hours spent reading is centered around 5 hours.
The range for time spent online is 7-0=7.
The range for time spent reading is 6-0=6.

Question 2.
Calculate the medians of the dot plots.
Time online: __________

Time online: 6 hours.
Time reading: 5 hours.

Explanation:
The data of time online is 0,4,4,5,5,6,6,6,6,6,6,7,7,7,7
The Median is 6 hours.
The data of time reading is 0,0,0,0,1,1,2,5,5,5,6,6,6,6,6
The Median is 5 hours.

Question 3.
Calculate the ranges of the dot plots.
Time online: __________

Time online: 7 hours.
Time reading: 6 hours.

Explanation:
The range of time online is 7-0= 7.
The range of time reading is 6-0= 6.

### Page No. 358

Question 4.
The average times (in minutes) a group of students spend studying and watching TV per school day are given.
Studying: 25, 30, 35, 45, 60, 60, 70, 75
Watching TV: 0, 35, 35, 45, 50, 50, 70, 75
a. Find the mean times for studying and for watching TV.
Studying: __________
Watching TV: __________

Studying: 50.
Watching TV: 40.

Explanation:
The mean for studying is $$\frac{25+30+35+45+60+60+0+75}{8} = \frac{400}{8}$$
= 50.
The mean for watching TV is $$\frac{0+35+35+45+50+50+70+75}{8} = \frac{360}{8}$$
= 45.

Question 4.
b. Find the mean absolute deviations (MADs) for each data set.
Studying: __________
Watching TV: __________

Studying: 16.25
Watching TV: 16.25

Explanation:
|25-50|= 25
|30-50|= 20
|35-50|= 15
|45-50|= 5
|60-50|= 10
|60-50|= 10
|70-50|= 20
|75-50|= 25
The mean absolute deviation is $$\frac{25+20+15+5+10+10+20+25}{8} = \frac{130}{8}$$
= 16.25.
|0-45|= 45
|35-45|= 10
|35-45|= 10
|45-45|= 0
|50-45|= 5
|50-45|= 5
|70-45|= 25
|75-45|= 30
The mean absolute deviation is $$\frac{45+10+10+0+5+5+25+30}{8} = \frac{130}{8}$$
= 16.25.

Question 4.
c. Find the difference of the means as a multiple of the MAD, to two decimal places.
_____

Explanation: (50-45)/16.25 = 5/16.25
= 0.31.

### Unit 5 Performance Tasks

Question 5.
Entomologist
An entomologist is studying how two different types of flowers appeal to butterflies. The box-and-whisker plots show the number of butterflies that visited one of two different types of flowers in a field. The data were collected over a two-week period, for one hour each day.

a. Find the median, range, and interquartile range for each data set.

Type A:
The median is 11.5
The range is 4
The IQR is 3
Type B:
The median is 11
The range is 10
The IQR is 2

Explanation:
Type A:
The median is (11+12)/2
= 23/2
= 11.5
The range is 13-9= 4
The IQR is 12-9= 3
Type B:
The median is 11
The range is 17-7= 10
The IQR is 12-10= 2

Question 5.
b. Which measure makes it appear that flower type A had a more consistent number of butterfly visits? Which measure makes it appear that flower type B did? If you had to choose one flower as having the more consistent visits, which would you choose? Explain your reasoning.

Answer: As type A has a smaller range, the range makes it appear as if type A has a more consistent number of butterflies visits. And type B had a smaller IQR, the IQR makes it appear as if type A has a more consistent number of butterflies visits. We would choose type A has to have a more consistent number of butterflies visits and it has a much smaller range. The range of the fourth quartile for type Bis larger than the range for the entire data set of type A.

### Selected Response – Page No. 359

Question 1.
Which is a true statement based on the dot plots below?

Options:
a. Set B has a greater range.
b. Set B has a greater median.
c. Set B has the greater mean.
d. Set A is less symmetric than Set B.

Explanation:
Set A has a range of 60-20= 40
Set B has a range of 60-10= 50.
So Set B has a greater range.

Question 2.
Which is a solution to the equation 7g − 2 = 47?
Options:
a. g = 5
b. g = 6
c. g = 7
d. g = 8

Explanation:
7g-2= 47
7g= 47+2
7g= 49
g= 49/7
g= 7.

Question 3.
Which is a true statement based on the box plots below?

Options:
a. The data for Team B has a greater range.
b. The data for Team A is more symmetric.
c. The data for Team B has a greater interquartile range.
d. The data for Team A has a greater median.

Explanation: The box of Team B is much larger than the box of Team A, so the data for Team B have the greater interquartile range.

Question 4.
Which is the best way to choose a random sample of people from a sold-out movie audience for a survey?
Options:
a. Survey all audience members who visit the restroom during the movie.
b. Assign each seat a number, write each number on a slip of paper, and then draw several slips from a hat. Survey the people in those seats.
c. Survey all of the audience members who sit in the first or last row of seats in the movie theater.
d. Before the movie begins, ask for volunteers to participate in a survey. Survey the first twenty people who volunteer.

Explanation:
A is not random because the people are being chosen are being surveyed in one place.
B is random as all members of the population can be chosen and each member has an equal chance of being selected.
C is may not assign every member of the population an equal chance of being chosen since the number of seats in the first or last rows may have more or fewer seats than the other rows.
D is not random because participants are self selecting to do the survey.

Question 5.
Find the percent change from 84 to 63.
Options:
a. 30% decrease
b. 30% increase
c. 25% decrease
d. 25% increase

Explanation:
(84-63)/84 = 21/84
= 0.25
= 25% decrease

Question 6.
A survey asked 100 students in a school to name the temperature at which they feel most comfortable. The box plot below shows the results for temperatures in degrees Fahrenheit. Which could you infer based on the box plot below?

Options:
a. Most students prefer a temperature less than 65 degrees.
b. Most students prefer a temperature of at least 70 degrees.
c. Almost no students prefer a temperature of fewer than 75 degrees.
d. Almost no students prefer a temperature of more than 65 degrees.

Explanation: The last half of the data is about 73-85 which means 50% prefer a temperature above 73. This means that the most prefer a temperature of at least 70 degrees since more than 50% of the box plot is 70 degrees are more.

### Page No. 360

Question 7.
The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students?

Options:
a. Most students draw at least 12 days a month.
b. Most students read less than 12 days a month.
c. Most students read more often than they draw.
d. Most students draw more often than they read.

Explanation: As 4 out of 5 key values for reading are greater than the corresponding values for drawing which means most of the students read more often than they draw.

Question 8.
Which describes the relationship between ∠NOM and ∠JOK in the diagram?

Options:
b. complementary angles
c. supplementary angles
d. vertical angles

Explanation: ∠NOM and ∠JOK are vertical angles.

Question 9.
The tables show the typical number of minutes spent exercising each week for a group of fourth-grade students and a group of seventh-grade students.

a. What is the mean number of minutes spent exercising for fourth graders? For seventh graders?

Explanation:
The mean for fourth grade is $$\frac{120+75+30+30+240+90+100+180+125+300}{10} = \frac{1290}{10}$$
= 129
The mean for fourth grade is $$\frac{410+145+240+250+125+95+210+190+245+300}{10} = \frac{2210}{10}$$
= 221

Question 9.
b. What is the mean absolute deviation of each data set?

Explanation:
|120-129|= 9
|75-129|= 54
|30-129|= 99
|30-129|= 99
|240-129|=111
|90-129|= 39
|100-129|= 29
|180-129|= 51
|125-129|= 4
|300-129|= 171
The mean absolute deviation for fourth grade is $$\frac{9+54+99+99+111+39+29+51+4+171}{10} = \frac{666}{10}$$
= 66.6
|410-221|= 189
|145-221|= 76
|240-221|= 19
|250-221|= 29
|125-221|= 96
|95-221|= 126
|210-221|= 11
|190-221|= 31
|245-221|= 24
|300-221|= 79
The mean absolute deviation for fourth grade is $$\frac{189+76+19+29+96+126+11+31+24+79}{10} = \frac{680}{10}$$
= 68

Question 9.
c. Compare the two data sets with respect to their measures of center and their measures of variability.

Answer: The center of the fourth grade is much smaller than the center for 7th grade. The range is much smaller for a fourth grade than 7th grade which means that fourth graders spend less time exercising and have less variability in the number of minutes that they exercise.

Explanation:
The data of fourth grade is 30,30,75,90,100,120,125,180,240,300
Median is (100+120)/2
= 220/2
= 110
The range is 300-30= 270
The data of seventh grade is 95,125,145,190,210,240,245,250,300,410
Median is (210+240)/2
= 450/2
= 225
The range is 410-95= 315.
The center of the fourth grade is much smaller than the center for 7th grade. The range is much smaller for a fourth grade than 7th grade which means that fourth graders spend less time exercising and have less variability in the number of minutes that they exercise.

Question 9.
d. How many times the MADs is the difference between the means, to the nearest tenth?
_______

Answer: As the MADs are not the same we will find the average of them and then find the difference of the mean and divide by the average of the MADs.

Explanation:
(66.6+68)/2
= 134.6/2
= 67.3
(221-129)/67.3
= 92/67.3
= 1.37

### Guided Practice – Page No. 371

Question 1.
In a hat, you have index cards with the numbers 1 through 10 written on them. Order the events from least likely to happen (1) to most likely to happen (8) when you pick one card at random. In the boxes, write a number from 1 to 8 to order the eight different events.
You pick a number greater than 0. __________
You pick an even number. __________
You pick a number that is at least 2. __________
You pick a number that is at most 0. __________
You pick a number divisible by 3. __________
You pick a number divisible by 5. __________
You pick a prime number. __________
You pick a number less than the greatest prime number. __________

Explanation:
As there are 10 numbers from 1 to 10 and thus there will be 10 possible outcomes. So,
The number greater than 0 is 1,2,3,4,5,6,7,8,9,10.
Even numbers are 2,4,6,8,10.
The number at least 2 is 2,3,4,5,6,7,8,9,10.
The number that is at most 0: as none of the integers are from 1 to 10 are at most 0.
The number divisible by 3 is 3,6,9.
The number divisible by 5 is 5,10.
The prime numbers are 2,3,5,7.
The number less than the greatest prime numbers are 1,2,3,4,5,6 as 7 is the greatest prime number from the numbers 1 to 10.
The more favorable outcomes correspond with an event, the more likely the events happen. Thus the number is at most 0 is the least likely and the greater than 0 is the most likely.
The number of events from the least likely to the most likely is
The number greater than 0 is 8
Even numbers are 5
The number at least 2 is 7
The number that is at most 0: 1
The number divisible by 3 is 3
The number divisible by 5 is 2
The prime numbers are 4
The number less than the greatest prime number is 6.

Conclusion:

Do not move anywhere, stay on Go Math Answer Key, and enhance your math skills. After completion of your preparation go check your skills by solving the questions provided at the end of the chapter. In addition to the exercise problems, we have also given the answers with an explanation for the performance tasks.

## Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions

### Add and Subtract Parts of a Whole Page No – 389

Use the model to write an equation.

Question 1:

Question 2:

Question 3:

Question 4:

$$\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { }{ }$$

Question 5:

$$\frac { 3 }{ 5 } -\frac { 2 }{ 5 } =\frac { }{ }$$

Question 6:
Jake ate $$\frac { 4 }{ 8 }$$ of a pizza. Millie ate $$\frac { 3}{ 8 }$$ of the same pizza. How much of the pizza was eaten by Jake and Millie?

Question 7:
Kate ate $$\frac { 1 }{ 4 }$$ of her orange. Ben ate $$\frac { 2 }{ 4 }$$ of his banana. Did Kate and Ben eat $$\frac { 1 }{ 4 } +\frac { 2}{ 4 } =\frac { 3}{ 4 }$$ of their fruit?

### Add and Subtract Parts of a Whole Page No – 390

Question 1:
A whole pie is cut into 8 equal slices. Three of the slices are served. How much of the pie is left?
(a) $$\frac { 1 }{ 8 }$$
(b) $$\frac { 3 }{ 8 }$$
(c) $$\frac { 5 }{ 8}$$
(d)$$\frac { 7 }{ 8 }$$

Question 2:
An orange is divided into 6 equal wedges. Jody eats 1 wedge. Then she eats 3 more wedges. How much of the orange did Jody eat?
(a) $$\frac { 1 }{ 6}$$
(b) $$\frac { 4}{ 6 }$$
(c) $$\frac { 5}{ 6 }$$
(d) $$\frac { 6}{ 6}$$

Question 3:
Which list of distances is in order from least to greatest?
(a) $$\frac { 1 }{ 8 }$$ Mile, $$\frac { 3 }{ 16 }$$ Mile, $$\frac { 3 }{ 4 }$$ Mile
(b) $$\frac { 3 }{ 4 }$$ Mile, $$\frac { 1 }{ 8 }$$ Mile, $$\frac { 3 }{ 16 }$$ Mile
(c) $$\frac { 1 }{ 8}$$ Mile, $$\frac { 3 }{ 4 }$$ Mile, $$\frac { 3 }{ 16 }$$ Mile
(d)$$\frac { 3 }{ 16 }$$ Mile, $$\frac { 1 }{ 8 }$$ Mile, $$\frac { 3 }{ 4 }$$ Mile

Question 4:
Jeremy walked 68 of the way to school and ran the rest of the way. What fraction, in simplest form, shows the part of the way that Jeremy walked?
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 3 }{ 8 }$$
(c) $$\frac { 1 }{ 2}$$
(d)$$\frac { 3 }{ 4 }$$

Question 5:
An elevator starts on the 100th floor of a building. It descends 4 floors every 10 seconds. At what floor will the elevator be 60 seconds after it starts?
(a) 60th floor
(b) 66th floor
(c) 72nd floor
(d) 76th floor

Question 6:
For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row. After setting up all the chairs, they were 5 chairs short. How many chairs did the class set up?
(a) 400
(b) 450
(c) 495
(d) 500

### Add and Subtract Parts of a Whole Page No – 393

Question 1:
Write $$\frac { 3 }{ 4 }$$ as a sum of unit fractions.

$$\frac { 3 }{ 4 } =$$

Write the fraction as a sum of unit fractions.
Question 2:

$$\frac { 5 }{ 6 } =$$

Question 3:

$$\frac { 2 }{ 3 } =$$

Question 4:
$$\frac { 4 }{ 12 } =$$

Question 5:
$$\frac { 6 }{ 8 } =$$

Question 6:
$$\frac { 8 }{ 10 } =$$

Question 7:
$$\frac { 6 }{ 6 } =$$

Question 8:
Compare Representations How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions? Explain.

### Add and Subtract Parts of a Whole Page No – 394

Question 9:
Holly’s garden is divided into 5 equal sections. She will fence the garden into 3 areas by grouping some equal sections together. What part of the garden could each fenced area be?

a. What information do you need to use?
b. How can writing an equation help you solve the problem?
c. How can drawing a model help you write an equation?
d. Show how you can solve the problem.

Question 9:
Complete the sentence.
The garden can be fenced into ______, ______, and ______ parts or ______, ______, and ______ parts.

### Add and Subtract Parts of a Whole Page No – 395

Question 1:

Question 2:
$$\frac { 3 }{ 8 }=$$

Question 3:
$$\frac { 6 }{ 12 }=$$

Question 4:
$$\frac { 4 }{ 4 }=$$

Question 5:
$$\frac { 7 }{ 10 }=$$

Question 6:
$$\frac { 6 }{ 6 } =$$

Question 7:
Miguel’s teacher asks him to color $$\frac { 4 }{ 8 }$$ of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. How can Miguel color the sections of his grid to follow all the rules?

Question 8:
Petra is asked to color $$\frac { 6 }{ 6 }$$ of her grid. She must use 3 colors: blue, red, and pink. There must be more blue sections than red sections or pink sections. What are the different ways Petra can color the sections of her grid and follow all the rules?

### Add and Subtract Parts of a Whole Page No – 396

Question 1:
Jorge wants to write $$\frac { 4 }{ 5 }$$ as a sum of unit fractions. Which of the following should he write?
(a) $$\frac { 3 }{ 5 } +\frac { 1 }{ 5 }$$
(b) $$\frac { 2 }{ 5 } +\frac { 2 }{ 5 }$$
(c) $$\frac { 1 }{ 5 } +\frac { 1 }{ 5 }+\frac { 2 }{ 5 }$$
(d) $$\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 }$$

Question 2:
Which expression is equivalent to $$\frac { 7 }{ 8 }$$ ?
(a) $$\frac { 5 }{ 8 } +\frac { 2 }{ 8}+\frac { 1 }{ 8 }$$
(b) $$\frac { 3 }{ 8 } +\frac {3 }{ 8 } +\frac { 1 }{ 8 } +\frac { 1 }{ 8 }$$
(c) $$\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 }$$
(d) $$\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 2 }{ 8 }$$

Question 3:
An apple is cut into 6 equal slices. Nancy eats 2 of the slices. What fraction of the apple is left?
(a) $$\frac { 1 }{ 6 }$$
(b) $$\frac { 2 }{ 6 }$$
(c) $$\frac { 3 }{ 6 }$$
(d) $$\frac { 4 }{ 6 }$$

Question 4:
Which of the following numbers is a prime number?
(a) 1
(b) 11
(c) 21
(d) 51

Question 5:
A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class. She gives each group as many cubes as she
can. How many unit cubes are left over?
(a) 1
(b) 2
(c) 3
(d) 6

Question 6:
Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. How many dimes and nickels does Jessie have in all?
(a) 84
(b) 82
(c) 80
(d) 28

### Add and Subtract Parts of a Whole Page No – 399

Question 1:
Adrian’s cat ate $$\frac { 3 }{ 5 }$$ of a bag of cat treats in September and $$\frac { 1 }{ 5 }$$ of the same bag of cat treats in October. What part of the bag of cat treats did Adrian’s cat eat in both months? Use the model to find the sum $$\frac { 3 }{ 5 }$$+$$\frac { 1 }{ 5 }$$. How many fifth-size pieces are shown?

Use the model to find the sum $$\frac { 3 }{ 5 }$$+$$\frac { 1 }{ 5 }$$. How many fifth-size pieces are shown? fifth-size pieces

Use the model to find the sum.
Question 2:

$$\frac { 1 }{ 4 } +\frac { 2 }{ 4 } =\frac { }{ }$$

Question 3:

$$\frac { 6 }{ 10 } +\frac { 3 }{ 10 } =\frac { }{ }$$

Find the sum. Use models to help.
Question 4:
$$\frac { 3 }{ 6 } +\frac { 3 }{ 6 } =\frac { }{ }$$

Question 5:
$$\frac { 1 }{ 3 } +\frac { 1 }{ 3 } =\frac { }{ }$$

Question 6:
$$\frac { 5 }{ 8 } +\frac { 2 }{ 8 } =\frac { }{ }$$

Find the sum. Use models or iTools to help.
Question 7:
$$\frac { 5 }{ 8 } +\frac { 2 }{ 8 } =\frac { }{ }$$

Question 8:
$$\frac { 2 }{ 5 } +\frac { 2 }{ 5 } =\frac { }{ }$$

Question 9:
$$\frac { 4 }{ 6 } +\frac { 1 }{ 6 } =\frac { }{ }$$

Question 10:
Jason is making a fruit drink. He mixes $$\frac { 2 }{ 8 }$$ quart of grape juice with $$\frac { 3 }{ 8 }$$ quart of apple juice. Then he adds $$\frac { 1 }{ 8 }$$ quart of lemonade. How much fruit drink does Jason make?
$$\frac { }{ }$$ quart.

Question 11:
A sum has five addends. Each addend is a unit fraction. The sum is 1. What are the addends?

Question 12:
In a survey, $$\frac { 4 }{ 12 }$$ of the students chose Friday and $$\frac { 5 }{ 12 }$$ chose Saturday as their favorite day of the week. What fraction shows the students who chose Friday or Saturday as their favorite day? Shade the model to show your answer.

$$\frac { }{ }$$

### Add and Subtract Parts of a Whole Page No – 400

Question 13:
Model Mathematics Jin is putting colored sand in a jar. She filled $$\frac {2 }{ 10}$$ of the jar with blue sand and $$\frac { 4}{ 10}$$ of the jar with pink sand. Describe one way to model the part of the jar filled with sand.

Have you ever seen a stained glass window in a building or home? Artists have been designing stained glass windows for hundreds of years.

Help design the stained glass sail on the boat below.

Materials • color pencils

Look at the eight triangles in the sail. Use the guide below to color the triangles:

• $$\frac {2 }{8 }$$ blue
• $$\frac {3 }{8 }$$ red
• $$\frac { 2}{ 8}$$ orange
• $$\frac {1 }{8 }$$ yellow

Question 14:
Write an Equation Write an equation that shows the fraction of triangles that are red or blue.

Question 15:
What color is the greatest part of the sail? Write a fraction for that color. How do you know that fraction is greater than the other fractions? Explain.

### Add Fractions Using Models – Page No 401

Find the sum. Use fraction strips to help.

Question 1:

Question 2:
$$\frac { 4 }{ 10 } +\frac { 5 }{ 10 } =\frac { }{ }$$

Question 3:
$$\frac { 1 }{ 3 } +\frac { 2 }{ 3 } =\frac { }{ }$$

Question 4:
$$\frac { 2 }{ 4 } +\frac { 1 }{ 4 } =\frac { }{ }$$

Question 5:
$$\frac { 2 }{ 12 } +\frac { 4 }{ 12 } =\frac { }{ }$$

Question 6:
$$\frac { 1 }{ 6 } +\frac { 3 }{ 6 } =\frac { }{ }$$

Question 7:
$$\frac { 3 }{ 12 } +\frac { 9 }{ 12 } =\frac { }{ }$$

Question 8:
$$\frac { 3 }{ 8 } +\frac { 4 }{ 8 } =\frac { }{ }$$

Question 9:
$$\frac { 3 }{ 4 } +\frac { 1 }{ 4 } =\frac { }{ }$$

Question 9:
$$\frac { 1 }{ 5 } +\frac { 2 }{ 5 } =\frac { }{ }$$

Question 10:
$$\frac { 6 }{ 10 } +\frac { 3 }{ 10 } =\frac { }{ }$$

Question 11:
Lola walks $$\frac { 4 }{ 10}$$ mile to her friend’s house. Then she walks $$\frac { 5 }{ 10 }$$ mile to the store. How far does she walk in all?

Question 12:
Evan eats $$\frac { 1 }{ 8 }$$ of a pan of lasagna and his brother eats $$\frac { 2 }{ 8 }$$ of it. What fraction of the pan of lasagna do they eat in all?

Question 13:
Jacqueline buys $$\frac { 2 }{ 4 }$$ yard of green ribbon and $$\frac { 1 }{ 4 }$$ yard of pink ribbon. How many yards of ribbon does she buy in all?

Question 14:
Shu mixes $$\frac { 2 }{ 3 }$$ pound of peanuts with $$\frac { 1 }{ 3 }$$ pound of almonds. How many pounds of nuts does Shu mix in all?

### Add Fractions Using Models – Lesson Check – Page No 402

Question 1:
Mary Jane has $$\frac { 3 }{ 8 }$$ of a medium pizza left. Hector has $$\frac { 2 }{ 8 }$$ of another medium pizza left. How much pizza do they have altogether?

(a) $$\frac { 1 }{ 8 }$$
(b) $$\frac { 4 }{ 8 }$$
(c) $$\frac { 5 }{ 8 }$$
(d) $$\frac { 6 }{ 8 }$$

Question 2:
Jeannie ate $$\frac { 1 }{ 4 }$$ of an apple. Kelly ate $$\frac { 2 }{ 4 }$$ of the apple. How much did they eat in all?

(a) $$\frac { 1 }{ 8 }$$
(b) $$\frac { 2 }{ 8 }$$
(c) $$\frac { 3 }{ 8 }$$
(d) $$\frac { 3 }{ 4 }$$

Question 3:
Karen is making 14 different kinds of greeting cards. She is making 12 of each kind. How many greeting cards is she making?

(a) 120
(b) 132
(c) 156
(d) 168

Question 4:
Jefferson works part-time and earns $1,520 in four weeks. How much does he earn each week? Answer: (a)$305
(b) $350 (c)$380
(d) $385 Question 5: By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day. Using such water fixtures, about how many gallons of water would the average American use in December? Answer: (a) about 1,200 gallons (b) about 1,500 gallons (c) about 1,600 gallons (d) about 2,000 gallons Question 6: Collin is making a bulletin board and note center. He is using square cork tiles and square dry-erase tiles. One of every 3 squares will be a cork square. If he uses 12 squares for the center, how many will be cork squares? Answer: (a) 3 (b) 4 (c) 6 (d) 8 ### Add Fractions Using Models – Lesson Check – Page No 405 Question 1: Lisa needs 45 pound of shrimp to make shrimp salad. She has 15 pound of shrimp. How much more shrimp does Lisa need to make the salad? Subtract $$\frac { 4 }{ 5 } – \frac { 1 }{ 5 }$$. Use the model to help. Shade the model to show how much shrimp Lisa needs. Then shade the model to show how much shrimp Lisa has. Compare the difference between the two shaded rows. $$\frac { 4 }{ 5 } – \frac { 1 }{ 5 } = \frac {■ }{ 5}$$ Lisa needs _____ pound more shrimp. Answer: Use the model to find the difference. Question 2: $$\frac { 3 }{ 6 } – \frac { 2 }{ 6 } = \frac {■ }{ 6}$$ Answer: Question 3: $$\frac { 8 }{ 10 } – \frac { 5 }{ 10 } = \frac {■ }{ 10}$$ Answer: Subtract. Use models to help. Question 4: $$\frac { 5 }{ 8 } – \frac { 2 }{ 8 } = \frac { }{ }$$ Answer: Question 5: $$\frac { 7 }{ 12 } – \frac { 2 }{ 12 } = \frac { }{ }$$ Answer: Question 6: $$\frac { 3 }{4 } – \frac { 2 }{ 4 } = \frac { }{ }$$ Answer: Question 7: $$\frac { 2 }{ 3 } – \frac { 1 }{ 3 } = \frac { }{ }$$ Answer: Question 8: $$\frac { 7 }{ 8 } – \frac { 5 }{ 8 } = \frac { }{ }$$ Answer: Question 9: Explain how you could find the unknown addend in $$\frac { 2 }{ 6 }$$ + _____ = 1 without using a model. Answer: ### Add Fractions Using Models – Lesson Check – Page No 406 Question 10: Mrs. Ruiz served a pie for dessert two nights in a row. The drawings below show the pie after her family ate dessert on each night. What fraction of the pie did they eat on the second night? $$\frac { }{ }$$ a. What do you need to know? b. How can you find the number of pieces eaten on the second night? c. Explain the steps you used to solve the problem. Complete the sentences. After the first night, _______ pieces were left. After the second night, _______ pieces were left. So, _______ of the pie was eaten on the second night. Answer: Question 11: Make Connection Between Models Judi ate $$\frac { 7}{8}$$ of a small pizza and Jack ate $$\frac { 2}{ 8 }$$ of a second small pizza. How much more of a pizza did Judi eat? $$\frac { }{ }$$ Answer: Question 12: Keiko sewed $$\frac { 3}{4}$$ yard of lace on her backpack. Pam sewed $$\frac { 1}{4}$$ yard of lace on her backpack. Shade the model to show how much more lace Keiko sewed on her backpack than Pam $$\frac { ■ }{ ■ }$$ Answer: ### Subtract Fractions Using Models – Page No 407 Subtract. Use fraction strips to help. Question 1: Answer: Question 2: $$\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { —}{ — }$$ Question 3: $$\frac { 5}{ 6 } – \frac { 1}{ 6 } = \frac { —}{ — }$$ Answer: Question 4: $$\frac { 7}{ 8 } – \frac { 1}{ 8 } = \frac { —}{ — }$$ Answer: Question 5: $$\frac { 1}{ } – \frac { 2}{ 3 } = \frac { —}{ — }$$ Answer: Question 6: $$\frac { 8}{ 10 } – \frac { 2}{ 10 } = \frac { —}{ — }$$ Answer: Question 7: $$\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { —}{ — }$$ Answer: Question 8: $$\frac { 7}{ 6 } – \frac {5}{ 6 } = \frac { —}{ — }$$ Answer: Problem Solving Use the table for 9 and 10. Question 9: Ena is making trail mix. She buys the items shown in the table. How many more pounds of pretzels than raisins does she buy? $$\frac { —}{ — }$$ Answer: Question 10: How many more pounds of granola than banana chips does she buy? $$\frac { —}{ — }$$ Answer: ### Subtract Fractions Using Models – Page No 408 Question 1: Lee reads for $$\frac { 3}{ 4}$$ hour in the morning and $$\frac {2}{ 4}$$ hour in the afternoon. How much longer does Lee read in the morning than in the afternoon? (a) 5 hours (b) $$\frac { 5}{ 4}$$ (c) $$\frac { 4}{ 4}$$ (d) $$\frac { 1}{ 4}$$ Answer: Question 2: Which equation does the model below represent? (a) $$\frac { 3}{ 6} – \frac { 2}{ 6} = \frac { 1}{ 6}$$ (b) $$\frac { 2}{ 6} – \frac { 1}{ 6} = \frac { 1}{ 6}$$ (c) $$\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6}$$ (d) 1 – $$\frac { 3}{ 6} = \frac {3}{ 6}$$ Answer: Question 3: A city received 2 inches of rain each day for 3 days. The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow. How much snow would that city have received in the 3 days? (a) 20 inches (b) 30 inches (c) 50 inches (d) 60 inches Answer: Question 4: At a party there were four large submarine sandwiches, all the same size. During the party, $$\frac { 2}{ 3}$$ of the chicken sandwich, $$\frac { 3}{ 4}$$ of the tuna sandwich, $$\frac { 7}{ 12}$$ of the roast beef sandwich, and $$\frac { 5}{ 6}$$ of the veggie sandwich were eaten. Which sandwich had the least amount left? (a) chicken (b) tuna (c) roast beef (d) veggie Answer: Question 5: Deena uses $$\frac { 3}{ 8}$$ cup milk and $$\frac { 2}{ 8}$$ cup oil in a recipe. How much liquid does she use in all? (a) $$\frac {1}{ 8}$$ cup (b) $$\frac {5}{ 8}$$ cup (c) $$\frac {6}{ 8}$$ cup (d) 5 cups Answer: Question 6: In the car lot, $$\frac { 4}{ 12}$$ of the cars are white and $$\frac { 3}{ 12}$$ of the cars are blue. What fraction of the cars in the lot are either white or blue? (a) $$\frac { 1}{ 12}$$ (b) $$\frac { 7}{ 24}$$ (c) $$\frac { 7}{ 12}$$ (d) 7 Answer: ### Subtract Fractions Using Models – Page No 411 Question 1: 9 twelfth-size parts − 5 twelfth-size parts = $$\frac { —}{ — }$$ Answer: Question 2: $$\frac { 3}{ 12} + \frac {8}{ 12 } = \frac { —}{ — }$$ Answer: Question 3: $$\frac { 1}{ 3 } + \frac {1}{ 3 } = \frac { —}{ — }$$ Answer: Question 4: $$\frac { 3}{ 4 } – \frac {1}{ 4 } = \frac { —}{ — }$$ Answer: Question 5: $$\frac { 2}{ 6 } + \frac {2}{ 6 } = \frac { —}{ — }$$ Answer: Question 6: $$\frac { 3}{ 8 } – \frac {1}{ 8 } = \frac { —}{ — }$$ Answer: Question 7: $$\frac { 6}{ 10 } – \frac {2}{ 10 } = \frac { —}{ — }$$ Answer: Question 8: $$\frac { 1}{ 2 } – \frac {1}{2 } = \frac { —}{ — }$$ Answer: Question 9: $$\frac {5}{ 6 } – \frac {4}{ 6 } = \frac { —}{ — }$$ Answer: Question 10: $$\frac { 4}{ 5 } – \frac {2}{ 5 } = \frac { —}{ — }$$ Answer: Question 11: $$\frac { 1}{ 4 } + \frac {1}{ 4 } = \frac { —}{ — }$$ Answer: Question 12: $$\frac { 9}{ 10 } – \frac {5}{ 10 } = \frac { —}{ — }$$ Answer: Question 13: $$\frac { 1}{ 12 } + \frac {7}{ 12 } = \frac { —}{ — }$$ Answer: Question 14: Christopher mixes $$\frac { 3}{ 8}$$ gallon of red paint with $$\frac { 5}{ 8}$$ gallon of blue paint to make purple paint. He uses $$\frac { 2}{8}$$ gallon of the purple paint. How much purple paint is left? $$\frac { —}{ — }$$ gallon Answer: Question 15: A city worker is painting a stripe down the center of Main Street. Main Street is $$\frac { 8}{ 10}$$ mile long. The worker painted $$\frac { 4}{ 10}$$ mile of the street. Explain how to find what part of a mile is left to paint. $$\frac { —}{ — }$$ mile Answer: Question 16: Sense or Nonsense? Brian says that when you add or subtract fractions with the same denominator, you can add or subtract the numerators and keep the same denominator. Is Brian correct? Explain. Answer: Question 17: The length of a rope was $$\frac { 6}{8}$$ yard. Jeff cut the rope into 3 pieces. Each piece is a different length measured in eighths of a yard. What is the length of each piece of rope? Answer: Question 18: For 18a–18d, choose Yes or No to show if the sum or difference is correct. a. $$\frac { 3}{ 5 } – \frac {1}{ 5 } = \frac {4 }{5 }$$ (i) yes (ii) no b. $$\frac { 1}{ 4 } – \frac {2}{4 } = \frac {3 }{8 }$$ (i) yes (ii) no c. $$\frac { 5}{ 8} – \frac {4}{ 8 } = \frac {1 }{8 }$$ (i) yes (ii) no d. $$\frac { 4}{ 9 } – \frac {2}{ 9 } = \frac {6 }{9 }$$ (i) yes (ii) no Answer: ### Sense or Nonsense? – Page No. 412 Question 19. Harry says that $$\frac{1}{4}$$ + $$\frac{1}{8}$$ = $$\frac{2}{8}$$. Jane says $$\frac{1}{4}$$ + $$\frac{1}{8}$$ = $$\frac{3}{8}$$. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning. Draw a model to help. Type below: ___________ ### Add and Subtract Fractions – Page No. 413 Find the sum or difference. Question 1. Question 2. $$\frac{3}{6}-\frac{1}{6}$$ = $$\frac{□}{□}$$ Question 3. $$\frac{4}{5}-\frac{3}{5}$$ = $$\frac{□}{□}$$ Question 4. $$\frac{6}{10}+\frac{3}{10}$$ = $$\frac{□}{□}$$ Question 5. 1 – $$\frac{3}{8}$$ = $$\frac{□}{□}$$ Question 6. $$\frac{1}{4}+\frac{2}{4}$$ = $$\frac{□}{□}$$ Question 7. $$\frac{9}{12}-\frac{5}{12}$$ = $$\frac{□}{□}$$ Question 8. $$\frac{5}{6}-\frac{2}{6}$$ = $$\frac{□}{□}$$ Question 9. $$\frac{2}{3}+\frac{1}{3}$$ = $$\frac{□}{□}$$ Problem Solving Use the table for 10 and 11. Question 10. Guy finds how far his house is from several locations and makes the table shown. How much farther away from Guy’s house is the library than the cafe? $$\frac{□}{□}$$ Question 11. If Guy walks from his house to school and back, how far does he walk? $$\frac{□}{□}$$ ### Add and Subtract Fractions – Lesson Check – Page No. 414 Question 1. Mr. Angulo buys $$\frac{5}{8}$$ pound of red grapes and $$\frac{3}{8}$$pound of green grapes. How many pounds of grapes did Mr. Angulo buy in all? Options: a. $$\frac{1}{8}$$ pound b. $$\frac{2}{8}$$ pound c. 1 pound d. 2 pounds Question 2. Which equation does the model below represent? Options: a. $$\frac{7}{8}$$ + $$\frac{2}{8}$$ = $$\frac{9}{8}$$ b. $$\frac{5}{8}$$ – $$\frac{2}{8}$$ = $$\frac{3}{8}$$ c. $$\frac{8}{8}$$ – $$\frac{5}{8}$$ = $$\frac{3}{8}$$ d. $$\frac{7}{8}$$ – $$\frac{2}{8}$$ = $$\frac{5}{8}$$ Spiral Review Question 3. There are 6 muffins in a package. How many packages will be needed to feed 48 people if each person has 2 muffins? Options: a. 4 b. 8 c. 16 d. 24 Question 4. Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice. Each shelf in the cupboard can hold 8 boxes of juice. What is the least number of shelves needed for all the juice boxes? Options: a. 4 b. 7 c. 11 d. 88 Question 5. A machine makes 18 parts each hour. If the machine operates 24 hours a day, how many parts can it make in one day Options: a. 302 b. 332 c. 362 d. 432 Question 6. Which equation does the model below represent? Options: a. $$\frac{5}{6}$$ – $$\frac{4}{6}$$ = $$\frac{1}{6}$$ b. $$\frac{4}{5}$$ – $$\frac{1}{5}$$ = $$\frac{3}{5}$$ c. $$\frac{5}{5}$$ – $$\frac{4}{5}$$ = $$\frac{1}{5}$$ d. $$\frac{6}{6}$$ – $$\frac{4}{6}$$ = $$\frac{2}{6}$$ ### Add and Subtract Fractions – Page No. 415 Choose the best term from the box. Question 1. A ___________ always has a numerator of 1. ________________ Write the fraction as a sum of unit fractions. Question 2. Type below: ____________ Question 3. Type below: ____________ Use the model to write an equation. Question 4. Type below: _________ Question 5. Type below: _________ Use the model to solve the equation. Question 6. $$\frac{3}{8}+\frac{2}{8}$$ = $$\frac{□}{□}$$ Question 7. $$\frac{4}{10}+\frac{5}{10}$$ = $$\frac{□}{□}$$ Find the sum or difference. Question 8. $$\frac{9}{12}-\frac{7}{12}$$ = $$\frac{□}{□}$$ Question 9. $$\frac{2}{3}+\frac{1}{3}$$ = $$\frac{□}{□}$$ Question 10. $$\frac{1}{5}+\frac{3}{5}$$ = $$\frac{□}{□}$$ Question 11. $$\frac{2}{6}+\frac{2}{6}$$ = $$\frac{□}{□}$$ Question 12. $$\frac{4}{4}-\frac{2}{4}$$ = $$\frac{□}{□}$$ Question 13. $$\frac{7}{8}-\frac{4}{8}$$ = $$\frac{□}{□}$$ ### Add and Subtract Fractions – Page No. 416 Question 14. Tyrone mixed $$\frac{7}{12}$$ quart of red paint with $$\frac{1}{12}$$ quart of yellow paint. How much paint does Tyrone have in the mixture? $$\frac{□}{□}$$ quart Question 15. Jorge lives $$\frac{6}{8}$$ mile from school and $$\frac{2}{8}$$ mile from a ballpark. How much farther does Jorge live from school than from the ballpark? $$\frac{□}{□}$$ mile Question 16. Su Ling started an art project with 1 yard of felt. She used $$\frac{2}{6}$$ yard on Tuesday and $$\frac{3}{6}$$ yard on Wednesday. How much felt does Su Ling have left? $$\frac{□}{□}$$ yard Question 17. Eloise hung artwork on $$\frac{2}{5}$$ of a bulletin board. She hung math papers on $$\frac{1}{5}$$ of the same bulletin board. What part of the bulletin board has artwork or math papers? $$\frac{□}{□}$$ ### Add and Subtract Fractions – Page No. 419 Write the unknown numbers. Write mixed numbers above the number line and fractions greater than one below the number line. Question 1. Type below: ___________ Write the mixed number as a fraction. Question 2. 1 $$\frac{1}{8}$$ = $$\frac{□}{□}$$ Question 3. 1 $$\frac{3}{5}$$ = $$\frac{□}{□}$$ Question 4. 1 $$\frac{2}{3}$$ = $$\frac{□}{□}$$ Write the fraction as a mixed number. Question 5. $$\frac{11}{4}$$ = _____ $$\frac{□}{□}$$ Question 6. $$\frac{6}{5}$$ = _____ $$\frac{□}{□}$$ Question 7. $$\frac{13}{10}$$ = _____ $$\frac{□}{□}$$ Write the mixed number as a fraction. Question 8. 2 $$\frac{7}{10}$$ = $$\frac{□}{□}$$ Question 9. 3 $$\frac{2}{3}$$ = $$\frac{□}{□}$$ Question 10. 4 $$\frac{2}{5}$$ = $$\frac{□}{□}$$ Use Repeated Reasoning Algebra Find the unknown numbers. Question 11. $$\frac{13}{7}$$ = 1 $$\frac{■}{7}$$ ■ = _____ Question 12. ■ $$\frac{5}{6}$$ = $$\frac{23}{6}$$ ■ = _____ Question 13. $$\frac{57}{11}$$ = ■ $$\frac{■}{11}$$ _____ $$\frac{□}{□}$$ Question 14. Pen has $$\frac{1}{2}$$-cup and $$\frac{1}{8}$$-cup measuring cups. What are two ways he could measure out 1 $$\frac{3}{4}$$ cups of flour? Type below: _________________ Question 15. Juanita is making bread. She needs 3 $$\frac{1}{2}$$ cups of flour. Juanita only has a $$\frac{1}{4}$$-cup measuring cup. How many $$\frac{1}{4}$$ cups of flour will Juanita use to prepare the bread? _____ $$\frac{1}{4}$$ cups of flou ### Add and Subtract Fractions – Page No. 420 Use the recipe to solve 16–18. Question 16. Reason Quantitatively Cal is making energy squares. How many $$\frac{1}{2}$$ cups of peanut butter are used in the recipe? _____ $$\frac{1}{2}$$ cups of peanut butter Question 17. Suppose Cal wants to make 2 times as many energy squares as the recipe makes. How many cups of bran cereal should he use? Write your answer as a mixed number and as a fraction greater than 1 in simplest form. Type below: ____________ Question 18. Cal added 2 $$\frac{3}{8}$$ cups of raisins. Write this mixed number as a fraction greater than 1 in simplest form. $$\frac{□}{□}$$ Question 19. Jenn is preparing brown rice. She needs 1 $$\frac{1}{2}$$ cups of brown rice and 2 cups of water. Jenn has only a $$\frac{1}{8}$$– cup measuring cup. How many $$\frac{1}{8}$$ cups each of rice and water will Jenn use to prepare the rice? brown rice: ________ $$\frac{1}{8}$$ cups water: _________ $$\frac{1}{8}$$ cups Question 20. Draw a line to show the mixed number and fraction that have the same value. Type below: ____________ ### Rename Fractions and Mixed Numbers – Page No. 421 Write the mixed number as a fraction. Question 1. 2 $$\frac{3}{5}$$ Question 2. 4 $$\frac{1}{3}$$ $$\frac{□}{□}$$ Question 3. 1 $$\frac{2}{5}$$ $$\frac{□}{□}$$ Question 4. 3 $$\frac{3}{2}$$ $$\frac{□}{□}$$ Question 5. 4 $$\frac{1}{8}$$ $$\frac{□}{□}$$ Question 6. 1 $$\frac{7}{10}$$ $$\frac{□}{□}$$ Question 7. 5 $$\frac{1}{2}$$ $$\frac{□}{□}$$ Question 8. 2 $$\frac{3}{8}$$ $$\frac{□}{□}$$ Write the fraction as a mixed number. Question 9. $$\frac{31}{6}$$ ______ $$\frac{□}{□}$$ Question 10. $$\frac{20}{10}$$ ______ $$\frac{□}{□}$$ Question 11. $$\frac{15}{8}$$ ______ $$\frac{□}{□}$$ Question 12. $$\frac{13}{6}$$ ______ $$\frac{□}{□}$$ Question 13. $$\frac{23}{10}$$ ______ $$\frac{□}{□}$$ Question 14. $$\frac{19}{5}$$ ______ $$\frac{□}{□}$$ Question 15. $$\frac{11}{3}$$ ______ $$\frac{□}{□}$$ Question 16. $$\frac{9}{2}$$ ______ $$\frac{□}{□}$$ Question 17. A recipe calls for 2 $$\frac{2}{4}$$ cups of raisins, but Julie only has a $$\frac{1}{4}$$ -cup measuring cup. How many $$\frac{1}{4}$$ cups does Julie need to measure out 2 $$\frac{2}{4}$$ cups of raisins? She needs ______ $$\frac{1}{4}$$ cups Question 18. If Julie needs 3 $$\frac{1}{4}$$ cups of oatmeal, how many $$\frac{1}{4}$$ cups of oatmeal will she use? She will use ______ $$\frac{1}{4}$$ cups of oatmeal ### Rename Fractions and Mixed Numbers – Lesson Check – Page No. 422 Question 1. Which of the following is equivalent to $$\frac{16}{3}$$ ? Options: a. 3 $$\frac{1}{5}$$ b. 3 $$\frac{2}{5}$$ c. 5 $$\frac{1}{3}$$ d. 5 $$\frac{6}{3}$$ Question 2. Stacey filled her $$\frac{1}{2}$$cup measuring cup seven times to have enough flour for a cake recipe. How much flour does the cake recipe call for? Options: a. 3 cups b. 3 $$\frac{1}{2}$$ cups c. 4 cups d. 4 $$\frac{1}{2}$$ cups Spiral Review Question 3. Becki put some stamps into her stamp collection book. She put 14 stamps on each page. If she completely filled 16 pages, how many stamps did she put in the book? Options: a. 224 b. 240 c. 272 d. 275 Question 4. Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. How many miles does he need to drive each hour? Options: a. 48 miles b. 50 miles c. 52 miles d. 54 miles Question 5. During a bike challenge, riders have to collect various colored ribbons. Each $$\frac{1}{2}$$ mile they collect a red ribbon, each $$\frac{1}{8}$$ mile they collect a green ribbon, and each $$\frac{1}{4}$$ mile they collect a blue ribbon. Which colors of ribbons will be collected at the $$\frac{3}{4}$$ mile marker? Options: a. red and green b. red and blue c. green and blue d. red, green, and blue Question 6. Stephanie had $$\frac{7}{8}$$ pound of bird seed. She used $$\frac{3}{8}$$ pound to fill a bird feeder. How much bird seed does Stephanie have left? Options: a. $$\frac{3}{8}$$ pound b. $$\frac{4}{8}$$ pound c. 1 pound d. $$\frac{10}{8}$$ pound ### Rename Fractions and Mixed Numbers – Page No. 425 Write the sum as a mixed number with the fractional part less than 1. Question 1. 1 $$\frac{1}{6}$$ +3 $$\frac{3}{6}$$ ———————– _______ $$\frac{□}{□}$$ Question 2. 1 $$\frac{4}{5}$$ +7 $$\frac{2}{5}$$ ———————– _______ $$\frac{□}{□}$$ Question 3. 2 $$\frac{1}{2}$$ +3 $$\frac{1}{2}$$ ———————– _______ Find the difference. Question 4. 3 $$\frac{7}{12}$$ -2 $$\frac{5}{12}$$ ———————– _______ $$\frac{□}{□}$$ Question 5. 4 $$\frac{2}{3}$$ -3 $$\frac{1}{3}$$ ———————– _______ $$\frac{□}{□}$$ Question 6. 6 $$\frac{9}{10}$$ -3 $$\frac{7}{10}$$ ———————– _______ $$\frac{□}{□}$$ Write the sum as a mixed number with the fractional part less than 1. Question 7. 7 $$\frac{4}{6}$$ +4 $$\frac{3}{6}$$ ———————– _______ $$\frac{□}{□}$$ Question 8. 8 $$\frac{1}{3}$$ +3 $$\frac{2}{3}$$ ———————– _______ $$\frac{□}{□}$$ Question 9. 5 $$\frac{4}{8}$$ +3 $$\frac{5}{8}$$ ———————– _______ $$\frac{□}{□}$$ Question 10. 5 $$\frac{5}{12}$$ +4 $$\frac{2}{12}$$ ———————– _______ $$\frac{□}{□}$$ Find the difference. Question 11. 5 $$\frac{7}{8}$$ -2 $$\frac{3}{8}$$ ———————– _______ $$\frac{□}{□}$$ Question 12. 5 $$\frac{7}{12}$$ -4 $$\frac{1}{12}$$ ———————– _______ $$\frac{□}{□}$$ Question 13. 3 $$\frac{5}{10}$$ -1 $$\frac{3}{10}$$ ———————– _______ $$\frac{□}{□}$$ Question 14. 7 $$\frac{3}{4}$$ -2 $$\frac{2}{4}$$ ———————– _______ $$\frac{□}{□}$$ Practice: Copy and Solve Find the sum or difference. Question 15. $$1 \frac{3}{8}+2 \frac{7}{8}$$ = _______ $$\frac{□}{□}$$ Question 16. $$6 \frac{5}{8}$$ – 4 = _______ $$\frac{□}{□}$$ Question 17. $$9 \frac{1}{2}+8 \frac{1}{2}$$ = _______ Question 18. $$6 \frac{3}{5}+4 \frac{3}{5}$$ = _______ $$\frac{□}{□}$$ Question 19. $$8 \frac{7}{10}-\frac{4}{10}$$ = _______ $$\frac{□}{□}$$ Question 20. $$7 \frac{3}{5}-6 \frac{3}{5}$$ = _______ ### Rename Fractions and Mixed Numbers – Page No. 426 Solve. Write your answer as a mixed number. Question 21. Make Sense of Problems The driving distance from Alex’s house to the museum is 6 $$\frac{7}{10}$$ miles. What is the round-trip distance? _______ $$\frac{□}{□}$$ miles Question 22. The driving distance from the sports arena to Kristina’s house is 10 $$\frac{9}{10}$$ miles. The distance from the sports arena to Luke’s house is 2 $$\frac{7}{10}$$ miles. How much greater is the driving distance between the sports arena and Kristina’s house than between the sports arena and Luke’s house? _______ $$\frac{□}{□}$$ miles Question 23. Pedro biked from his house to the nature preserve, a distance of 23 $$\frac{4}{5}$$ miles. Sandra biked from her house to the lake, a distance of 12 $$\frac{2}{5}$$ miles. How many miles less did Sandra bike than Pedro? _______ $$\frac{□}{□}$$ miles Question 24. During the Martinez family trip, they drove from home to a ski lodge, a distance of 55 $$\frac{4}{5}$$ miles, and then drove an additional 12 $$\frac{4}{5}$$ miles to visit friends. If the family drove the same route back home, what was the distance traveled during their trip? _______ $$\frac{□}{□}$$ miles Question 25. For 25a–25d, select True or False for each statement. a. 2 $$\frac{3}{8}$$ + 1 $$\frac{6}{8}$$ is equal to 4 $$\frac{1}{8}$$. i. True ii. False Question 25. b. 1 $$\frac{1}{6}$$ + 1 $$\frac{4}{12}$$ is equal to 2 $$\frac{2}{12}$$. i. True ii. False Question 25. c. 5 $$\frac{5}{6}$$ – 2 $$\frac{4}{6}$$ is equal to 1 $$\frac{3}{6}$$. i. True ii. False Question 25. d. 5 $$\frac{5}{8}$$ – 3 $$\frac{2}{8}$$ is equal to 2 $$\frac{3}{8}$$. i. True ii. False ### Add and Subtract Mixed Numbers – Page No. 427 Find the sum. Write the sum as a mixed number, so the fractional part is less than 1. Question 1. Question 2. 4 $$\frac{1}{2}$$ +2 $$\frac{1}{2}$$ _______ $$\frac{□}{□}$$ Question 3. 2 $$\frac{2}{3}$$ +3 $$\frac{2}{3}$$ _______ $$\frac{□}{□}$$ Question 4. 6 $$\frac{4}{5}$$ +7 $$\frac{4}{5}$$ _______ $$\frac{□}{□}$$ Question 5. 9 $$\frac{3}{6}$$ +2 $$\frac{2}{6}$$ _______ $$\frac{□}{□}$$ Question 6. 8 $$\frac{4}{12}$$ +3 $$\frac{6}{12}$$ _______ $$\frac{□}{□}$$ Question 7. 4 $$\frac{3}{8}$$ +1 $$\frac{5}{8}$$ _______ $$\frac{□}{□}$$ Question 8. 9 $$\frac{5}{10}$$ +6 $$\frac{3}{10}$$ _______ $$\frac{□}{□}$$ Find the difference. Question 9. 6 $$\frac{7}{8}$$ -4 $$\frac{3}{8}$$ _______ $$\frac{□}{□}$$ Question 10. 4 $$\frac{2}{3}$$ -3 $$\frac{1}{3}$$ _______ $$\frac{□}{□}$$ Question 11. 6 $$\frac{4}{5}$$ -3 $$\frac{3}{5}$$ _______ $$\frac{□}{□}$$ Question 12. 7 $$\frac{3}{4}$$ -2 $$\frac{1}{4}$$ _______ $$\frac{□}{□}$$ Problem Solving Question 13. James wants to send two gifts by mail. One package weighs 2 $$\frac{3}{4}$$ pounds. The other package weighs 1 $$\frac{3}{4}$$ pounds. What is the total weight of the packages? _______ $$\frac{□}{□}$$ Question 14. Tierra bought 4 $$\frac{3}{8}$$ yards blue ribbon and 2 $$\frac{1}{8}$$ yards yellow ribbon for a craft project. How much more blue ribbon than yellow ribbon did Tierra buy? _______ $$\frac{□}{□}$$ ### Add and Subtract Mixed Numbers – Lesson Check – Page No. 428 Question 1. Brad has two lengths of copper pipe to fit together. One has a length of 2 $$\frac{5}{12}$$ feet and the other has a length of 3 $$\frac{7}{12}$$ feet. How many feet of pipe does he have in all? Options: a. 5 feet b. 5 $$\frac{6}{12}$$ feet c. 5 $$\frac{10}{12}$$ feet d. 6 feet Question 2. A pattern calls for 2 $$\frac{1}{4}$$ yards of material and 1 $$\frac{1}{4}$$ yards of lining. How much total fabric is needed? Options: a. 2 $$\frac{2}{4}$$ yards b. 3 yards c. 3 $$\frac{1}{4}$$ yards d. 3 $$\frac{2}{4}$$ yards Spiral Review Question 3. Shanice has 23 baseball trading cards of star players. She agrees to sell them for$16 each. How much will she get for the cards?
Options:
a. $258 b.$358
c. $368 d.$468

Question 4.
Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs. About how much time can she spend with each dog?
Options:
a. about 10 minutes
b. about 20 minutes
c. about 25 minutes
d. about 26 minutes

Question 5.
Frieda has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples
will Frieda keep for herself?
Options:
a. 3
b. 4
c. 6
d. 7

Question 6.
The Lynch family bought a house for $75,300. A few years later, they sold the house for$80,250. How much greater was the selling price than the purchase price?
Options:
a. $4,950 b.$5,050
c. $5,150 d.$5,950

### Add and Subtract Mixed Numbers – Page No. 431

Question 1.
Rename both mixed numbers as fractions. Find the difference.
3 $$\frac{3}{6}$$ = $$\frac{■}{6}$$
−1 $$\frac{4}{6}$$ = – $$\frac{■}{6}$$
—————————————-
_______ $$\frac{□}{□}$$

Find the difference.

Question 2.
1 $$\frac{1}{3}$$
− $$\frac{2}{3}$$
———————
$$\frac{□}{□}$$

Question 3.
4 $$\frac{7}{10}$$
− 1 $$\frac{9}{10}$$
———————
______ $$\frac{□}{□}$$

Question 4.
3 $$\frac{5}{12}$$
− $$\frac{8}{12}$$
———————
_____ $$\frac{□}{□}$$

Question 5.
8 $$\frac{1}{10}$$
− 2 $$\frac{9}{10}$$
———————
$$\frac{□}{□}$$

Question 6.
2
− 1 $$\frac{1}{4}$$
———————
$$\frac{□}{□}$$

Question 7.
4 $$\frac{1}{5}$$
− 3 $$\frac{2}{5}$$
———————
$$\frac{□}{□}$$

Practice: Copy and Solve Find the difference.

Question 8.
$$4 \frac{1}{6}-2 \frac{5}{6}$$
_____ $$\frac{□}{□}$$

Question 9.
$$6 \frac{9}{12}-3 \frac{10}{12}$$
_____ $$\frac{□}{□}$$

Question 10.
$$3 \frac{3}{10}-\frac{7}{10}$$
_____ $$\frac{□}{□}$$

Question 11.
4 – 2 $$\frac{3}{5}$$
_____ $$\frac{□}{□}$$

Question 12.
Lisa mixed 4 $$\frac{2}{6}$$ cups of orange juice with 3 $$\frac{1}{6}$$ cups of pineapple juice to make fruit punch. She and her friends drank 3 $$\frac{4}{6}$$ cups of the punch. How much of the fruit punch is left?
_____ $$\frac{□}{□}$$ cups

### Add and Subtract Mixed Numbers – Page No. 432

Rename the fractions to solve.

Many instruments are coiled or curved so that they are easier for the musician to play, but they would be quite long if straightened out completely.

Question 13.
Analyze Relationships Trumpets and cornets are brass instruments. Fully stretched out, the length of a trumpet is 5 $$\frac{1}{4}$$ feet and the length of a cornet is 4 $$\frac{2}{4}$$ feet. The trumpet is how much longer than the cornet?
$$\frac{□}{□}$$ feet

Question 14.
Tubas, trombones, and French horns are brass instruments. Fully stretched out, the length of a tuba is 18 feet, the length of a trombone is 9 $$\frac{11}{12}$$ feet, and the length of a French horn is 17 $$\frac{1}{12}$$ feet. The tuba is how much longer than the French horn? The French horn is how much longer than the trombone?
Type below:
_____________

Question 15.
The pitch of a musical instrument is related to its length. In general, the greater the length of a musical instrument, the lower its pitch. Order the brass instruments identified on this page from lowest pitch to the highest pitch.
____________
____________
____________

Question 16.
Alicia had 3 $$\frac{1}{6}$$yards of fabric. After making a tablecloth, she had 1 $$\frac{3}{6}$$ yards of fabric. Alicia said she used 2 $$\frac{3}{6}$$ yards of fabric for the tablecloth. Do you agree? Explain.
______

### Record Subtraction with Renaming – Page No. 433

Find the difference.

Question 1.

Question 2.
6
− 3 $$\frac{2}{5}$$
_______ $$\frac{□}{□}$$

Question 3.
5 $$\frac{1}{4}$$
− 2 $$\frac{3}{4}$$
_______ $$\frac{□}{□}$$

Question 4.
9 $$\frac{3}{8}$$
− 8 $$\frac{7}{8}$$
$$\frac{□}{□}$$

Question 5.
12 $$\frac{3}{10}$$
− 7 $$\frac{7}{10}$$
______ $$\frac{□}{□}$$

Question 6.
8 $$\frac{1}{6}$$
− 3 $$\frac{5}{6}$$
_____ $$\frac{□}{□}$$

Question 7.
7 $$\frac{3}{5}$$
− 4 $$\frac{4}{5}$$
_____ $$\frac{□}{□}$$

Question 8.
10 $$\frac{1}{2}$$
− 8 $$\frac{1}{2}$$
_____ $$\frac{□}{□}$$

Question 9.
7 $$\frac{1}{6}$$
− 2 $$\frac{5}{6}$$
_____ $$\frac{□}{□}$$

Question 10.
9 $$\frac{3}{12}$$
− 4 $$\frac{7}{12}$$
_____ $$\frac{□}{□}$$

Question 11.
9 $$\frac{1}{10}$$
− 8 $$\frac{7}{10}$$
_____ $$\frac{□}{□}$$

Question 12.
9 $$\frac{1}{3}$$
− $$\frac{2}{3}$$
_____ $$\frac{□}{□}$$

Question 13.
3 $$\frac{1}{4}$$
− 1 $$\frac{3}{4}$$
_____ $$\frac{□}{□}$$

Question 14.
4 $$\frac{5}{8}$$
− 1 $$\frac{7}{8}$$
_____ $$\frac{□}{□}$$

Question 15.
5 $$\frac{1}{12}$$
− 3 $$\frac{8}{12}$$
_____ $$\frac{□}{□}$$

Question 16.
7
− 1 $$\frac{3}{5}$$
_____ $$\frac{□}{□}$$

Problem Solving

Question 17.
Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 $$\frac{1}{8}$$ pounds for a small fish bowl. How much is left?
_____ $$\frac{□}{□}$$

Question 18.
Xavier made 25 pounds of roasted almonds for a fair. He has 3 $$\frac{1}{2}$$ pounds left at the end of the fair. How many pounds of roasted almonds did he sell at the fair?
_____ $$\frac{□}{□}$$

### Record Subtraction with Renaming – Lesson Check – Page No. 434

Question 1.
Reggie is making a double-layer cake. The recipe for the first layer calls for 2 $$\frac{1}{4}$$ cups sugar. The recipe for the second layer calls for 1 $$\frac{1}{4}$$ cups sugar. Reggie has 5 cups of sugar. How much will he have left after making both recipes?
Options:
a. 1 $$\frac{1}{4}$$ cups
b. 1 $$\frac{2}{4}$$ cups
c. 2 $$\frac{1}{4}$$ cups
d. 2 $$\frac{2}{4}$$ cups

Question 2.
Kate has 4 $$\frac{3}{8}$$ yards of fabric and needs 2 $$\frac{7}{8}$$ yards to make a skirt. How much extra fabric will she have left after making the skirt?
Options:
a. 2 $$\frac{4}{8}$$ yards
b. 2 $$\frac{2}{8}$$ yards
c. 1 $$\frac{4}{8}$$ yards
d. 1 $$\frac{2}{8}$$ yards

Spiral Review

Question 3.
Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame. If he decorates 8 picture frames, how many beads will he put on each frame?
Options:
a. 6
b. 7
c. 14
d. 16

Question 4.
Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors. She knows there will be 6 or 8 guests at the party. What is the least number of party favors Madison should make?
Options:
a. 18
b. 24
c. 30
d. 32

Question 5.
A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people. If the bus is full on each one-way trip, how many passengers are carried by the bus each day?
Options:
a. 96
b. 162
c. 182
d. 192

Question 6.
To make a fruit salad, Marvin mixes 1 $$\frac{3}{4}$$ cups of diced peaches with 2 $$\frac{1}{4}$$ cups of diced pears. How many cups of peaches and pears are in the fruit salad?
Options:
a. 4 cups
b. 3 $$\frac{2}{4}$$ cups
c. 3 $$\frac{1}{4}$$ cups
d. 3 cups

### Record Subtraction with Renaming – Page No. 437

Question 1.
Complete. Name the property used.
$$\left(3 \frac{4}{10}+5 \frac{2}{10}\right)+\frac{6}{10}$$
______ $$\frac{□}{□}$$

Use the properties and mental math to find the sum.

Question 2.
$$\left(2 \frac{7}{8}+3 \frac{2}{8}\right)+1 \frac{1}{8}$$
______ $$\frac{□}{□}$$

Question 3.
$$1 \frac{2}{5}+\left(1+\frac{3}{5}\right)$$
______

Question 4.
$$5 \frac{3}{6}+\left(5 \frac{5}{6}+4 \frac{3}{6}\right)$$
______ $$\frac{□}{□}$$

Question 5.
$$\left(1 \frac{1}{4}+1 \frac{1}{4}\right)+2 \frac{3}{4}$$
______ $$\frac{□}{□}$$

Question 6.
$$\left(12 \frac{4}{9}+1 \frac{2}{9}\right)+3 \frac{5}{9}$$
______ $$\frac{□}{□}$$

Question 7.
$$\left(\frac{3}{12}+1 \frac{8}{12}\right)+\frac{9}{12}$$
______ $$\frac{□}{□}$$

Use the properties and mental math to find the sum.

Question 8.
$$\left(45 \frac{1}{3}+6 \frac{1}{3}\right)+38 \frac{2}{3}$$
______ $$\frac{□}{□}$$

Question 9.
$$\frac{1}{2}+\left(103 \frac{1}{2}+12\right)$$
______ $$\frac{□}{□}$$

Question 10.
$$\left(3 \frac{5}{10}+10\right)+11 \frac{5}{10}$$
______

Question 11.
Pablo is training for a marathon. He ran 5 $$\frac{4}{8}$$ miles on Friday, 6 $$\frac{5}{8}$$ miles on Saturday, and 7 $$\frac{4}{8}$$ miles on Sunday. How many miles did he run on all three days?
______ $$\frac{□}{□}$$ miles

Question 12.
At lunchtime, Dale’s Diner served a total of 2 $$\frac{2}{6}$$ pots of vegetable soup, 3 $$\frac{5}{6}$$ pots of chicken soup, and 4 $$\frac{3}{6}$$ pots of tomato soup. How many pots of soup were served in all?
______ $$\frac{□}{□}$$ pots

Use the expressions in the box for 13–14.

Question 13.
Which property of addition would you use to regroup the addends in Expression A?
______ property

Question 14.
Which two expressions have the same value?
________ and _________

Question 15.
Match the equation with the property used.

Type below:
_________

### Record Subtraction with Renaming – Page No. 438

Pose a Problem

Question 16.
Costumes are being made for the high school musical. The table at the right shows the amount of fabric needed for the costumes of the male and female leads. Alice uses the expression $$7 \frac{3}{8}+1 \frac{5}{8}+2 \frac{4}{8}$$ to find the total amount of fabric needed for the costume of the female lead. To find the value of the expression using mental math, Alice used the properties of addition.
$$7 \frac{3}{8}+1 \frac{5}{8}+2 \frac{4}{8}=\left(7 \frac{3}{8}+1 \frac{5}{8}\right)+2 \frac{4}{8}$$
Alice added 7 + 1 and was able to quickly add $$\frac{3}{8}$$ and $$\frac{5}{8}$$ to the sum of 8 to get 9. She added 2 $$\frac{4}{8}$$ to 9, so her answer was 11 $$\frac{4}{8}$$.
So, the amount of fabric needed for the costume of the female lead actor is 11 $$\frac{4}{8}$$ yards.
Write a new problem using the information for the costume for the male lead actor.
Pose a Problem                     Solve your problem. Check your solution.
Type below:
_____________

Question 16.
Identify Relationships Explain how using the properties of addition makes both problems easier to solve.
Type below:
____________

### Fractions and Properties of Addition – Page No. 439

Use the properties and mental math to find the sum.

Question 1.

Question 2.
$$10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)$$
_______ $$\frac{□}{□}$$

Question 3.
$$8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)$$
_______ $$\frac{□}{□}$$

Question 4.
$$6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)$$
_______ $$\frac{□}{□}$$

Question 5.
$$\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}$$
_______ $$\frac{□}{□}$$

Question 6.
$$\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}$$
_______ $$\frac{□}{□}$$

Question 7.
$$7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)$$
_______ $$\frac{□}{□}$$

Question 8.
$$14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)$$
_______ $$\frac{□}{□}$$

Question 9.
$$\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}$$
_______ $$\frac{□}{□}$$

Problem Solving

Question 10.
Nate’s classroom has three tables of different lengths. One has a length of 4 $$\frac{1}{2}$$ feet, another has a length of 4 feet, and a third has a length of 2 $$\frac{1}{2}$$ feet. What is the length of all three tables when pushed end to end?
_______ $$\frac{□}{□}$$

Question 11.
Mr. Warren uses 2 $$\frac{1}{4}$$ bags of mulch for his garden and another 4 $$\frac{1}{4}$$ bags for his front yard. He also uses $$\frac{3}{4}$$ bag around a fountain. How many total bags of mulch does Mr. Warren use?
_______ $$\frac{□}{□}$$

### Fractions and Properties of Addition – Lesson Check – Page No. 440

Question 1.
A carpenter cut a board into three pieces. One piece was 2 $$\frac{5}{6}$$ feet long. The second piece was 3 $$\frac{1}{6}$$ feet long. The third piece was 1 $$\frac{5}{6}$$ feet long. How long was the board?
Options:
a. 6 $$\frac{5}{6}$$ feet
b. 7 $$\frac{1}{6}$$ feet
c. 7 $$\frac{5}{6}$$ feet
d. 8 $$\frac{1}{6}$$ feet

Question 2.
Harry works at an apple orchard. He picked 45 $$\frac{7}{8}$$ pounds of apples on Monday. He picked 42 $$\frac{3}{8}$$ pounds of apples on Wednesday. He picked 54 $$\frac{1}{8}$$ pounds of apples on Friday. How many pounds of apples did Harry pick those three days?
Options:
a. 132 $$\frac{3}{8}$$ pounds
b. 141 $$\frac{3}{8}$$ pounds
c. 142 $$\frac{1}{8}$$ pounds
d. 142 $$\frac{3}{8}$$ pounds

Spiral Review

Question 3.
There were 6 oranges in the refrigerator. Joey and his friends ate 3 $$\frac{2}{3}$$ oranges. How many oranges were left?
Options:
a. 2 $$\frac{1}{3}$$ oranges
b. 2 $$\frac{2}{3}$$ oranges
c. 3 $$\frac{1}{3}$$ oranges
d. 9 $$\frac{2}{3}$$ oranges

Question 4.
Darlene was asked to identify which of the following numbers is prime. Which number should she choose?
Options:
a. 2
b. 12
c. 21
d. 39

Question 5.
A teacher has 100 chairs to arrange for an assembly. Which of the following is NOT a way the teacher could arrange the chairs?
Options:
a. 10 rows of 10 chairs
b. 8 rows of 15 chairs
c. 5 rows of 20 chairs
d. 4 rows of 25 chairs

Question 6.
Nic bought 28 folding chairs for $16 each. How much money did Nic spend on chairs? Options: a.$196
b. $348 c.$448
d. $600 ### Fractions and Properties of Addition – Lesson Check – Page No. 443 Question 1. Last week, Sia ran 1 $$\frac{1}{4}$$ miles each day for 5 days and then took 2 days off. Did she run at least 6 miles last week? First, model the problem. Describe your model. Type below: _________ Question 1. Then, regroup the parts in the model to find the number of whole miles Sia ran. Sia ran ___________ whole miles and ___________ mile. Finally, compare the total number of miles she ran to 6 miles. So, Sia ___________ run at least 6 miles last week. 6 $$\frac{1}{4}$$ miles _____ 6 miles Question 2. What if Sia ran only $$\frac{3}{4}$$ mile each day. Would she have run at least 6 miles last week? Explain. _____ Question 3. A quarter is $$\frac{1}{4}$$ dollar. Noah has 20 quarters. How much money does he have? Explain.$ _____

Question 4.
How many $$\frac{2}{5}$$ parts are in 2 wholes?
_____

### Fractions and Properties of Addition – Lesson Check – Page No. 444

Question 5.
A company shipped 15,325 boxes of apples and 12,980 boxes of oranges. How many more boxes of apples than oranges did the company ship?
_____ boxes

Question 6.
Analyze A fair sold a total of 3,300 tickets on Friday and Saturday. It sold 100 more on Friday than on Saturday. How many tickets did the fair sell on Friday?
_____ tickets

Question 7.
Emma walked $$\frac{1}{4}$$ mile on Monday, $$\frac{2}{4}$$ mile on Tuesday, and $$\frac{3}{4}$$ mile on Wednesday. If the pattern continues, how many miles will she walk on Friday? Explain how you found the number of miles.
$$\frac{□}{□}$$ miles

Question 8.
Jared painted a mug $$\frac{5}{12}$$ red and $$\frac{4}{12}$$ blue. What part of the mug is not red or blue?
$$\frac{□}{□}$$

Question 9.
Choose the number that correctly completes the sentence.
Each day, Mrs. Hewes knits $$\frac{1}{3}$$ of a scarf in the morning and $$\frac{1}{3}$$ of a scarf in the afternoon.
It will take Mrs. Hewes days to knit 2 scarves.
_____

### Fractions and Properties of Addition – Page No. 445

Read each problem and solve.

Question 1.
Each child in the Smith family was given an orange cut into 8 equal sections. Each child ate $$\frac{5}{8}$$ of the orange. After combining the leftover sections, Mrs. Smith noted that there were exactly 3 full oranges left. How many children are in the Smith family?

Question 2.
Val walks 2 $$\frac{3}{5}$$ miles each day. Bill runs 10 miles once every 4 days. In 4 days, who covers the greater distance?
_________

Question 3.
Chad buys peanuts in 2-pound bags. He repackages them into bags that hold $$\frac{5}{6}$$ pound of peanuts. How many 2-pound bags of peanuts should Chad buy so that he can fill the $$\frac{5}{6}$$ -pound bags without having any peanuts left over?
_________ 2-pound bags

Question 4.
A carpenter has several boards of equal length. He cuts $$\frac{3}{5}$$ of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with?
_________

### Fractions and Properties of Addition – Lesson Check – Page No. 446

Question 1.
Karyn cuts a length of ribbon into 4 equal pieces, each 1 $$\frac{1}{4}$$ feet long. How long was the ribbon?
Options:
a. 4 feet
b. 4 $$\frac{1}{4}$$ feet
c. 5 feet
d. 5 $$\frac{1}{4}$$ feet

Question 2.
Several friends each had $$\frac{2}{5}$$ of a bag of peanuts left over from the baseball game. They realized that they could have bought 2 fewer bags of peanuts between them. How many friends went to the game?
Options:
a. 6
b. 5
c. 4
d. 2

Spiral Review

Question 3.
A frog made three jumps. The first was 12 $$\frac{5}{6}$$ inches. The second jump was 8 $$\frac{3}{6}$$ inches. The third jump was 15 $$\frac{1}{6}$$ inches. What was the total distance the frog jumped?
Options:
a. 35 $$\frac{3}{6}$$ inches
b. 36 $$\frac{1}{6}$$ inches
c. 36 $$\frac{3}{6}$$ inches
d. 38 $$\frac{1}{6}$$ inches

Question 4.
LaDanian wants to write the fraction $$\frac{4}{6}$$ as a sum of unit fractions. Which expression should he write?
Options:
a. $$\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}$$
b. $$\frac{2}{6}+\frac{2}{6}$$
c. $$\frac{3}{6}+\frac{1}{6}$$
d. $$\frac{1}{6}+\frac{1}{6}+\frac{2}{6}$$

Question 5.
Greta made a design with squares. She colored 8 out of the 12 squares blue. What fraction of the squares did she color blue?
Options:
a. $$\frac{1}{4}$$
b. $$\frac{1}{3}$$
c. $$\frac{2}{3}$$
d. $$\frac{3}{4}$$

Question 6.
The teacher gave this pattern to the class: the first term is 5 and the rule is add 4, subtract 1. Each student says one number. The first student says 5. Victor is tenth in line. What number should Victor say?
Options:
a. 17
b. 19
c. 20
d. 21

### Fractions and Properties of Addition – Page No. 447

Question 1.
A painter mixed $$\frac{1}{4}$$ quart of red paint with $$\frac{3}{4}$$ blue paint to make purple paint.

How much purple paint did the painter make?
_____ quart of purple paint

Question 2.
Ivan biked 1 $$\frac{2}{3}$$ hours on Monday, 2 $$\frac{1}{3}$$ hours on Tuesday, and 2 $$\frac{2}{3}$$ hours on Wednesday. What is the total number of hours Ivan spent biking?
Ivan spen _______ hours biking.
_____ $$\frac{□}{□}$$

Question 3.
Tricia had 4 $$\frac{1}{8}$$ yards of fabric to make curtains. When she finished she had 2 $$\frac{3}{8}$$ yards of fabric left. She said she used 2 $$\frac{2}{8}$$ yards of fabric for the curtains. Do you agree? Explain.
______

### Fractions and Properties of Addition – Page No. 448

Question 4.
Miguel’s class went to the state fair. The fairground is divided into sections. Rides are in $$\frac{6}{10}$$ of the fairground. Games are in $$\frac{2}{10}$$ of the fairground. Farm exhibits are in $$\frac{1}{10}$$ of the fairground.
Part A
Use the model. What fraction of the fairground is rides and games?

The fraction of the fairground with games and rides is ______ .
$$\frac{□}{□}$$

Question 4.
Part B
How much greater is the part of the fairground with rides than with farm exhibits? Explain how the model could be used to find the answer.
$$\frac{□}{□}$$

Question 5.
Rita is making chili. The recipe calls for 2 $$\frac{3}{4}$$ cups of tomatoes. How many cups of tomatoes, written as a fraction greater than one, are used in the recipe?
_____ cups

Question 6.
Lamar’s mom sells sports equipment online. She sold $$\frac{9}{10}$$ of the sports equipment. Select a way $$\frac{9}{10}$$ can be written as a sum of fractions. Mark all that apply.
Options:
a. $$\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{2}{10}$$
b. $$\frac{3}{10}+\frac{2}{10}+\frac{3}{10}+\frac{1}{10}$$
c. $$\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{2}{10}$$
d. $$\frac{4}{10}+\frac{1}{10}+\frac{1}{10}+\frac{3}{10}$$
e. $$\frac{4}{10}+\frac{3}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}$$
f. $$\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{3}{10}$$

### Fractions and Properties of Addition – Page No. 449

Question 7.
Bella brought $$\frac{8}{10}$$ gallon of water on a hiking trip. She drank $$\frac{6}{10}$$ gallon of water. How much water is left?
$$\frac{□}{□}$$ gallons

Question 8.
In a survey, $$\frac{6}{10}$$ of the students chose Saturday and $$\frac{1}{10}$$ chose Monday as their favorite day of the week. What fraction shows the students who chose Saturday or Monday as their favorite day?
Part A

$$\frac{□}{□}$$

Question 8.
Part B
How are the numerator and denominator of your answer related to the model? Explain.
Type below:
___________

Question 9.
Match the equation with the property used.

Type below:
__________________

### Fractions and Properties of Addition – Page No. 450

Question 10.
For numbers 10a–10e, select Yes or No to show if the sum or difference is correct.
(a) $$\frac{2}{8}+\frac{1}{8}=\frac{3}{8}$$
i. yes
ii. no

Question 10.
(b) $$\frac{4}{5}+\frac{1}{5}=\frac{5}{5}$$
i. yes
ii. no

Question 10.
(c) $$\frac{4}{6}+\frac{1}{6}=\frac{5}{12}$$
i. yes
ii. no

Question 10.
(d) $$\frac{6}{12}-\frac{4}{12}=\frac{2}{12}$$
i. yes
ii. no

Question 10.
(e) $$\frac{7}{9}-\frac{2}{9}=\frac{9}{9}$$
i. yes
ii. no

Question 11.
Gina has 5 $$\frac{2}{6}$$ feet of silver ribbon and 2 $$\frac{4}{6}$$ of gold ribbon. How much more silver ribbon does Gina have than gold ribbon?
______ $$\frac{□}{□}$$ feet more silver ribbon

Question 12.
Jill is making a long cape. She needs 4 $$\frac{1}{3}$$ yards of blue fabric for the outside of the cape. She needs 3 $$\frac{2}{3}$$ yards of purple fabric for the lining of the cape.
Part A
Jill incorrectly subtracted the two mixed numbers to find how much more blue fabric than purple fabric she should buy. Her work is shown below.
$$4 \frac{1}{3}-3 \frac{2}{3}=\frac{12}{3}-\frac{9}{3}=\frac{3}{3}$$
Why is Jill’s work incorrect?
Type below:
__________________

Question 12.
Part B
How much more blue fabric than purple fabric should Jill buy? Show your work.
$$\frac{□}{□}$$

### Fractions and Properties of Addition – Page No. 451

Question 13.
Russ has two jars of glue. One jar is $$\frac{1}{5}$$ full. The other jar is $$\frac{2}{5}$$ full.

Use the fractions to write an equation to find the amount of glue Russ has.

Type below:
_________________

Question 14.
Gertie ran $$\frac{3}{4}$$ mile during physical education class. Sarah ran $$\frac{2}{4}$$ mile during the same class. How much farther did Gertie run than Sarah? Shade the model to show your answer.

$$\frac{□}{□}$$

Question 15.
Teresa planted marigolds in $$\frac{2}{8}$$ of her garden and petunias in $$\frac{3}{8}$$ of her garden. What fraction of the garden has marigolds and petunias?
$$\frac{□}{□}$$

Question 16.
Draw a line to show the mixed number and fraction that have the same value.

Question 17.
Each day, Tally’s baby sister eats $$\frac{1}{4}$$ cup of rice cereal in the morning and $$\frac{1}{4}$$ cup of rice cereal in the afternoon. It will take Tally’s sister days to eat 2 cups of rice cereal.
Type below:
_________________

### Fractions and Properties of Addition – Page No. 452

Question 18.
Three girls are selling cases of popcorn to earn money for a band trip. In week 1, Emily sold 2 $$\frac{3}{4}$$ cases, Brenda sold 4 $$\frac{1}{4}$$ cases, and Shannon sold 3 $$\frac{1}{2}$$ cases.
Part A
How many cases of popcorn have the girls sold in all? Explain how you found your answer.
______ $$\frac{□}{□}$$

Question 18.
Part B
The girls must sell a total of 35 cases in order to have enough money for the trip. Suppose they sell the same amount in week 2 and week 3 of the sale as in week 1. Will the girls have sold enough cases of popcorn to go on the trip? Explain.
______

Question 19.
Henry ate $$\frac{3}{8}$$ of a sandwich. Keith ate $$\frac{4}{8}$$ of the same sandwich. How much more of the sandwich did Keith eat than Henry?
$$\frac{□}{□}$$ of the sandwich

Question 20.
For numbers 20a–20d, choose True or False for each sentence.
a. $$1 \frac{4}{9}+2 \frac{6}{9}$$ is equal to 4 $$\frac{1}{9}$$
i. True
ii. False

Question 20.
b. $$3 \frac{5}{6}+2 \frac{3}{6}$$ is equal to 5 $$\frac{2}{6}$$
i. True
ii. False

Question 20.
c. $$4 \frac{5}{8}-2 \frac{4}{8}$$ is equal to 2 $$\frac{3}{8}$$
i. True
ii. False

Question 20.
d. $$5 \frac{5}{8}-3 \frac{2}{8}$$ is equal to 2 $$\frac{3}{8}$$
i. True
ii. False

Question 21.
Justin lives 4 $$\frac{3}{5}$$ miles from his grandfather’s house. Write the mixed number as a fraction greater than one.
4 $$\frac{3}{5}$$ = $$\frac{□}{□}$$

### Fractions and Properties of Addition – Page No. 457

Question 1.
Use the picture to complete the equations.

$$\frac{3}{4}$$ = _ + _ + _
$$\frac{3}{4}$$ = _ × $$\frac{1}{4}$$
Type below:
___________

Write the fraction as a product of a whole number and a unit fraction.

Question 2.
$$\frac{4}{5}$$ = ______ × $$\frac{1}{5}$$

Question 3.
$$\frac{3}{10}$$ = ______ × $$\frac{1}{10}$$

Question 4.
$$\frac{8}{3}$$ = ______ × $$\frac{1}{3}$$

List the next four multiples of the unit fraction.

Question 5.
$$\frac{1}{6}$$ ,
Type below:
___________

Question 6.
$$\frac{1}{3}$$ ,
Type below:
___________

Write the fraction as a product of a whole number and a unit fraction.

Question 7.
$$\frac{5}{6}$$ = ______ × $$\frac{1}{6}$$

Question 8.
$$\frac{9}{4}$$ = ______ × $$\frac{1}{4}$$

Question 9.
$$\frac{3}{100}$$ = ______ × $$\frac{1}{100}$$

List the next four multiples of the unit fraction.

Question 10.
$$\frac{1}{10}$$ ,
Type below:
___________

Question 11.
$$\frac{1}{8}$$ ,
Type below:
___________

Question 12.
Robyn uses $$\frac{1}{2}$$ cup of blueberries to make each loaf of blueberry bread. Explain how many loaves of blueberry bread she can make with 2 $$\frac{1}{2}$$ cups of blueberries.
_____ loaves of blueberry bread

Question 13.
Nigel cut a loaf of bread into 12 equal slices. His family ate some of the bread and now $$\frac{5}{12}$$ of the loaf is left. Nigel wants to put each of the leftover slices in its own bag. How many bags does Nigel need?
_____ bags

Question 14.
Which fraction is a multiple of $$\frac{1}{5}$$? Mark all that apply.
Options:
a. $$\frac{4}{5}$$
b. $$\frac{5}{7}$$
c. $$\frac{5}{9}$$
d. $$\frac{3}{5}$$

### Fractions and Properties of Addition – Page No. 458

Sense or Nonsense?

Question 15.
Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.

Type below:
_________________

Question 15.
For the statement that is nonsense, write a new statement that makes sense.
Type below:
_________________

## Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million

### Common Core – Model Place Value Relationships (Page 5)

Question 1.
Describe the pattern in the shapes of the models. What will be the shape of the model for 10,000?

Question 2.
Describe the pattern you see in the sizes of the models. How will the size of the model for 100,000 compare to the size of the model for 10,000?

### Common Core – Model Place Value Relationships (Page 6)

Value of a Digit

The value of a digit depends on its place-value position in the number. A place-value chart can help you understand the value of each digit in a number. The value of each place is 10 times the value of the place to the right.

Question 1.
The value of the digit 9 is 9 ten thousands, or:

Compare the values of the underlined digits.
2,304 16,135

Question 2.
STEP 1 Find the value of 3 in 2,304.
Show 2,304 in a place-value chart.

Question 2.
STEP 2 Find the value of 3 in 16,135.

Show 16,135 in a place-value chart.
So, the value of 3 in 2,304 is ___________ times the value of 3 in 16,135.

### Common Core – Model Place Value Relationships (Page 7)

Question 1.
Complete the table below.

Find the value of the underlined digit.

Question 2.
703,890

Question 3.
63,540

Question 4.
182,034

Question 5.
345,890

Compare the values of the underlined digits.

Question 6.
2,000 and 200

The value of 2 in 2,000 is ___________ times the value of 2 in 200

Question 7.
40 and 400

The value of 4 in 400 is ___________ times the value of 4 in 40

Find the value of the underlined digit.

Question 8.
230,001

Question 9.
803,040

Question 10.
46,842

Question 11.
980,650

Compare the values of the underlined digits.

Question 12.
67,908 and 76,908

Question 13.
546,300 and 3,456

Question 14.
Greg has collected 4,385 pennies and Hannah has collected 3,899 pennies. How many times as great as the value of 3 in 4,385 is the value of 3 in 3,899?

Question 15.
Shawn wants to model the number 13,450 using base-ten blocks. How many large cubes, flats, and longs does he need to model the number?

### Common Core – Model Place Value Relationships (Page 8)

Question 14.
What is the value of the digit 7 in the population of Memphis?

Question 14.
What is the value of the digit 1 in the population of Denver?

Question 14.
How many times as great as the value of the digit 1 in the population of Cleveland is this value?

Question 14.
Which city’s population has a 4 in the hundred thousands place?

Question 15.
How many models of 100 do you need to model 3,200? Explain.

Question 16.
Sid wrote 541,309 on his paper. Using numbers and words, explain how the number would change if he switched the digits in the hundred thousands and tens places.

Question 17.
There are 686,147 books at the Greenville Library. What is the value of the digit 8 in this number?
(a) 80
(b) 8,000
(c) 80,000
(d) 800.000

Question 18.
The value of 7 in 375,081 is 7,000.
(a) True
(b) False

Question 18.
The value of 6 in 269,480 is 600,000.
(a) True
(b) False

Question 18.
The value of 5 in 427,593 is 500.
(a) True
(b) False

Question 18.
The value of 1 in 375,081 is 10.
(a) True
(b) False

Question 18.
The value of 4 in 943,268 is 40,000.
(a) True
(b) False

### Model Place Value Relationships

Find the value of the underlined digit.

Question 1.
6,035
30

Question 2.
43,782

Question 3.
506,087

Question 4.
49,254

Question 5.
136,422

Question 6.
673,512

Question 7.
814,295

Question 8.
736,144

Compare the values of the underlined digits.

Question 9.
6,300 and 530

The value of 3 in ___________ is ___________ times the value of 3 in ___________ .

Question 10.
2,783 and 7,283

The value of 2 in ___________ is ___________ times the value of 2 in ___________ .

Question 11.
34,258 and 47,163

The value of 4 in ___________ is ___________ times the value of 4 in ___________.

Question 12.
503,497 and 26,475

The value of 7 in ___________ is ___________ times the value of 7 in ___________ .

Problem Solving

Use the table for 13–14.

Question 13.
What is the value of the digit 9 in the attendance at the Redskins vs. Titans game?

The value of 9 is ___________ .

Question 14.
The attendance at which game has a 7 in the ten thousands place?

### Common Core – Model Place Value Relationships (Page 10)

Lesson Check

Question 1.
During one season, a total of 453,193 people attended a baseball team’s games. What is the value of the digit 5 in the number of people?
(a) 500
(b) 5,000
(c) 50,000
(d) 500,000

Question 2.
Hal forgot the number of people at the basketball game. He does remember that the number had a 3 in the tens place. Which number could Hal be thinking of?
(a) 7,321
(b) 3,172
(c) 2,713
(d) 1,237

Spiral Review

Question 3.
Hot dog buns come in packages of 8. For the school picnic, Mr. Spencer bought 30 packages of hot dog buns. How many hot dog buns did he buy?
(a) 24
(b) 38
(c) 110
(d) 240

Question 4.
There are 8 students on the minibus. Five of the students are boys. What fraction of the students are boys?
(a) $$\frac{3}{8}$$
(b) $$\frac{5}{8}$$
(c) $$\frac{5}{5}$$
(d) $$\frac{8}{8}$$

Question 5.
The clock below shows the time when Amber leaves home for school. At what time does Amber leave home?

(a) 2:41
(b) 8:02
(c) 8:10
(d) 8:20

Question 6.
Jeremy drew a polygon with four right angles and four sides with the same length.

What kind of polygon did Jeremy draw?
(a) hexagon
(b) square
(c) trapezoid
(d) triangle

### Common Core – Read and Write Numbers (Page 11)

Question 1.
The International Space Station uses 262,400 solar cells to change sunlight to electricity. Write 262,400 in standard form, word form, and expanded form.

Use a place-value chart. Each group of three digits separated by a comma is called a period. Each period has hundreds, tens, and ones. The greatest place-value position in the thousands period is hundred thousands.

Write 262,400 in the place-value chart below.

Use place value to read and write numbers.

Question 2.
Word Form: ninety-two thousand,one hundred seventy
Standard Form: ___________
Expanded Form: 90,000 + 2,000 + ___________ + 70

Question 2.
Standard Form: 200,007
Word Form: two hundred ___________
Expanded Form: ___________ + 7

### Common Core – Read and Write Numbers (Page 12)

Question 1.
How can you use place value and period names to read and write 324,904 in word form?

Read and write the number in two other forms.

Question 2.
four hundred eight thousand, seventeen

Question 3.
65,058

Read and write the number in two other forms.

Question 4.
five hundred eight thousand

Question 5.
forty thousand, six hundred nineteen

Question 6.
570,020

Question 7.
400,000 + 60,000 + 5,000 + 100

Question 8.
During the week of the county fair, fifteen thousand, six hundred nine entry tickets were sold. Is it correct to write the number as 15,069? Explain.

Question 9.
There were 94,172 people at a football game on Saturday. On Monday, 1,000 fewer people were at a football game. In word form, how many people were at the football game on Monday?

Question 10.
Richard got 263,148 hits when he did an Internet search. What is the value of the digit 6 in this number? Explain.

### Common Core – Read and Write Numbers (Page 13)

Question 11.
Yvonne wrote the numbers sixteen thousand, nine hundred eighteen and 64,704 on the board. Which of the numbers has a greater value in the thousands place?

Question 12.
Matthew found the sum of 3 thousands 4 hundreds 3 tens 1 one + 4 thousands 8 hundreds 3 tens 5 ones. Victoria found the sum of 5 thousands 7 hundreds 4 ones + 3 thousands 2 hundreds 3 tens 1 one. Who had the greater sum? What was the greater sum?

Who had the greater sum?
What was the greater sum?

Use the table for 13–15.

Question 13.
Use Graphs Which city has a population of two hundred fifty-five thousand, one hundred twenty-four?

Question 14.
Write the population of Raleigh in expanded form and word form.

Question 15.
What’s the Error? Sophia said that the expanded form for 605,970 is 600,000 + 50,000 + 900 + 70. Describe Sophia’s error and give the correct answer.

### Common Core – Read and Write Numbers (Page 14)

Question 16.
Mark tossed six balls while playing a number game. Three balls landed in one section, and three balls landed in another section. His score is greater than one hundred thousand. What could his score be?

a. What do you know?

Question 16.
b. How can you use what you know about place value to find what Mark’s score could be?

Question 16.
c. Draw a diagram to show one way to solve the problem.

Question 16.
Complete the sentences.
Three balls could have landed in the ___________ section.
Three balls could have landed in the ___________ section.
Mark’s score could be ___________

Question 17.
What is another way to write 615,004?
Mark all that apply.
(a) six hundred fifteen thousand, four
(b) six hundred five thousand, fourteen
(c) 60,000 + 10,000 + 5,000 + 4
(d) 600,000 + 10,000 + 5,000 + 4

### Common Core – Read and Write Numbers (Page 15)

Read and Write Numbers

Read and write the number in two other forms.

Question 1.
six hundred ninety-two thousand, four
standard form: 692,004;
expanded form: 600,000 + 90,000 + 2,000 + 4

Question 2.
314,207

Question 3.
600,000 + 80,000 + 10

Use the number 913,256.

Question 4.
Write the name of the period that has the digits 913.

Question 5.
Write the digit in the ten thousands place.

Question 6.
Write the value of the digit 9.

Problem Solving

Use the table for 7 and 8.

Question 7.
Which state had a population of eight hundred four thousand, one hundred ninety-four?

Question 8.
What is the value of the digit 8 in Alaska’s population?

### Common Core – Read and Write Numbers (Page 16)

Lesson Check

Question 1.
Based on a 2008 study, children 6–11 years old spend sixty-nine thousand, one hundred eight minutes a year watching television. What is this number written in
standard form?
(a) 6,918
(b) 69,108
(c) 69,180
(d) 690,108

Question 2.
What is the value of the digit 4 in the number 84,230?
(a) 4
(b) 400
(c) 4,000
(d) 40,000

Spiral Review

Question 3.
An ant has 6 legs. How many legs do 8 ants have in all?
(a) 14
(b) 40
(c) 45
(d) 48

Question 4.
Latricia’s vacation is in 4 weeks. There are 7 days in a week. How many days is it until Latricia’s vacation?
(a) 9 days
(b) 11 days
(c) 20 days
(d) 28 days

Question 5.
Marta collected 363 cans. Diego collected 295 cans. How many cans did Marta and Diego collect in all?
(a) 668
(b) 658
(c) 568
(d) 178

Question 6.
The city Tim lives in has 106,534 people. What is the value of the 6 in 106,534?
(a) 6,000
(b) 600
(c) 60
(d) 6

### Common Core – Compare and Order Numbers (Page 18)

Question 1.
Compare 15,327 and 15,341.
Write <, >, or =. Use the number line to help.

15,327 _______ 15,341

Compare. Write <, >, or =.

Question 2.
$631,328 _______$640,009

Question 3.
56,991 _______ 52,880

Question 4.
708,561 _______ 629,672

Question 5.
143,062 _______ 98,643

Order from greatest to least.

Question 6.
20,650; 21,150; 20,890
________ ; ________ ; ________.

Common Core – Read and Write Numbers (Page 19)

Compare. Write <, >, or =.

Question 7.
$2,212 _______$2,600

Question 8.
88,304 _______ 88,304

Question 9.
$524,116 _______$61,090

Question 10.
751,272 _______ 851,001

Order from least to greatest.

Question 11.
41,090; 41,190; 40,009
_______ ; _______ ; _______

Question 12.
910,763; 912,005; 95,408
_______ ; _______ ; _______

Identify Relationships Algebra Write all of the digits that can replace each

Question 13.
567 < 5 _______ 5 < 582

Question 14.
464,545 > 4 _______ 3,535 > 443,550
464,545 > 4 _______ 3,535 > 443,550

Question 15.
Leah’s car has 156,261 miles on the odometer. Casey’s car has 165,002 miles on the odometer. Mike’s car has 145,834 miles on the odometer. Whose car has the most miles? Order the number of miles from least to greatest.

Question 16.
At Monica’s Used Cars, the sales staff set a goal of $25,500 in sales each week. The sales for three weeks were$28,288; $25,369; and$25,876. Which total did not meet the goal?
(a) $28,288 (b)$25,369
(c) $25,876 Question 17. What’s the Error? Max said that 36,594 is less than 5,980 because 3 is less than 5. Describe Max’s error and give the correct answer. ### Common Core – Compare and Order Numbers (Page 20) Use the picture graph for 18–20. Question 18. Use Graphs In which month shown did Grand Canyon National Park have about 7,500 tent campers? Question 19. How many more campers were there in July and August than in June and September? Question 20. What if during the month of October, the park had 22,500 tent campers? How many symbols would be placed on the pictograph for October? Question 21. What’s the Question? Compare: 643,251; 633,512; and 633,893. The answer is 633,512. Question 22. Zachary’s school set a goal of collecting 12,155 cans of food each day. In the first 3 days the school collected 12,250 cans; 10,505 cans; and 12,434 cans. Write each number in the box that tells whether or not the school met its goal. (a) 12,250 cans (b) 10,505 cans (c) 12,434 cans ### Common Core – Compare and Order Numbers (Page 21) Compare and Order Numbers Compare. Write < .> or =. Question 1. 3,273 < 3,279 Question 2.$1,323 _______ $1,400 Question 3. 52,692 _______ 52,692 Question 4.$413,005 _______ $62,910 Question 5. 382,144 _______ 382,144 Question 6. 157,932 _______ 200,013 Question 7. 401,322 _______ 410,322 Question 8. 989,063 _______ 980,639 Question 9. 258,766 _______ 258,596 Order from least to greatest. Question 10. 23,710; 23,751; 23,715 _______< _______ < _______ Question 11. 52,701; 54,025; 5,206 _______ < _______ < _______ Question 12. 465,321; 456,321; 456,231 _______ < _______ < _______ Question 13.$330,820; $329,854;$303,962
_______ < _______ < _______

Problem Solving

Question 14.
An online newspaper had 350,080 visitors in October, 350,489 visitors in November, and 305,939 visitors in December. What is the order of the months from greatest to least number of visitors?
1. _______
2. _______
3. _______

Question 15.
The total land area in square miles of each of three states is shown below.
New Mexico: 121,356
Arizona: 113,635
What is the order of the states from least to greatest total land area?
1. _______
2. _______
3. _______

### Common Core – Compare and Order Numbers (Page 22)

Lesson Check

Question 1.
At the yearly fund-raising drive, the nonprofit company’s goal was to raise $55,500 each day. After three days, it had raised$55,053; $56,482; and$55,593. Which amount was less than the daily goal?
(a) $55,500 (b)$55,053
(c) $55,593 (d)$56,482

Question 2.
Which of the following lists of numbers is in order from greatest to least?
(a) 60,343; 60,433; 63,043
(b) 83,673; 86,733; 86,373
(c) 90,543; 90,048; 93,405
(d) 20,433; 20,343; 20,043

Spiral Review

Question 3.
Jess is comparing fractions. Which fraction is greater than 56?
(a) $$\frac{7}{8}$$
(b) $$\frac{4}{5}$$
(c) $$\frac{3}{4}$$
(d) $$\frac{2}{3}$$

Question 4.
What is the perimeter of the rectangle below?

(a) 14 inches
(b) 26 inches
(c) 28 inches
(d) 48 inches

Question 5.
A website had 826,140 hits last month. What is the value of the 8 in 826,140?
(a) 800
(b) 8,000
(c) 80,000
(d) 800,000

Question 6.
Which is 680,705 written in expanded form?
(a) 680 + 705
(b) 68,000 + 700 + 5
(c) 600,000 + 8,000 + 700 + 5
(d) 600,000 + 80,000 + 700 + 5

### Common Core – Round Numbers (Page 24)

Question 1.
What number is halfway between 100,000 and 200,000?

Question 2.
How does knowing where the halfway point is help you find which hundred thousand 138,202 is closest to? Explain.

Question 3.
What number is halfway between 70,000 and 80,000?

Question 4.
What is 75,000 rounded to the nearest ten thousand? Explain.

Round to the place value of the underlined digit.

Question 5.
64,999

Question 5.
850,000

Question 5.
301,587

Question 5.
10,832

### Common Core – Round Numbers (Page 25)

Question 1.
Suppose 255,113 people live in a city. Is it reasonable to say that about 300,000 people live in the city? Use the number line to help you solve the problem. Explain.

Round to the place value of the underlined digit.

Question 2.
934,567

Question 3.
641,267

Question 4.
234,890

Question 5.
347,456

Question 6.
To the nearest hundred, a factory produced 3,600 jars of applesauce on Thursday and 4,200 jars of apple juice on Friday. To the nearest thousand, how many jars of apple juice did they produce during the two days?

Question 7.
The number 2,000 is missing a digit. The number rounded to the nearest thousand is 3,000. List all of the possibilities for the missing digit. Explain your answer.

### Common Core – Round Numbers (Page 26)

Question 8.
A male elephant weighs 6,728 pounds. A female elephant weighs 5,843 pounds. To the nearest hundred, what is the total weight of the two elephants?

Question 9.
About 300,000 people attended a festival. For numbers 9a–9e choose Yes or No to show whether each number could be the exact number of people that attended the festival.

a. 351,213
(a) yes
(b) no

Question 9.
b. 249,899
(a) yes
(b) no

Question 9.
c. 252,348
(a) yes
(b) no

Question 9.
d. 389,001
(a) yes
(b) no

Question 9.
e. 305,992
(a) yes
(b) no

### Common Core – Round Numbers (Page 27)

Round Numbers

Round to the place value of the underlined digit.

Question 1.

Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.

Change all the digits to the right of the rounding place to zero.

Question 2.
123,499

Question 3.
552,945

Question 4.
389,422

Question 5.
209,767

Question 6.
191,306

Question 7.
66,098

Question 8.
73,590

Question 9.
149,903

Question 10.
684,303

Question 11.
499,553

Problem Solving

Use the table for 12–13.

Question 12.
Find the height of Mt. Whitney in the table. Round the height to the nearest thousand feet.
_______ feet

Question 13.
What is the height of Mt. Bona rounded to the nearest ten thousand feet?
_______ feet

### Common Core – Round Numbers (Page 28)

Lesson Check

Question 1.
Which number is 247,039 rounded to the nearest thousand?
(a) 200,000
(b) 250,000
(c) 247,000
(d) 7,000

Question 2.
To the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008. Which might have been the exact population of Vermont in 2008?
(a) 626,013
(b) 621,270
(c) 614,995
(d) 609,964

Spiral Review

Question 3.
Which symbol makes the following number sentence true?
$546,322 Ο$540,997
(a) <
(b) >
(c) =
(d) +

Question 4.
Pittsburgh International Airport had approximately 714,587 passengers in August 2009. Which number is greater than 714,587?
(a) 714,578
(b) 704,988
(c) 714,601
(d) 714,099

Question 5.
June made a design with 6 equal tiles. One tile is yellow, 2 tiles are blue, and 3 tiles are purple. What fraction of the tiles are yellow or purple?
(a) $$\frac{1}{6}$$
(b) $$\frac{2}{6}$$
(c) $$\frac{3}{6}$$
(d) $$\frac{4}{6}$$

Question 6.
The fourth grade collected 40,583 cans and plastic bottles. Which of the following shows that number in word form?
(a) forty thousand, five hundred eighty
(b) forty thousand, five hundred eighty-three
(c) four thousand, five hundred eighty-three
(d) four hundred thousand, five hundred eighty

### Common Core – Chapter 1 -Mid-Chapter Checkpoint (Page 29)

Choose the best term from the box.

Question 1.
The _______ of 23,850 is 20,000 + 3,000 + 800 + 50.

Question 2.
You can _______ to find about how much or how many.

Question 3.
In 192,860 the digits 1, 9, and 2 are in the same _________

Find the value of the underlined digit.

Question 4.
380,671

Question 5.
10,698

Question 6.
650,234

Write the number in two other forms.

Question 7.
293,805

Question 8.
300,000 + 5,000 + 20 + 6

Compare. Write <, >, or =.

Question 9.
457,380 _______ 458,590

Question 10.
390,040 _______ 39,040

Question 11.
11,809 _______ 11,980

Round to the place of the underlined digit.

Question 12.
140,250

Question 13.
10,450

Question 14.
126,234

### Common Core – Chapter 1 -Mid-Chapter Checkpoint (Page 30)

Question 15.
Last year, three hundred twenty-three thousand people visited the museum. What is this number written in standard form?

Question 16.
Rachael rounded 16,473 to the nearest hundred. Then she rounded her answer to the nearest thousand. What is the final number?

Question 17.
What is the highest volcano in the Cascade Range?

Question 18.
Richard got 263,148 hits when he did an Internet search. What is the value of the digit 6 in this number?

### Common Core – Investigate • Rename Numbers (Page 32)

Question 1.
How is the number of large cubes and flats in the first model related to the number of flats in the second model?

Question 2.
Can you model 1,200 using only longs? Explain.

Question 3.
You renamed 1,200 as hundreds. How can you rename 1,200 as tens? Explain.

Question 4.
What would the models in Step A and Step B look like for 5,200? How can you rename 5,200 as hundreds?

### Common Core – Investigate • Rename Numbers (Page 33)

Rename the number. Draw a quick picture to help.

Question 1.
150
_______ tens

Question 2 (request help)
1,400
_______ hundreds

Question 3.
2 thousands 3 hundreds
_______ hundreds

Question 4.
13 hundreds
_______ thousand _______ hundreds

Rename the number. Use the place-value chart to help.

Question 5.

18 thousands = _______

Question 6.

570,000 = 57 _______

Rename the number.

Question 7 (request help)
580= _______ tens

Question 8.
740,000= _______ten thousands

Question 9.
8 hundreds 4 tens = 84 _______

Question 10.
29 thousands = _______

### Common Core – Investigate • Rename Numbers (Page 34)

Question 11.
A toy store is ordering 3,000 remote control cars. The store can order the cars in sets of 10. How many sets of 10 does the store need to order?
_______ sets

Question 11.
a. What information do you need to use?

Question 11.
b. What do you need to find?

Question 11.
c. How can renaming numbers help you solve this problem?

Question 11.
d. Describe a strategy you can use to solve the problem.

Question 11.
e. How many sets of 10 remote control cars does the store need to buy?
_______ sets

Question 12.
Ivan sold 53 boxes of oranges on Friday and 27 boxes on Saturday during a citrus sale. There were 10 oranges in each box. How many oranges did he sell in all?
_______ oranges

Question 12.
Use Reasoning A store sold a total of 15,000 boxes of buttons last month, and 12,000 boxes this month. If the store sold 270,000 buttons, how many buttons were in each box?
_______ butons

For numbers 14a–14d, select True or False for each statement.

Question 14.
a. 9 hundreds 3 tens can be renamed as 39 tens.
(a) True
(b) False

Question 14.
b. 370,000 can be renamed as 37 ten thousands.
(a) True
(b) False

Question 14.
c. 780 can be renamed as 78 tens.
(a) True
(b) False

Question 14.
d. 42,000 can be renamed as 42 thousands.
(a) True
(b) False

### Common Core – Investigate • Rename Numbers (Page 35)

Rename Numbers
Rename the number. Use the place-value chart to help.

Question 1.
760 hundreds = 76,000

Question 2.
805 tens = _______

 THOUSANDS ONES Hundreds Tens Ones Hundreds Tens Ones

Question 3.
24 ten thousands = ________

 THOUSANDS ONES Hundreds Tens Ones Hundreds Tens Ones

Rename the number.

Question 4.
720 = _______ tens

Question 5.
4 thousands 7 hundreds = 47 _______

Question 6.
25,600 = _______ hundreds

Question 7.
204 thousands = _______

Problem Solving

Question 8.
For the fair, the organizers ordered 32 rolls of tickets. Each roll of tickets has 100 tickets. How many tickets were ordered in all?
_______ tickets

Question 9.
An apple orchard sells apples in bags of 10. The orchard sold a total of 2,430 apples one day. How many bags of apples was this?
_______ bags

Question 10.
Explain how you can rename 5,400 as hundreds. Include a quick picture or a place-value chart in your explanation.
_______ hundreds

### Common Core – Investigate • Rename Numbers (Page 36)

Lesson Check

Question 1.
A dime has the same value as 10 pennies. Marley brought 290 pennies to the bank. How many dimes did Marley get?
(a) 29
(b) 290
(c) 2,900
(d) 29,000

Question 2.
A citrus grower ships grapefruit in boxes of 10. One season, the grower shipped 20,400 boxes of grapefruit. How many grapefruit were shipped?
(a) 204
(b) 2,040
(c) 20,400
(d) 204,000

Spiral Review

Question 3.
There were 2,605 people at the basketball game. A reporter rounded this number to the nearest hundred for a newspaper article. What number did the reporter use?
(a) 2,600
(b) 2,610
(c) 2,700
(d) 3,000

Question 4.
To get to Level 3 in a game, a player must score 14,175 points. Ann scores 14,205 points, Ben scores 14,089 points, and Chuck scores 10,463 points. Which score is greater than the Level 3 score?
(a) 14,205
(b) 14,175
(c) 14,089
(d) 10,463

Question 5.
Henry counted 350 lockers in his school. Hayley counted 403 lockers in her school. Which statement is true?
(a) The 3 in 350 is 10 times the value of the 3 in 403.
(b) The 3 in 350 is 100 times the value of the 3 in 403.
(c) The 3 in 403 is 10 times the value of the 3 in 350.
(d) The 3 in 403 is 100 times the value of the 3 in 350.

Question 6.
There are 4 muffins on each plate. There are 0 plates of lemon muffins. How many lemon muffins are there?
(a) 4
(b) 2
(c) 1
(d) 0

### Common Core – Add Whole Numbers (Page 39)

Question 1.
Use the grid to find 738,901 + 162,389.

Use the grid to align the addends by place value.

Estimate. Then find the sum.

Question 2.
72,931 + 18,563
Estimate: _______
Sum: _______

Question 3.
432,068 + 239,576
Estimate: _______
Sum: _______

Question 4.
64,505 + 38,972
Estimate: _______
Sum: _______

Question 5.
839,136 + 120,193
Estimate: _______
Sum: _______

Question 6.
186,231 + 88,941
Estimate: _______
Sum: _______

Question 7.
744,201 + 168,900
Estimate: _______
Sum: _______

Question 8.
For the first football game of the season, 62,732 fans attended. The number of fans at the second game was 469 more than at the first game. What is the total number of fans that attended the first two games?
_______ fans

Question 9.
Daisy’s Flower Shop sold 135,649 flowers during its first year. The second year, the shop sold 9,754 more flowers than it did its first year. The third year, it sold 1,343 more flowers than it did in the second year. How many flowers did the shop sell during the three years?
_______ flowers

Reason Abstractly Algebra Find the missing number and name the property you used to find it. Write Commutative or Associative.

Question 10.
(4,580 + 5,008) + 2,351 = 4,580 + ( _______ +2,351)

Question 11.
7,801+ _______ =4,890+7,801

Question 12.
2,592 + 3,385 = 3,385+ _______

### Common Core – Add Whole Numbers (Page 40)

Use the table for 13–14.

Question 13.
What is the combined population of the three major Alaskan cities? Estimate to verify your answer.
Estimate: _______
Sum: _______

Question 14.
The digit 5 occurs two times in the population of Fairbanks. What is the value of each 5? Explain your answer.
First 5: _______
Second 5: _______

Question 15.
Kaylie has 164 stamps in her collection. Her friend Nellie has 229 more stamps than Kaylie. How many stamps do Kaylie and Nellie have?
_______ stamps

Question 16.
Alaska’s Glacier Bay National Park had 431,986 visitors one year. The next year, the park had 22,351 more visitors than the year before. How many people visited during the two years? Show your work and explain how you found your answer.
_______ visitors

### Common Core – Add Whole Numbers (Page 41)

Estimate. Then find the sum.

Question 1.
Estimate: 90,000

Question 2.
73,404 + 27,865
Estimate: _______
Sum: _______

Question 3.
404,446 + 396,755
Estimate: _______
Sum: _______

Question 4.
137,638 + 52,091
Estimate: _______
Sum: _______

Question 5.
200,629 + 28,542
Estimate: _______
Sum: _______

Question 6.
212,514 + 396,705
Estimate: _______
Sum: _______

Question 7.
324,867 + 6,233
Estimate: _______
Sum: _______

Question 8.
462,809 + 256,738
Estimate: _______
Sum: _______

Question 9.
624,836 + 282,189

Estimate: _______
Sum: _______

Problem Solving

Use the table for 10–12.

Question 10.
Beth and Cade were on one team. What was their total score?
_______

Question 11.
Dillan and Elaine were on the other team. What was their total score?
_______

Question 12.
Which team scored the most points?
_______

Question 13.
Have students write a story problem that can be solved by finding the sum of 506,211 and 424,809. Have them solve the problem.

### Common Core – Add Whole Numbers (Page 42)

Lesson Check

Question 1.
The coastline of the United States is 12,383 miles long. Canada’s coastline is 113,211 miles longer than the coastline of the United States. How long is the coastline of Canada?
(a) 100,828 miles
(b) 115,594 miles
(c) 125,594 miles
(d) 237,041 miles

Question 2.
Germany is the seventh largest European country and is slightly smaller by area than Montana. Germany has a land area of 134,835 square miles and a water area of 3,011 square miles. What is the total area of Germany?
(a) 7,846 square miles
(b) 131,824 square miles
(c) 137,846 square miles
(d) 435,935 square miles

Spiral Review

Question 3.
In an election, about 500,000 people voted in all. Which number could be the exact number of people who voted in the election?
(a) 429,455
(b) 441,689
(c) 533,736
(d) 550,198

Question 4.
In 2007, Pennsylvania had approximately 121,580 miles of public roads. What is 121,580 rounded to the nearest thousand?
(a) 100,000
(b) 120,000
(c) 121,000
(d) 122,000

Question 5.
Which of the following lists of numbers is in order from greatest to least?
(a) 33,093; 33,903; 33,309
(b) 42,539; 24,995; 43,539
(c) 682,131; 628,000; 682,129
(d) 749,340; 740,999; 740,256

Question 6.
Which symbol makes the following statement true?
$413,115 ________$431,511
(a) <
(b) >
(c) =
(d) +

### Common Core – Subtract Whole Numbers (Page 44)

Question 1.
Subtract. Use the grid to record the problem.
637,350 − 43,832

Estimate. Then find the difference.

Question 2.
14,659 − 11,584
Estimate: _______
Difference: _______

Question 3.
456,912 − 37,800
Estimate: _______
Difference: _______

Question 4.
407,001 − 184,652
Estimate: _______
Difference: _______

Question 5.
942,385 − 461,803
Estimate: _______
Difference: _______

Question 6.
798,300 − 348,659
Estimate: _______
Difference: _______

Question 7.
300,980 − 159,000
Estimate: _______
Difference: _______

### Common Core – Subtract Whole Numbers (Page 45)

Practice: Copy and Solve Subtract. Add to check.

Question 8.
653,809 – 256,034 = _______

Question 9.
258,197 – 64,500 = _______

Question 10.
496,004 – 398,450 = _______

Question 11.
500,000 – 145,609 = _______

Reason Abstractly Algebra Find the missing digit.

Question 12.
6,532 − 4,1_3 = 2,407

Question 13.
_08,665−659,420 = 149,245

Question 14.
697,320 − 432,_08 = 264,712

Use the table for 15–16.

Question 15.
Estimate Reasonableness How many more acres were grown in 1996 than in 1986? Estimate to check the reasonableness of your answer.
_______ acres

Question 16.
What is the difference between the greatest number of acres and the least number of acres used for growing oranges?
_______ acres

Question 17.
Workers at a paper company count the number of boxes of paper in the warehouse each month. In January, there were 106,341 boxes of paper. In February, there were 32,798 fewer boxes than there were in January. In March, there were 25,762 fewer boxes than there were in February. How many boxes were in the warehouse in March?
_______ boxes

Question 18.
There are 135,663 kilometers of U.S. coastline that border the Pacific Ocean. There are 111,866 kilometers of U.S. coastline that border the Atlantic Ocean. How many more kilometers of U.S. coastline border the Pacific Ocean than the Atlantic Ocean? Solve the problem and show how to check your answer.
_______ km

### Common Core – Subtract Whole Numbers (Page 46)

Question 19.
What’s the Error? Maryland has an area of 12,407 square miles. Texas has an area of 268,601 square miles. How much larger is Texas than Maryland?

Read how Janice solved the problem.
Find her error.

Texas: 268,601 square miles
Maryland: 12,407 square miles
I can subtract to find the difference.
268,601
–12,407
144,531

Solve the problem and correct her error.

Question 20.
Verify Reasoning of Others Describe Janice’s error.

### Common Core – Subtract Whole Numbers (Page 47)

Subtract Whole Numbers
Estimate. Then find the difference.

Question 1.

Question 2.
428,731 – 175,842
Estimate: ______
Difference: ______

Question 3.
920,026 – 535,722
Estimate: ______
Difference: ______

Question 4.
253,495 – 48,617
Estimate: ______
Difference: ______

Subtract. Add to check.

Question 5.
735,249 – 575,388 = ______
______ + ______ = ______

Question 6.
512,724 – 96,473 = ______
______ + ______ = ______

Question 7.
600,000 – 145,782 = _______
_______ + ______ = _______

Problem Solving
Use the table for 8 and 9.

Question 8.
How many more people attended the Magic’s games than attended the Pacers’ games?
_______ people

Question 9.
How many fewer people attended the Pacers’ games than attended the Clippers’ games?
_______ people

Question 10.
Have students write a story problem that can be solved by finding the difference of 432,906 and 61,827. Then have them solve the problem.

### Common Core – Subtract Whole Numbers (Page 48)

Lesson Check

Question 1.
This year, a farm planted 400,000 corn stalks. Last year, the farm planted 275,650 corn stalks. How many more corn stalks did the farm plant this year than last year?
(a) 124,350
(b) 125,450
(c) 235,450
(d) 275,650

Question 2.
One machine can make 138,800 small paper clips in one day. Another machine can make 84,250 large paper clips in one day. How many more small paper clips than large paper clips are made by the two machines in one day?
(a) 44,550
(b) 54,550
(c) 54,650
(d) 154,650

Spiral Review

Question 3.
In three baseball games over a weekend, 125,429 people came to watch. The next weekend, 86,353 came to watch the games. How many people in all watched the six baseball games?
(a) 201,782
(b) 211,772
(c) 211,782
(d) 211,882

Question 4.
Kevin read the number “two hundred seven thousand, forty-eight” in a book. What is this number in standard form?
(a) 27,048
(b) 27,480
(c) 207,048
(d) 207,480

Question 5.
A museum had 275,608 visitors last year. What is this number rounded to the nearest thousand?
(a) 275,600
(b) 276,000
(c) 280,000
(d) 300,000

Question 6.
At the Millville Theater, a play ran for several weeks. In all, 28,175 people saw the play. What is the value of the digit 8 in 28,175?
(a) 8
(b) 800
(c) 8,000
(d) 80,000

### Problem Solving • Comparison Problems with Addition and Subtraction (Page 50)

During an event, a hot air balloon traveled a distance of 5,110 feet during the first trip and 850 feet more during the second trip. How far did it travel during the second trip?

Question 1.
What do I need to find?

Question 2.
What information do I need to use?

Question 3.
How will I use the information?

Question 4.
How far did it travel during the second trip?
______ feet

Question 5.
Is your answer reasonable? Explain how you know.

### Problem Solving • Comparison Problems with Addition and Subtraction (Page 51)

Hot air balloons are able to fly at very high altitudes. A world record height of 64,997 feet was set in 1988. In 2005, a new record of 68,986 feet was set. How many feet higher was the 2005 record than the 1988 record?

Question 1.
First, draw a diagram to show the parts of the problem.

Question 1.
Next, write the problem you need to solve.

Question 1.
Last, solve the problem to find how many feet higher the 2005 record was than the 1988 record
______ feet higher

Question 2.
What if a new world altitude record of 70,000 feet was set? How many feet higher would the new record be than the 2005 record?
______ feet

Question 3.
Last year, the ticket sales for a commercial hot air balloon ride were $109,076. This year, the ticket sales were$125,805. How much more were the ticket sales this year?
$______ Question 4. There were 665 hot air balloon pilots at a hot air balloon race. There were 1,550 more ground crew members than there were pilots. How many ground crew members were there in all? ______ ground crew members ### Problem Solving • Comparison Problems with Addition and Subtraction (Page 52) Question 5. Steve Fossett attempted to fly around the world in a balloon several times before he succeeded in 2002. How many more miles did he fly during the 2002 flight than during the August 1998 flight? ______ miles Question 6. Is the combined distance for the 1998 flights more or less than the distance for the 2002 flight? Question 7. Estimate the total number of miles Fossett flew during the six hot air balloon flights. Explain how you estimated. ______ miles Question 8. Rusty wants to buy a small hot air balloon that costs$23,950. The cost of training for a license is $2,750. How much will Rusty pay for the balloon and the training? (a)$21,200
(b) $26,600 (c)$26,700
(d) $36,700 ### Problem Solving • Comparasion Problems with Addition and Substraction (Page 53) Problem Solving • Comparasion Problems with Addition and Substraction Use the information in the table for 1–3. Question 1. How many square miles larger is the surface area of Lake Huron than the surface area of Lake Erie? Think: How can a bar model help represent the problem? What equation can be written? Question 1. Question 2. Which lake has a surface area that is 14,938 square miles greater than the surface area of Lake Ontario? Draw a model and write a number sentence to solve the problem. Question 3. Lake Victoria has the largest surface area of all lakes in Africa. Its surface area is 26,828 square miles. How much larger is the surface area of Lake Superior than that of Lake Victoria? ______ square milles Question 4. At 840,000 square miles, Greenland is the largest island in the world. The second-largest island is New Guinea, at 306,000 square miles. How much larger is Greenland than New Guinea? ______ square miles ### Problem Solving • Comparasion Problems with Addition and Substraction (Page 54) Lesson Check Question 1. The Mariana Trench in the Pacific Ocean is about 36,201 feet deep. The Puerto Rico Trench in the Atlantic Ocean is about 27,493 feet deep. Based on these data, how many feet deeper is the Mariana Trench than the Puerto Rico Trench? (a) 8,708 feet (b) 9,718 feet (c) 9,808 feet (d) 63,694 feet Question 2. At 1,932 feet, Crater Lake, Oregon, is the deepest lake in the United States. The world’s deepest lake, Lake Baykal in Russia, is 3,383 feet deeper. How deep is Lake Baykal? (a) 3,383 feet (b) 4,215 feet (c) 4,315 feet (d) 5,315 feet Spiral Review Question 3. Which of the following amounts is greater than$832,458?
(a) $82,845 (b)$832,458
(c) $823,845 (d)$832,485

Question 4.
A stadium in Pennsylvania seats 107,282 people. A stadium in Arizona seats 71,706 people. Based on these facts, how many more people does the stadium in Pennsylvania seat than the stadium in Arizona?
(a) 35,576
(b) 35,586
(c) 36,576
(d) 178,988

Question 5.
Which of the following numbers is 399,713 rounded to the place value of the underlined digit?
(a) 390,000
(b) 398,000
(c) 399,800
(d) 400,000

Question 6.
About 400,000 people visited an art museum in December. Which number could be the exact number of people who visited the art museum?
(a) 478,051
(b) 452,223
(c) 352,483
(d) 348,998

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 55)

Question 1.
Select a number for ■ that will make a true comparison. Mark all that apply.
703,209 > ■
Options:
(a) 702,309
(b) 703,029
(c) 703,209
(d) 703,290
(e) 730,029
(f) 730,209

Question 2.
Nancy wrote the greatest number that can be made using each of these digits exactly once.

Part A
What was Nancy’s number? How do you know this is the greatest possible number for these digits?
Type below:
____________

Question 2.
Part B
What is the least number that can be made using each digit exactly once? Explain why the value of the 4 is greater than the value of the 5.
Type below:
____________

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 56)

For 3–4, use the table.

Question 3.
Write the name of each mountain peak in the box that describes its height, in feet.
Between 14,000 feet and        Between 14,301 feet and
14,300 feet                              14,500 feet
Type below:
____________

Question 4.
Circle the name of the tallest peak. Explain how you know which of the mountain peaks is the tallest.
Type below:
____________

Question 5.
Mr. Rodriguez bought 420 pencils for the school. If there are 10 pencils in a box, how many boxes did he buy?
Options:
(a) 42
(b) 420
(c) 430
(d) 4,200

Question 6.
Bobby and Cheryl each rounded 745,829 to the nearest ten thousand. Bobby wrote 750,000 and Cheryl wrote 740,000. Who is correct? Explain the error that was made.
_________

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 57)

Question 7.
The total season attendance for a college team’s home games, rounded to the nearest ten thousand, was 270,000. For numbers 7a–7d, select Yes or No to tell whether the number could be the exact attendance.
a. 265,888
i. yes
ii. no

Question 7.
b. 260,987
i. yes
ii. no

Question 7.
c. 274,499
i. yes
ii. no

Question 7.
d. 206,636
i. yes
ii. no

For 8–10, use the table.

The table shows recent population data for Sacramento, California.

Question 8.
How many children are under 10 years old? Show your work.
_____ children

Question 9.
How many people are between the ages of 20 and 49? Show your work.
_____ people

Question 10.
How many more children are under the age of 5 than between the ages of 10 and 14? Show your work.
_____ children

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 58)

Question 11.
For numbers 11a–11d, select True or False for each sentence.
a. The value of 7 in 375,092 is 7,000.
i. True
ii. False

Question 11.
b. The value of 5 in 427,593 is 500.
i. True
ii. False

Question 11.
c. The value of 2 in 749,021 is 200.
i. True
ii. False

Question 11.
d. The value of 4 in 842,063 is 40,000.
i. True
ii. False

Question 12.
Select another way to show 403,871. Mark all that apply.
Options:
(a) four hundred three thousand, eight hundred one
(b) four hundred three thousand, seventy-one
(c) four hundred three thousand, eight hundred seventy-one
(d) 400,000 + 38,000 + 800 + 70 + 1
(e) 400,000 + 3,000 + 800 + 70 + 1
(f) 4 hundred thousands + 3 thousands + 8 hundreds + 7 tens + 1 one

Question 13.
Lexi, Susie, and Rial are playing an online word game. Rial scores 100,034 points. Lexi scores 9,348 fewer points than Rial and Susie scores 9,749 more points han Lexi. What is Susie’s score? Show your work.
_____

Question 14.
There were 13,501 visitors to a museum in June. What is this number rounded to the nearest ten thousand? Explain how you rounded.
_____

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 59)

Question 15.
New Mexico has an area of 121,298 square miles. California has an area of 155,779 square miles. How much greater is the area, in square miles, of California than the area of New Mexico? Show your work and explain how you know the answer is reasonable.
______ square miles

Question 16.
Circle the choice that completes the statement.
10,000 less than 24,576 is 1,000 less than 14,576.
_________

Question 17.
Match the number to the value of its 5.

Type below:
__________

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 60)

Question 18.
During September and October, a total of 825,150 visitors went to Grand Canyon National Park. If 448,925 visitors went to the park in September, how many visitors went to the park in October? Show your work.
_____ people

Question 19.
A college baseball team had 3 games in April. Game one had an attendance of 14,753 people. Game two had an attendance of 20,320 people. Game three had an attendance of 14,505 people. Write the games in order from the least attendance to the greatest attendance. Use pictures, words, or numbers to show how you know.
Game _____ ; _____ ; _____

Question 20.
Caden made a four-digit number with a 5 in the thousands place, a 5 in the ones place, a 6 in the tens place, and a 4 in the hundreds place. What was the number?
_____

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 65)

Question 1.
There are 8 students in the art club. There are 3 times as many students in chorus. How many students are in chorus?
So, there are _____ students in chorus.

Draw a model and write an equation.

Question 2.
6 times as many as 2 is 12.
Type below:
____________

Question 3.
20 is 4 times as many as 5.
Type below:
____________

Write a comparison sentence.

Question 4.
18 = 9 × 2
_____ is _____ times as many as _____ .

Question 5.
8 × 4 = 32
_____ times as many as _____ is _____ .

Write a comparison sentence.

Question 6.
5 × 7 = 35
_____ times as many as _____ is _____ .

Question 7.
54 = 6 × 9
_____ is _____ times as many as _____ .

Question 8.
One week, Jake and Sally collected canned goods for a food drive. On Monday, Jake collected 4 boxes and Sally collected 2 boxes. At the end of the week, Jake had 3 times as many boxes as he had on Monday. Sally had 4 times as many boxes as she had on Monday. Together, how many boxes of canned goods did they have at the end of the week?
_____ boxes

Question 9.
Nando has 4 goldfish. Jill has 3 goldfish. Cooper has 2 times as many goldfish as Nando and Jill combined. Write an equation that compares the number of goldfish Cooper has with the number of goldfish that Nando and Jill have.
Type below:
_________

Question 10.
Represent a Problem Write a comparison sentence about pet food that could be represented using the equation 12 = 4 × 3.
Type below:
_________

### Problem Solving • Comparasion Problems with Addition and Substraction (Page 66)

Question 11.
Luca has 72 baseball cards. This is 8 times as many cards as Han has. How many baseball cards does Han have?

a. What do you need to find?
Type below:
_________

Question 11.
b. How can you use a model to find the number of cards Han has?
Type below:
_________

Question 11.
c. Draw the model.
Type below:
_________

Question 11.
d. Write an equation and solve.
Type below:
_________

Question 12.
Complete the statements to describe each model.

24 is _____ times as many as _____ .           24 is _____ times as many as _____ .