McGraw Hill Math

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 21–23 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 21–23 Answer Key

Review the graph and answer the following questions.

Question 1.
Is there more trash on the beach due to plastic or paper?
Answer:
Plastic
Explanation:
Observe the graph of Trash on Beach,
Plastic is more than paper.
Total amount of plastic is 5000 and paper less than it.

Question 2.
Which material accounts for more than twice as much trash on the beach as Styrofoam?
Answer:
Cigarettes
Explanation:
Observe the graph of Trash on Beach,
Styrofoam is around 7000,
Cigarettes is around 14000,
So, Cigarettes are as twice as much trash on the beach as Styrofoam.

Question 3.
What material accounts for the least amount of trash on the beach?
Answer:
Wood
Explanation:
Observe the graph of Trash on Beach,
The least amount of trash is wood i.e., around 2000.

Use data from the graphs to answer the following questions.

Question 4.
Which city has the highest average temperature in the summer? ____________
The lowest? ____________________________
Answer:
Highest temperature is Orlando,
Lowest temperature is Omaha.
Explanation:
The above chart shows the U.S city summer temperatures.
When compared with all the city temperatures,
Highest temperature is Orlando more than 80 °F,
Lowest temperature is Omaha below 70 °F.

Question 5.
The average temperature of Chicago is 4 degrees warmer than Cleveland, true or false? ___________
Answer:
True
Explanation:
The above chart shows the U.S city summer temperatures.
When compared with the average temperature of Chicago it is 4 degrees warmer than Cleveland.

Question 6.
Which city is cooler during the summertime, San Francisco or Milwaukee?
Answer:
San Francisco
Explanation:
The above chart shows the U.S city summer temperatures.
When compared with the average temperature of San Francisco and Milwaukee,
San Francisco is cooler during summer time.

Question 7.
On what day did Jason practice his guitar the most? __________
The least? ___________________
Answer:
Jason practice his guitar the most on Thursday.
The least on Monday.
Explanation:
Observe the above chart of Jason’s Guitar practice schedule.
On Thursday he practiced more number of hours rather than other days.
On Monday he practiced less hours.

Question 8.
Jason practices 2.5 hours more on Thursday than on what other day?
Answer:
Monday.
Explanation:
Observe the above chart of Jason’s Guitar practice schedule.
On Thursday he practiced he practiced for 3.5 hours
On Monday he practiced for one hour.
3.5 – 1 = 2.5
So, Jason practices 2.5 hours more on Thursday than on Monday.

Question 9.
What is the total number of hours that Jason practices from Monday to Saturday?
Answer:
13\(\frac{1}{2}\) or 13.5 hours.
Explanation:
Observe the above chart of Jason’s Guitar practice schedule.
On Monday he practiced for 1 hour.
On Tuesday he practiced for 1.5 hours.
On Wednesday he practiced for 3 hours.
On Thursday he practiced for 3.5 hours.
On Friday he practiced for 2 hours.
On Saturday he practiced for 2.5 hours.
The total number of hours that Jason practices from Monday to Saturday is,
1 + 1.5 + 3 + 3.5 + 2 + 2.5 = 13.5 hours
13\(\frac{1}{2}\) hours.

Question 10.
In what year did Rocco hit more home runs than doubles?
Answer:
2009
Explanation:
From the above given chart of Rocco’s Baseball Statistics,
Rocco hit more home runs than doubles in 2006.

Question 11.
One year, Rocco injured his leg sliding into second base and missed some games while he recovered. What year do you think that was?
Answer:
2006
Explanation:
From the above given chart of Rocco’s Baseball Statistics,
In 2006 his score is less than compared with other years.
So, Rocco injured his leg sliding into second base and missed some games while he recovered.

Question 12.
Fredo is planning the menu for his restaurant. He conducted a survey of restaurant guests and converted that information into a circle graph. Based on the data, what is the most popular type of entree that Fredo’s restaurant serves?

Answer:
Chicken
Explanation:
The above chart shows the Meal Entree Orders of Fredo’s Restaurant.
The most popular type of entree that Fredo’s restaurant serves is chicken.

Question 13.
Based on the data, which is more popular as an entree, fish or meat?
Answer:
Fish
Explanation:
The above chart shows the Meal Entree Orders of Fredo’s Restaurant.
When compared with the fish or meat serves in the entree of Fredo’s restaurant is Fish.

Question 14.
Fredo would like to add more vegetarian entrees, but he won’t until at least 10% of the patrons want them. Should Fredo add more vegetarian entrees, and why?
Answer:
Yes, 17% ordered vegetarian meals.
Explanation:
The above chart shows the Meal Entree Orders of Fredo’s Restaurant.
Yes, Fredo would add more vegetarian entrees,
because 17% ordered vegetarian meals.

Question 15.
Look at the following data group: 2, 3, 5, 8, 8, 9, 16, 24, 28, 40, 44
What is the median of the data group? ____________________
What is the mean? ______________________
What is the range? ____________________
Answer:
Median = 9
Mean = 17
Range = 42
Explanation:
First Range of data is the difference between the highest and the lowest values of the data
data group: 2, 3, 5, 8, 8, 9, 16, 24, 28, 40, 44
Range = 44 – 2 = 42
Mean:
Find the sum of the values by adding them all up.
Divide the sum by the number of values in the data set.
Mean = \(\frac{2+3+5+8+8+9+16+24+28+40+44}{11}\)
= \(\frac{187}{11}\) = 17
Median:
 First, arrange the given data in ascending order.

Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 9 as rounded shown in the

Question 16.
Put the following data into a stem-and-leaf plot:
19, 22, 22, 25, 26, 27, 28, 30, 34, 36, 37, 44, 44, 44, 45, 48, 48, 49, 50, 53, 55, 57, 58, 64, 67
What is the mode of the set of data? ___________________
What is the median? ___________________
What is the mean? ___________________
Answer:
Mode = 44
Median = 44
Mean = 41.3
Explanation:
a stem-and-leaf plot:

The mode is the number or numbers that occur the most frequently.
44 is occur most frequently
as per the above stem leaf plot
mode of the above data is 44
Median:
 First, arrange the given data in ascending order.

Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 44 as rounded shown in the
Mean:
Find the sum of the values by adding them all up.
Divide the sum by the number of values in the data set.
Mean = \(\frac{19, 22, 22, 25, 26, 27, 28, 30, 34, 36, 37, 44, 44, 44, 45, 48, 48, 49, 50, 53, 55, 57, 58, 64, 67}{25}\)
= \(\frac{1032}{25}\) = 41.3

Question 17.
What is the approximate range of the third quartile?

What is the median of the data? ___________________
What is the range of the data? ___________________
Answer:
Third quartile range = 14
Median = 22
Range of data = 45
Explanation:

First Range of data is the difference between the highest and the lowest values of the data
max – min = 50 – 5 = 45
Median = 22 is the Q2 center of the data given in the picture
Third quartile range = Q3 – Q2 = 36 – 22 = 14

Question 18.
How many of the outcomes in this tree diagram result in having less than two tails?

Answer:
4
Explanation:

Less then two tails combination are rounded in the above picture, total 4 combinations are identified

Question 19.
James conducted a survey of students in his class. He found that out of the 50 people he surveyed, 35 used a backpack to carry their books and 28 carried calculators. If 13 students carried a calculator and a backpack, how many students carry only a backpack?

Fill in the Venn Diagram to model the problem.
Answer:
22

Explanation:
As in the above venn diagram yellow circle 22 students used backpack to carry their books.
A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.

Question 20.
What does this Venn Diagram tell you?

Answer:
7 people liked both volleyball and football;
47 people in total were surveyed;
20 people liked only volleyball and
20 people only liked football.
Explanation:
As in the above venn diagram
7 people liked both volleyball and football;
47 people in total were surveyed;
20 people liked only volleyball and
20 people only liked football.
A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits.

Question 21.
You have a bag of 20 markers, 5 of which are green, 3 of which are red, 7 of which are yellow, 3 of which are blue, and 2 of which are orange. What is the chance of reaching into the bag and pulling out a yellow marker? _________________
Anything but a green marker? _________________
Answer:
Yellow marker \(\frac{7}{20}\);
Green marker \(\frac{15}{20}\) or \(\frac{3}{4}\)
Explanation:
First sample space ={5(green)+3(red)+7(yellow)+3(blue)+2(orange)} = 20 markers,
means if we pic one marker we can get either of the 5 of which are green, 3 of which are red, 7 of which are yellow, 3 of which are blue, and 2 of which are orange marker.
the chance of reaching into the bag and pulling out a yellow marker is the probability of yellow marker
Yellow marker = \(\frac{7}{20}\)
any market except Green marker = all markers – green markers divided by total markers
= \(\frac{20 – 5}{20}\)
= \(\frac{15}{20}\) or \(\frac{3}{4}\)

Question 22.
A grocery store did a taste test of 3 brands of cookies. In a random survey of 50 people walking down the street in front of the store, 20 people said they preferred Brand A, 14 people preferred Brand B, and 16 people preferred Brand C. Which of the following is the most valid conclusion?
(a) The grocery store should stop selling Brand B.
(b) Brands B and C have roughly the same popularity.
(c) Brand A is twice as popular as Brand B.
Answer:
B
Explanation:
A taste test of 3 brands of cookies in a random survey of 50 people walking down the street in front of the store, 20 people said they preferred brand A,
14 people preferred brand B,
and 16 people preferred brand C
brands B and C have roughly the same popularity.

Question 23.
Find the mean absolute deviation for the values below.

Answer:
MAD = 8
Explanation:
Average = \(\frac{sum of the scores}{number of the scores}\)
= \(\frac{84 + 68 + 92 + 76}{4}\)
= \(\frac{320}{4}\) = 80
finding the difference between score and average score
I 84 – 80 I = 4
I 68 – 80 I = 12
I 92 – 80 I = 12
I 76 – 80 I = 4
average of the differences,
= \(\frac{4 + 12 + 12 + 4}{4}\)
= \(\frac{32}{4}\) = 8
mean absolute deviation (MAD) = 8.

Question 24.
Andy did a random survey to find out what type of pet is most popular in his town. 17 people chose dogs, 18 people chose cats, and 6 people chose fish. Complete the probability model.

Answer:

Explanation:
The probability model total samples are 17 + 18 + 6 = 41
probability of 17 people chose dogs out of 41 samples is
P(Dog) = \(\frac{Number of Dogs}{total samples}\)
= \(\frac{17}{41}\)
= 0.41
probability of 18 people chose cats out of 41 samples is
P(Dog) = \(\frac{Number of Cats}{total samples}\)
= \(\frac{18}{41}\)
= 0.44
probability of 6 people chose dogs out of 41 samples is
P(Dog) = \(\frac{Number of fish}{total samples}\)
= \(\frac{6}{41}\)
= 0.15

Question 25.
Alex rolls a pair of six-sided dice. What is the probability that he will roll a 2 and a 6?
Answer:
\(\frac{1}{36}\)
Explanation:
Alex rolls a pair of six-sided dice,
Probability of two dies with 6 sides.
6 x 6 = 36 samples
only one time we can see the combination that he will roll a 2 and a 6
as all combinations are given below.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 18–20 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 18–20 Answer Key

Question 1.
Armando is going to replace the trim around all of the doors in his house. The outside of each door measures 18 \(\frac{1}{2}\) feet. If he has 9 doors, how many inches of trim does he need to replace?
Answer:
1998 inches of trim.
Explanation:
18\(\frac{1}{2}\) convert in to inches
18 x 12 + \(\frac{1}{2}\) x 12
= 216 + 6
= 222
So, 222 x 9 = 1998 inches of trim.

Question 2.
Ashley wants to empty her fish tank before she cleans it. The fish tank holds 34 gallons. She is using a one-quart container to empty the tank by hand. How many full containers will she need to empty the tank?
Answer:
136 quarter containers need to empty the tank.
Explanation:
1 gallon = 4 quarters
The fish tank holds 34 gallons,
= 4 x 34 = 136 quarters
136 quarter containers need to empty the tank.

Question 3.
Annika weighed boxes for shipping books to customers. The first box weighed 160 ounces, the second box 3 weighed 10 \(\frac{3}{8}\) pounds, and the third box weighed \(\frac{1}{200}\) ton. Which box weighed the most?
Answer:
Second box weighed the most.
Explanation:

To compare the three boxes all should be of same units,
first convert the weights are in one unit pounds,
first box weighed 160 ounces = 10 pounds,
the second box 3 weighed 10 \(\frac{3}{8}\) pounds,
the third box weighed \(\frac{1}{200}\) ton = 1 pound,
Second box weighed the most.

Question 4.
Mandie wants to fence in her corral, and needs to know how much fencing to purchase. The corral has an irregular shape, with sides of 25 \(\frac{1}{4}\) feet, 330 inches, 6 yards, one foot, \(\frac{3}{160}\) of a mile, and 9 feet. How much fence material will she need?
________________ feet
Answer:
179.75 ft
Explanation:
All measures are converted in to one units as feet.
25 \(\frac{1}{4}\) feet = 25.25ft
330 inches = 27.5 ft
6 yards = 18 ft
one foot = 1
\(\frac{3}{160}\) of a mile = 99 ft
9 feet = 9 ft
25 \(\frac{1}{4}\) feet, 330 inches, 6 yards,
one foot, \(\frac{3}{160}\) of a mile, and 9 feet.
= 25.25 + 27.50 + 18 + 1 + 99 + 9
= 179.75 ft

Question 5.
What is the area of a rectangle with a length of 20 feet and a width of 144 inches?

_____________ square feet
Answer:
240 square feet.
Explanation:
144 in to be converted in to ft by dividing 12.
144/12 = 12 ft
the area of a rectangle = length x width.
A = l x w
A = 20 x 12
A = 240 sq ft

Question 6.
What is the area of a right triangle with sides of 6 feet, 8 feet, and 120 inches?

_____________ square feet
Answer:
24 sq ft.
Explanation:
120 in to be converted in to ft by dividing 12.
120/12 = 10 ft
the area of a triangle = (1/2) base x height,
A = (1/2) b x h
A = 0.5 x 6 x 8
A = 24 sq ft.

Question 7.
What is the volume of a rectangular box with sides of 48 inches and 3 \(\frac{1}{2}\) feet, and a height of 30 inches?

______________ cubic feet
Answer:
V = 35cu ft
Explanation:
To be converted in to ft by divide by 12.
30/12 = 2.5 ft
48/12 = 4 ft
Volume of a rectangular box V = l x b x h
V = 3.5 x 2.5 x 4
V = 35cu ft

Question 8.
A modern spacecraft must travel 8.1 miles per second in order to reach the planet Mars. How far does the spacecraft travel in a minute?
in an hour? ______________
in a day? ______________
Answer:
486 miles in a minute,
160 miles in an hour,
699,840 miles in a day.
Explanation:
8.1 miles per second.
1 minute = 60 seconds.
8.1 x 60 = 486 miles in a minute.
1 hour = 60 minutes.
486 x 60 = 29,160 miles in an hour.
1 day = 24 hours.
29,160 x 24 = 699,840 miles in a day.

Question 9.
If the distance to the moon from the earth is 248,000 miles, how long does it take the spacecraft in the previous exercise to travel to the moon? How many times a day could the spacecraft go back and forth between the moon and the earth?
Answer:
8.5 hours and 3 times.
Explanation:
The distance to the moon from the earth is 248,000 miles.
A modern spacecraft must travel 8.1 miles per second in order to reach the planet Mars,
486 x 60 = 29,160 miles in an hour.
248,000/29,160 = 8.5 hours.
8 x 3 = 24 hours.
Number of times in a day the spacecraft could go back and forth between the moon and the earth,
24 / 8.5 = 2.8 or 3 times.

Question 10.
The world record for the shot put is 23.12 meters. The world record for the discus throw is 74.08 meters. How many centimeters longer is the record for the discus throw than the record for the shot put?
Answer:
5096 cm
Explanation:
The shot put is 23.12 meters.
The discus throw is 74.08 meters.
Difference between disc throw and shot put,
74.08 – 23.12 = 50.96 meters.
1 meter = 100 cm.
50.96 x 100 = 5096 cm.

Question 11.
Stacey is measuring fabric for her grandmother, who is going to make a rectangular banner for the school. The banner will be 6.5 meters in length and 2,350 millimeters in width. How much fabric will Stacey’s grandmother need to buy?
______________ sq cm
Answer:
152,750sq cm
Explanation:
The banner will be 6.5 meters in length and 2,350 millimeters in width.
In the above given information, both units are of different to be converted to one unit.
Lets convert in to centimeters as below,
length = 6.5 meter x 100 cm = 650 cm
width = 2,350millimeters /10 = 235.0 cm
Area of a rectangle = Length x width
A = 650 x 235
A = 152,750 sq cm.

Question 12.
Sharon has three cans of latex paint to recycle. One can holds 2,957 milliliters of paint, the second can holds 105.6 centiliters of paint, and the third can holds 3.9 liters of paint. How much paint, in total, will Sharon be recycling?
______________ liters
Answer:
7.913 liters
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as below to find out the total paint recycling.
One can holds 2,957 milliliters = 2.957 liters of paint,
the second can holds 105.6 centiliters =1.056 liters of paint,
and the third can holds 3.9 liters of paint.
paint, in total, will Sharon be recycling = 2.957 + 1.056 + 3.9
= 7.913 liters.

Question 13.
What is the area of a triangle with sides of 8 cm, 8 cm, a base of 4 cm, and a height of 6 cm?

_______________ sq cm
Answer:
12 sq cm
Explanation:
The area of a triangle with  a base of 4 cm, and a height of 6 cm.
A = (1/2) x base x height
A = 0.5 x 4 x 6
A = 12 sq cm.

Question 14.
Jerrie walked around the entire rectangular school parking lot, which measures 106 meters by 7,500 centimeters. How far did Jerrie walk?
______________ meters
Answer:
Jerrie walks 362 meters.
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as shown below.
Rectangular school parking lot, measures 106 meters long and 7,500 centimeters.
1 meter = 100 cm
7500 ÷ 100 =75 meters wide.
The perimeter of a rectangular park to be calculate as shown below.
P = 2(Length + Width)
P = 2 (106 + 75)
P = 2 (181)
P = 362 meters
So, Jerrie walks 362 meters.

Question 15.
How much topsoil can fit into a rectangular dump truck that measures 3.6 meters in width, 6.5 meters in length, and 3.5 meters high?
______________ cu meters
Answer:
81.9 cu meters.
Explanation:
The given information to find out the volume of the rectangular cuboid is,
3.6 meters in width, 6.5 meters in length, and 3.5 meters high.
Volume V = Length x Width x Height
V = 3.6 x 6.5 x 3.5
V = 81.9 cu meters

Question 16.
The average player on the soccer team measures 5 feet, 11 inches tall. About how tall is that in centimeters?
Answer:
180.34 cm
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as shown below.
player on the soccer team measures 5 feet, 11 inches tall.
5 feet x 30 cm = 152.4 cm
11 inches x 2.5 = 27.94 cm
5 feet, 11 inches = 152.4 + 27.94
= 180.34 cm

Question 17.
The average taxicab has a gas tank that holds 85 liters of gasoline. How much is that in quarts?
______________ quarts
In gallons?
______________ quarts
Answer:
89.8 quarts;
22.45 gallons.
Explanation:
we know,
1 quart = 1.0567 liters
A gas tank holds 85 liters of gasoline.
85 x 1.0567 = 89.8 quarts,
1 gallon = 4 quarters = 3.7854 liters
85 /3.7854 = 22.45 gallons

Question 18.
Pauline measured a rectangular box and found that its dimensions were 55 inches by 32 inches by 20 inches tall. What is the total outside surface area in square inches?
_______________ sq in
In square feet? ______________ sq ft
Answer:
7000 sq in;
48.61 sq ft.
Explanation:
To find the surface area of a cuboid, add the areas of all 6 faces.
Dimensions were length 55 inches, width 32 inches and height 20 inches.
We can also label the length (l), width (w), and height (h) of the prism and use the formula as,
the surface area SA = 2lw + 2lh + 2hw
SA = 2 (55 x 32 + 32 x 20 + 20 x 55)
SA = 2 x (1760 + 640 +1100 )
SA = 2 x 3500
SA = 7000 sq in
To convert square in to sq foot by multiplying by 0.006944.
SA = 7000 sq in
SA = 7000 x 0.006944 = 48.61 sq ft.

Question 19.
A body temperature of 103.6° F is considered an extremely high fever. What temperature is that in Celsius?
Answer:
C = 39.7738° C
Explanation:
To convert temperatures in degrees Fahrenheit to Celsius,
subtract 32 and multiply by 0.5555 (or 5/9).
The notation C represents the temperature in Celsius, and F is the temperature in Fahrenheit.
C = 5/9 x (F – 32)
C = 0.5555 x (103.6 – 32)
C = 0.5555 x (71.6)
C = 39.7738° C

Question 20.
In track and field, the standard middle distance event is the 5,000 meters. About how many feet is 5,000 meters?
_____________ feet
Answer:
16,404 ft.
Explanation:
1 meter = 3.28 feet
5,000 meters = 5000 x 3.2808 ft
= 16,404 ft.

Question 21.
What is the volume of the rectangular pyramid?

Answer:
35 cu cm.
Explanation:
Area of rectangular base = length x width
B = 7 x 3 = 21 sq cm
volume of the rectangular pyramid = 1/3 x B x h
V = (1/3) x 21 x 5 = 35 cu cm.

Question 22.
What is the volume of the triangular solid?

Answer:
144 cubic in.
Explanation:
Volume of the triangular solid = Bh (Area of base x height)
B = Area of base = 1/2 bxh
B = 1/2 x 6 x 8 = 24 sq in
Volume V = Bh
V = 24 x 6
V = 144 cubic in

Question 23.
The air conditioning company suggests that people keep the temperature in their homes between 23 and 26 degrees Celsius during the summer. What is that range in degrees Fahrenheit?
Answer:
73.4 – 78.8 degrees Fahrenheit.
Explanation:
To convert temperatures in degrees Celsius to Fahrenheit,
add 32 and multiply by 1.8 (or 9/5).
The notation C represents the temperature in Celsius, and F is the temperature in Fahrenheit.
F = 9/5 x (C + 32)
If C = 23
F = 9/5 x (23 + 32)
F = \(\frac{9 X 23}{5}\) + 32
F = \(\frac{207}{5}\) + 32
F = 41.4 + 32
F = 73.4° F
If C = 26
F = 9/5 x (26 + 32)
F = \(\frac{9 X 26}{5}\) + 32
F = \(\frac{234}{5}\) + 32
F = 46.8 + 32
F = 78.8° F

Question 24.
The distance of a flight from Boston to Chicago is about 1,200 miles. The average ground speed for a commercial airliner is about 850 kilometers per hour. About how long will it take to fly from Boston to Chicago?
_______________ hours
Answer:
2\(\frac{1}{4}\)
Explanation:
Converting kilometers per hour in to miles per hour.
By multiplying the kilometer number with 0.62137 to get in miles.
850 x 0.62137 = 528.1645 miles per hour
Distance = Speed x Time
to calculate, how long will it take to fly from Boston to Chicago
Time = distance / speed
Time = 1200/528.1645 = 2.27 hours or 2\(\frac{1}{4}\) hours.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 16–17 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 16–17 Answer Key

Restate in exponential form then calculate.

Question 1.
8 × 8 × 2 + 3 × 3 × 3
Answer:
155
Explanation:
8 × 8 × 2 + 3 × 3 × 3
= 8²× 2 + 3³
= 155
Question 2.
2 × 2 × 4 × 4 – 3 × 3 × 3
Answer:
37
Explanation:
2 × 2 × 4 × 4 – 3 × 3 × 3
= 2² × 4² – 3³
= 2² x 2² × 2² – 3³
= 2⁶ – 3³
= 64 – 27
=37
Question 3.
5 × 25 × 2 × 2 × 4 × 4 + 7 × 7 – 5 × 5
Answer:
8024
Explanation:
5 × 25 × 2 × 2 × 4 × 4 + 7 × 7 – 5 × 5
=5³ × 2² x 4² x 7² – 5²
=125 x 4 x 16 x 49 – 25
= 8024

Restate using scientific notation.

Question 4.
13,654,764.011
Answer:
1.3654764011 x 10⁷
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.
b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.
1.3654764011 x 10⁷

Question 5.
28,397.01
Answer:
2.839701 x 10⁴
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 6.
.100745
Answer:
1.00745 x 10^-1
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 7.
21,194,668,041.1
Answer:
2.11946680411 x 10¹⁰
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 8.
813.056
Answer:
8.13056 x 10²
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Calculate.

Question 9.
3³
Answer:
aⁿ = a x a x a ….a(n times)
3³ = 3 x 3 x 3
= 27
Question 10.
8⁴
Answer:
4096
Explanation:
aⁿ = a x a x a ….a(n times)
8⁴ = 8 x 8 x 8 x 8
= 4096

Question 11.
2³ × 2^-2
Answer:
2
Explanation:
a^m + aⁿ = a^m+n
2³ × 2^-2
= 2^3-2
= 2
Question 12.
10^-8 ÷ 10^-9
Answer:
Explanation:
10^-8 ÷ 10^-9
a^m ÷ aⁿ = a^m-n
10^-8 ÷ 10^-9
= 10^-8 × 10⁹
= 10^{9 – 8}
= 10

Question 13.
15¹¹ × 15^-11
Answer:
Explanation:
a^m + aⁿ = a^m+n
15¹¹ × 15^-11
= 15^{11 – 11}
= 15⁰
= 1  (a⁰ = 1)

Question 14.
\(\sqrt{49}\)
Answer:
7
Explanation:
\(\sqrt{49}\)
= \(\sqrt{7 X 7}\)
= 7

Question 15.
\(\sqrt{64}\)
Answer:
8
Explanation:
\(\sqrt{64}\)
= \(\sqrt{8 X 8}\)
= 8

Question 16.
\(\sqrt{16}\)
Answer:
4
Explanation:
\(\sqrt{16}\)
= \(\sqrt{4 X 4}\)
= 4

Question 17.
\(\sqrt{1}\)
Answer:
1
Explanation:
\(\sqrt{1}\)
= \(\sqrt{1 X 1}\)
= 1

Question 18.
\(\sqrt{25}\)
Answer:
5
Explanation:
\(\sqrt{25}\)
= \(\sqrt{5 X 5}\)
= 5

Solve for x.

Question 19.
x – 15 ≤ 23
Answer:
x ≤ 38
Explanation:
x – 15 ≤ 23
x ≤ 23 + 15
x ≤ 38

Question 20.
3 + x ≥ 4
Answer:
x ≥ 1
Explanation:
3 + x ≥ 4
x ≥ 4 – 3
x ≥ 1

Question 21.
5x < 650
Answer:
x < 130
Explanation:
5x < 650
x < 650/5
x < 130

Question 22.
3x – 6 > 36
Answer:
x > 14
Explanation:
3x – 6 > 36
3x > 36 + 6
3x > 42
x >42 / 3
x > 14

Question 23.
\(\frac{x}{4}\) ≤ 8
Answer:
x ≤ 32
Explanation:
\(\frac{x}{4}\) ≤ 8
x ≤ 8 x 4
x ≤ 32

Question 24.
6 + x = 13
Answer:
x = 7
Explanation:
6 + x = 13
x = 13 – 6
x = 7

Question 25.
x – 15 = 22
Answer:
x = 7
Explanation:
x – 15 = 22
x = 22 – 15
x = 7

Question 26.
39 – x = 25
Answer:
x = 14
Explanation:
39 – x = 25
39 – 25 = x
x = 14

Question 27.
x + 60 = 90
Answer:
x = 30
Explanation:
x + 60 = 90
x = 90 – 60
x = 30

Question 28.
6x + 3 = 33
Answer:
x = 5
Explanation:
6x + 3 = 33
6x = 33 – 3
6x = 30
x = 30/6
x = 5

Question 29.
4x – 5 = 19
Answer:
x = 6
Explanation:
4x – 5 = 19
4x = 19 + 5
4x = 24
x = 24/4
x = 6

Question 30.
6x + 3 = 45
Answer:
x = 7
Explanation:
6x + 3 = 45
6x = 45 – 3
6x = 42
x = 42/6
x = 7

Question 31.
2x + 14 = 42
Answer:
14
Explanation:
2x + 14 = 42
2x = 42 – 14
2x = 28
x = 28/2
x = 14

Question 32.
4 – 4x = -48
Answer:
x = 13
Explanation:
4 – 4x = -48
– 4x = -48 – 4
– 4x = -52
x = 52/4
x = 13

Question 33.
\(\frac{x}{6}\) + 3 = 12
Answer:
x = 54
Explanation:
\(\frac{x}{6}\) + 3 = 12
\(\frac{x}{6}\) = 12 – 3
x = 9 x 6
x = 54

Question 34.
\(\frac{x}{2}\) – 5 = 30
Answer:
x = 70
Explanation:
\(\frac{x}{2}\) – 5 = 30
\(\frac{x}{2}\) = 30 + 5
\(\frac{x}{2}\) = 35
x = 35 x 2
x = 70

Question 35.
\(\frac{1}{3}\)x – 4 = 16
Answer:
x = 60
Explanation:
\(\frac{1}{3}\)x – 4 = 16
\(\frac{1}{3}\)x = 16 + 4
\(\frac{1}{3}\)x = 20
x = 60

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 13–15 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 13–15 Answer Key

Determine if the following proportions are equal. (Write Yes or No.)

Question 1.
\(\frac{5}{4}\) = \(\frac{24}{16}\)
Answer:
NO
Explanation:
LHS = \(\frac{5}{4}\) x \(\frac{4}{4}\)
= \(\frac{20}{16}\)
LHS is not equal to RHS

Question 2.
\(\frac{21}{12}\) = \(\frac{7}{36}\)
Answer:
NO
Explanation:
LHS = \(\frac{21}{12}\) x \(\frac{3}{3}\)
= \(\frac{7}{4}\)
LHS is not equal to RHS

Question 3.
\(\frac{12}{19}\) = \(\frac{36}{57}\)
Answer:
YES
Explanation:
LHS = \(\frac{12}{19}\) x \(\frac{3}{3}\)
= \(\frac{36}{57}\) = RHS
LHS = RHS

Question 4.
\(\frac{1}{4}\) = \(\frac{6}{24}\)
Answer:
YES
Explanation:
LHS = \(\frac{1}{4}\) x \(\frac{6}{6}\)
= \(\frac{6}{24}\) = RHS
LHS = RHS

Solve for x.

Question 5.
\(\frac{x}{10}\) = \(\frac{30}{20}\)
Answer:
x = 15
Explanation:
\(\frac{x}{10}\) = \(\frac{30}{20}\)
x = \(\frac{30}{20}\) x 10
x =\(\frac{30 X 10}{20}\)
x =15

Question 6.
\(\frac{25}{x}\) = \(\frac{40}{100}\)
Answer:
x = 62.5
Explanation:
\(\frac{25}{x}\) = \(\frac{40}{100}\)
x = \(\frac{25}{40}\) x 100
x = 0.625 x 100
x = 62.5

Question 7.
\(\frac{33}{96}\) = \(\frac{11}{x}\)
Answer:
x = 32
Explanation:
\(\frac{33}{96}\) = \(\frac{11}{x}\)
by cross multiplying
33 x = 96 x 11
x = \(\frac{96 X 11}{33}\)
x = 32

Question 8.
\(\frac{1}{10}\) = \(\frac{20}{x}\)
Answer:
x = 200
Explanation:
\(\frac{1}{10}\) = \(\frac{20}{x}\)
by cross multiplying
1 x = 20 x 10
x = \(\frac{20 X 10}{1}\)
x = 200

Solve.

Question 9.
Create a ratio to compare the length of the side of a barn (140 ft) to the width of the barn (64 ft).
Answer:
\(\frac{35}{16}\) or 35 : 16
Explanation:
\(\frac{Length}{width}\)
= \(\frac{140}{64}\)
by dividing both numerator and denominator by 4 for simplification
we get = \(\frac{35}{16}\)

Question 10.
Create a ratio to compare the amount of unsaturated fat in salad dressing (5 grams) to the amount of carbohydrates (9 grams).
Answer:
\(\frac{5}{9}\) or 5 : 9
Explanation:
The amount of unsaturated fat in salad dressing (5 grams),
The amount of carbohydrates (9 grams).
= \(\frac{unsaturated fat in salad dressing (5 grams)}{carbohydrates (9 grams)}\)
= \(\frac{5}{9}\)

Question 11.
Wallace rides his bicycle at an average speed of 18 miles per hour. How many miles does he travel in 3 \(\frac{1}{3}\) hours?
Answer:
60 miles
Explanation:
Distance = Speed x Time
Distance = 18 x 3\(\frac{1}{3}\)
D = 18 x 3.33
D = 60 miles

Question 12.
Jermaine can make 29 loaves of bread for every 3 batches he bakes. How many batches of bread does he need to bake in order to make 232 loaves?
Answer:
24 batches
Explanation:
\(\frac{29}{3}\) = \(\frac{232}{x}\)
= \(\frac{3}{29}\) X \(\frac{232}{x}\)
x = \(\frac{232 X 3}{29}\)
x =8 x 3
x = 24

Question 13.
Phyllis drinks \(\frac{3}{4}\) of a pint of water after each mile she walks. How many pints of water will she drink if she walks 5 \(\frac{3}{4}\) miles?
Answer:
4\(\frac{5}{16}\)
Explanation:
\(\frac{3}{4}\) = 1 pints of water she drinks
5\(\frac{3}{4}\) = let x pints of water
x \(\frac{3}{4}\) = 5\(\frac{3}{4}\)
x = \(\frac{3}{4}\) x \(\frac{23}{4}\)
x = \(\frac{3 X 23}{4 x 4}\)
x = \(\frac{69}{16}\)
x= 4\(\frac{5}{16}\)

Question 14.
Ginny needs to check the air in her tires every 750 miles. How many times will she need to check her tires if she is taking a trip that is 6,750 miles in length?
Answer:
9 times
Explanation:
Ginny needs to check the air in her tires every 750 miles.
Number of times she need to check her tires,
if she is taking a trip that is 6,750 miles in length.
= \(\frac{6,750}{750}\)
= 9 times  (750 x 9 = 6,750)

Calculate.

Question 15.
30% of 1 \(\frac{2}{5}\)
Answer:
\(\frac{21}{50}\)
Explanation:
30% of 1 \(\frac{2}{5}\)
= 1 \(\frac{2}{5}\) x \(\frac{30}{100}\)
= \(\frac{7}{5}\) x \(\frac{3}{10}\)
= \(\frac{7 X 3}{5 X 10}\)
= \(\frac{21}{50}\)

Question 16.
40% of 440
Answer:
176
Explanation:
40% of 440
= 440 x \(\frac{40}{100}\)
= 4.4 x 40
= 176

Question 17.
\(\frac{1}{4}\) of 48%
Answer:
12%
Explanation:
\(\frac{1}{4}\) of 48%
= \(\frac{1}{4}\) x \(\frac{48}{100}\)
= 0.25 x 48%
= 12%

Question 18.
\(\frac{2}{5}\) of 70%
Answer:
28%
Explanation:
\(\frac{2}{5}\) of 70%
= 0.4 x 70%
= 28%

Question 19.
\(\frac{3}{8}\) of 340%
Answer:
127.5%
Explanation:
\(\frac{3}{8}\) of 340%
= 0.375 x 340%
= 127.5%

Question 20.
43% of 0.705
Answer:
0.30315
Explanation:
43% of 0.705
= \(\frac{43}{100}\) of 0.705
= 0.705 x 0.43
= 0.30315

Question 21.
84% of 1.906
Answer:
0.30315
Explanation:
84% of 1.906
= \(\frac{84}{100}\) of 1.906
= 1.906 x 0.84
= 1.60104

Question 22.
75% of .7575
Answer:
0.568125
Explanation:
75% of .7575
= \(\frac{75}{100}\) of 0.7575
= 0.7575 x 0.75
= 0.568125

Question 23.
Jessie deposited $824.25 of his babysitting money into . an account that pays 4.5% interest. How much will he have in his account at the end of one year?
Answer:
$861.35
Explanation:
Jessie deposited $824.25 of his babysitting money into an account that pays 4.5% interest.
SI = PRT/100
SI = 824.25 x 4.5 x 1 = 37.09125
Total amount in his account at the end of one year,
Amount = Principle + interest
Amount = 824.25 + 37.09125
Amount = $861.35

Question 24.
What is the annual rate of interest on a loan of $1,500 if you have paid a total of $120 in interest after two years?
Answer:
4%
Explanation:
The annual rate of interest on a loan of $1,500.
If paid a total of $120 in interest after two years,
SI = PRT/100
120 = 1500.00 x R x 2
R = 120 / 1500 x 2
R = 0.04
R= 4%

Question 25.
Chris bought a jacket that was marked $50 before tax. He paid $53.50 after tax. What percent tax did he pay? ______________
If the jacket was on sale and was originally marked $75, by what percent did the price decrease? ______________
Answer:
7%, 33%
Explanation:
A jacket that was marked $50 before tax.
He paid $53.50 after tax,
53.5 – 50 = 3
3.5/50 = 0.07 = 7%
The jacket was on sale and was originally marked $75,
by what percent did the price decrease.
50/75 x100 = 66.66
100 – 66.66 = 33.33
33% or 33.33%

Provide the ordered pairs for the points plotted on the graph.

Question 26.
A ______________
Answer:
A(1,3)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, A(1,3).

Question 27.
B _______________
Answer:
B(4, 4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, B(4, 4).

Question 28.
C _______________
Answer:
C(-5, 2)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, C(-5, 2)

Question 29.
D _______________
Answer:
B(4, -4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, B(4, -4).

Question 30.
E _______________
Answer:
E(-4, -2)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, E(-4, -2).

Question 31.
F _______________
Answer:
F(7, 6)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, F(7, 6).

Question 32.
G _______________
Answer:
G(-2, 5)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, G(-2, 5).

Question 33.
H _______________
Answer:
H(-6, -6)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, H(-6, -6).

Question 34.
I _______________
Answer:
H(-3, 8)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, H(-3, 8).

Question 35.
J _______________
Answer:
J(3,- 8)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, J(3,- 8).

Plot the following points on the grid provided:

Question 36.
A (1, 4)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, A(1, 4) is marked as above in the x, y plain.

Question 37.
B (4, 1)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, b(4, 1) is marked as above in the x, y plain.

Question 38.
C (3, 9)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, C(3, 9) is marked as above in the x, y plain.

Question 39.
D (-9, -3)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, D(-9, -3) is marked as above in the x, y plain.

Question 40.
E (-4, 4)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, E(-4, 4) is marked as above in the x, y plain.

Question 41.
F (-1, -4)

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, A(-1, -4) is marked as above in the x, y plain.

Question 42.
A train has 7 cars and can carry 224 people. If the train adds 2 extra cars, how many people can it carry? What is the unit rate per car?
Answer:
32 unit rate per car
64 people can carry
Explanation:
A train has 7 cars and can carry 224 people
one car carry = 224/7 = 32
each car carry 32 people
If the train adds 2 extra cars
7 + 2 = 9 cars
9 cars x 32 = 288
288 – 224 = 64 people.

Question 43.
How fast is Car A going?
Answer:
Speed = 1 mile per minute
Explanation:
Speed = Distance / Time
Speed = 5 / 5
Speed = 1 mile per minute

Question 44.
How fast is Car B going?
Answer:
Speed = 3 miles per minute
Explanation:
Speed = Distance / Time
Speed = 9 / 3
Speed = 3 miles per minute

Question 45.
How far will Car A have gone after 5 minutes?
Answer:
5 miles
Explanation:
Speed = 1 mile per minute
Time = 5 minutes.
Distance = speed x time
Distance = 1 x 5 miles

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 1–5 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 1-5 Answer Key

Add or subtract.

Question 1.

Answer:
311
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 2.

Answer:
505
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 3.

Answer:
1573
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 4.

Answer:
4906
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 5.

Answer:
652,576
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 6.

Answer:
838
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 7.

Answer:
1219
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 8.

Answer:
6395
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 9.

Answer:
4889
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 10.

Answer:
379
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Round to the nearest thousand, then add or subtract.

Question 11.

Answer:
Nearest thousand is 21,000.
sum = 21,022
Explanation:
Nearest thousand to 6234 is 6000,
Nearest thousand to 14788 is 15000.
6000 + 15000 = 21000.
So, 21022 is nearest to 21000.

Question 12.

Answer:
Nearest thousand is 54,000.
sum = 53,931
Explanation:
Nearest thousand to 24573 is 25000,
Nearest thousand to 29358 is 29000.
25000 + 29000 = 54000.
So, 53931 is nearest to 54000.

Question 13.

Answer:
Nearest thousand is 67,000.
sum = 66,587
Explanation:
Nearest thousand to 12661 is 13000,
Nearest thousand to 44867 is 45000.
Nearest thousand to 9059 is 9000.
13000 + 45000 + 9000 = 67000.
So, 66587 is nearest to 67000.

Question 14.

Answer:
Nearest thousand is 71,000.
sum = 70,364
Explanation:
Nearest thousand to 15768 is 16000,
Nearest thousand to 44903 is 45000.
Nearest thousand to 9693 is 10000.
16000 + 45000 + 10000 = 71000.
So, 70364 is nearest to 71000.

Question 15.

Answer:
Nearest thousand is 90,000.
sum = 89,853
Explanation:
Nearest thousand to 79255 is 790000,
Nearest thousand to 5828 is 6000.
Nearest thousand to 4770 is 5000.
79000 + 6000 + 5000 = 90000.
So, 89853 is nearest to 90000.

Question 16.

Answer:
Nearest thousand is 9,000;
Difference = 8,576
Explanation:
Nearest thousand to 9870 is 10000,
Nearest thousand to 1294 is 1000.
10000 – 1000 = 9000.
So, 8576 is nearest to 9000.

Question 17.

Answer:
Nearest thousand is 14,000;
Difference = 13,890
Explanation:
Nearest thousand to 17650 is 18000,
Nearest thousand to 3760 is 4000.
18000 – 4000 = 14000.
So, 13890 is nearest to 4000.

Question 18.

Answer:
Nearest thousand is 10,000;
Difference = 10,263
Explanation:
Nearest thousand to 28735 is 29000,
Nearest thousand to 18472 is 19000.
29000 – 19000 = 10000.
So, 10263 is nearest to 10000.

Question 19.

Answer:
Nearest thousand is 12,000;
Difference = 11,716
Explanation:
Nearest thousand to 22908 is 23000,
Nearest thousand to 11192 is 11000.
23000 – 11000 = 12000.
So, 11716 is nearest to 12000.

Question 20.

Answer:
Nearest thousand is 38,000;
Difference = 37,866
Explanation:
Nearest thousand to 93556 is 94000,
Nearest thousand to 55690 is 56000.
94000 – 56000 = 38000.
So, 37866 is nearest to 38000.

Multiply or divide. Round to the nearest hundredth.

Question 21.

Answer:
Nearest hundredth of 3192 is 3000.
Explanation:

Question 22.

Answer:
Nearest hundredth of 22,356 is 22,000.
Explanation:

Question 23.

Answer:
Nearest hundredth of 21,850 is 22,000.
Explanation:

Question 24.

Answer:
Nearest hundredth of 30,260 is 30,000.
Explanation:

Question 25.

Answer:
Nearest hundredth of 48,766 is 49,000.
Explanation:

Question 26.

Answer:
Nearest hundredth is 14.
Explanation:

Question 27.

Answer:
Nearest hundredth is 21.
Explanation:

Question 28.

Answer:
Nearest hundredth of 58.25 is 58.
Explanation:

Question 29.

Answer:
Nearest hundredth of 18.36 is 18.
Explanation:

Question 30.

Answer:
Nearest hundredth of 13.35 is 13.
Explanation:

Round, then multiply or divide.

Question 31.

Answer:
Nearest number is 72,000;
product = 77,112
Explanation:
Nearest number of 918 is 900.
Nearest number of 84 is 80.
Ignore the zeros and multiply the numbers.
8 x 9 = 72
Then add the number of zeros to the product as 72,000.
So, nearest product of 77,112 is 72,000.

Question 32.

Answer:
Nearest number is 300,000;
product = 297,724
Explanation:
Nearest number of 9604 is 10000.
Nearest number of 31 is 30.
10,000 x 3 = 300,000
So, nearest product of 297,724 is 300,000.

Question 33.

Answer:
Nearest number is 24,000,000;
product = 21,996,652
Explanation:
Nearest number of 77453 is 80000.
Nearest number of 300 is 300.
Ignore the zeros and then multiply the numbers.
8 x 3 = 24
Then add the zeros to the product as 24,000,000.
So, nearest product of 21,996,652 is 24,000,000.

Question 34.

Answer:
Nearest number is 5,600,000;
product = 5,067,270
Explanation:
Nearest number of 13845 is 140000.
Nearest number of 366 is 400.
140,000 x 400 = 5,600,000
So, nearest product of 5,067,270 is 5,600,000.

Question 35.

Answer:
Nearest number is 48,000,000;
product = 46,163,126
Explanation:
Nearest number of 79867 is 80000.
Nearest number of 578 is 600.
80,000 x 600 = 48,000,000
So, nearest product of 46,163,126 is 48,000,000.

Question 36.

Answer:
3.09
Explanation:

3.0887 is round off to 3.09

Question 37.

Answer:
5.86
Explanation:

5.8571 is round off to 5.86

Question 38.

Answer:
16.68
Explanation:

Question 39.

Answer:
121.89
Explanation:

Question 40.

Answer:
1,025.57
Explanation:

Give the place value of the number 7 for questions 41-44.

Question 41.
1,845,732
__________
Answer:
7 is in Hundredth place.
Explanation:
7 is in hundredth place as shown below.

Question 42.
45.357
__________
Answer:
7 is in Thousandth place.
Explanation:
The value of digit depends on the place it occupies.

Question 43.
73,561,132.001
__________
Answer:
7 is in Ten millions place.
Explanation:
The value of digit depends on the place it occupies.

Question 44.
20.075
__________
Answer:
7 is in Hundredths place.
Explanation:
The value of digit depends on the place it occupies.

Question 45.
Parks Commissioner Davis is planning for the town’s upcoming fiscal year. Last year the town had a total of 2,435 visitors to its nature center, 7,693 visitors to its children’s park, and 9,287 visitors to its arboretum. How many visitors did the town’s parks have, in total, last year?
Answer:
19415 visitors
Explanation:
Last year the town had a total of 2,435 visitors to its nature center,
7,693 visitors to its children’s park,
9,287 visitors to its arboretum.
Total number of visitors to the town’s parks last year,
2,435 + 7,693 + 9,287 = 19,415

Question 46.
Last year Trey had 435 coins in his collection. This year Trey added 124 more coins to his collection. How many coins does he now have in his collection?
Answer:
559 coins
Explanation:
Last year Trey had 435 coins in his collection.
This year Trey added 124 more coins to his collection.
Total coins he now have in his collection 435 + 124 = 559 coins.

Question 47.
Edie’s favorite magazine has a total of 1,476 pages of advertising each year. If the magazine is published every month, about how many pages of advertising are in each issue?
__________________
How many pages exactly?
__________________
Answer:
About 120 pages;
123 pages exactly.
Explanation:
Edie’s favorite magazine has a total of 1,476 pages of advertising each year.
If the magazine is published every month,
Total pages of advertising in each issue every month,
1 year has 12 months.
1476 ÷ 12 =123 pages exactly,
about 120 pages every month.

Question 48.
At 1,776 feet in height, the new Freedom Tower in New York will be one of the tallest buildings in the world. What is the height of the building written in expanded form?
Answer:
(1 x 1000) + (7 x 100) + (7 x 100  (6 x 1)
Explanation:
Given height is 1,776 feet ,
In expanded form we write the numbers according to their place values.
1 in thousands place, 7 is in hundreds place, 7 is in tens place and 6 is in ones place.
(1 x 1000) + (7 x 100) + (7 x 100  (6 x 1)

Question 49.
What is the word form of the number 19,238,976?
Answer:
Nineteen million, two hundred thirty eight thousand, nine  hundred seventy six.
Explanation:
Given number 19,238,976
In word form we write the numbers according to their place values.
So, 19,238,976 is written as,
Nineteen million, two hundred thirty eight thousand, nine  hundred seventy six.

Calculate using order of operations (PEMDAS).

Question 50.
5 × (7 – 3)² + (19 — 5) × 2 + (6 – 3) × 2 + 2³
Answer:
122
Explanation:
5 × (7 – 3)² + (19 — 5) × 2 + (6 – 3) × 2 + 2³
= 5 × (4)² + (14) × 2 + (3) × 2 + 8
= 5 x 16 + 28 + 6 + 8
= 80 + 28 + 6 + 8
= 122

Question 51.
29 + (3 × 5) × 2 + (8 – 3)²
Answer:
84
Explanation:
29 + (3 × 5) × 2 + (8 – 3)²
= 29 + (15) × 2 + (5)²
= 29 + (15) × 2 + (5)²
= 29 + 30 +25
= 84

What number property does each expression display?

Question 52.
5 + (4 + 6) = (5 + 4) + 6
Answer:
Associative property of Addition.
Explanation:
a + (b + c) = (a + b) + c
5 + (4 + 6) = (5 + 4) + 6
15 = 15
Question 53.
2(6 + 3) = 2(6) + 2(3)
Answer:
Distributive property of Multiplication over Addition.
Explanation:
a x (b + c) = a x b + a x c
2(6 + 3) = 2(6) + 2(3)
2(9) = 12 + 6
18 = 18

Question 54.
15 + 16 + 18 = 18 + 16 + 15
Answer:
Commutative property of Addition.
Explanation:
Commutative property of Addition
a + b + c = c + b + a
15 + 16 + 18 = 18 + 16 + 15
31 + 18 = 34 + 15
49 = 49

Question 55.
24(1) = 24
Answer:
Identity property of Multiplication.
Explanation:
a x 1 = a
Identity property of Multiplication.
21 x 1 = 24

Question 56.
8 + 0 = 8
Answer:
Identity property of Addition.
Explanation:
Identity property of Addition.
a + 0 = a
Question 57.
20 × 1 = 20
Answer:
Identity property of Multiplication.
Explanation:
a x 1 = a
Identity property of Multiplication.
20 x 1 = 20

Question 58.
4 × (5 × 3) = (4 × 5) × 3
Answer:
Associative property of Multiplication.
Explanation:
a x (b x c) = (a x b) x c
4 × (5 × 3) = (4 × 5) × 3
4 x 15 = 20 x 3
60 = 60
Question 59.
63(0) + (63 + 0) = 0 + 63 = 63
Answer:
Zero property of Addition and Multiplication..
Explanation:
a x 0 + a + 0 = a
Zero property of Addition
a + 0 = a
Zero property of Multiplication.
a x 0 = 0
63(0) + (63 + 0) = 0 + 63 = 63

Solve each equation and indicate the point on the number line that corresponds with the answer.

Question 60.
-6 + 10 – 6 = ____
Answer:
D
Explanation:

-6 + 10 – 6 = 10 – 12 = – 2
Question 61.
-10 + 5 – 4 = ___
Answer:
C
Explanation:

-10 + 5 – 4 = 5 – 14 = – 9

Question 62.
-10 + (-4) + 8 = ___
Answer:
B
Explanation:

-10 + (-4) + 8
= 8 – 14
= – 6

Question 63.
9 – 5 + (-8) = ___
Answer:
A
Explanation:

9 – 5 + (-8)
= 9 – 5 – 8
= 9 – 13
= -4

Calculate.

Question 64.
—5 × 15
Answer:
-75
Explanation:
As -5 is negative integer multiplicand,
the product also negative integer, as below.
– 5 x 15 = – 75

Question 65.
-45 ÷ 9
Answer:
-5
Explanation:
As -45 is negative integer dividend,
the quotient also negative integer, as below.
-45 ÷ 9 = -5

Question 66.
63 ÷ (-7)
Answer:
-9
Explanation:
As -7 is negative integer divisor,
the quotient also negative integer, as below.
63 ÷ (-7) = -9

Question 67.
4 × (-6) ÷ -3
Answer:
8
Explanation:
4 x -6 = -24
-24 ÷ -3
As both the devisor and dividend are negative integers,
the result is positive integer, as shown below.
24 ÷ 3 = 8

Question 68.
Calculate: |-45| + |45| ___________
Answer:
90
Explanation:
45 is a absolute value with mod symbol,
Mod of any symbol get positive.
|-45| + |45| = 45 + 45 = 90

Question 69.
Which is larger: |-134| or |-135|? ________
Answer:
|-135|
Explanation:
|-135| is larger due to the 135 is a absolute value with mod symbol.

Question 70.
If Noah arrives 23 minutes late for an appointment and Matthew arrives 28 minutes early, who arrived closer to the correct time? ________________________________________________
Answer:
Noah
Explanation:

23 is closer to 0
Noah arrived closer to the correct time.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Pretest existing for free of cost

Complete the following test items on pages 4-8.

Question 1.
Restate the number 4,587,902.453.
Expanded form: ________________
Written form: _________________
Answer:
Expanded form: (4 x 1,000,000) + (5 x 100,000) + (8 x 10,000) + (7 x 1,000) + (9 x 100) + (2 x 1) + (4 x 0.1) +
(5 x 0.01) + (3 x 0.001)
Written form: For million five hundred eighty seven thousand nine hundred two and four hundred and fifty three thousandths.
Explanation:
Numbers can be written in 3 ways like,
Standard form; Expanded form and Written form.
In Expanded form each number is multiplied with their place value, as shown above.
In written form each number is written in word form according to their place values.
Numbers can be written according to their place values as shown above.

Question 2.
Cheryl’s Department Store is having a sale. They have 145 coats in stock and are adding 55 more. If at the end of the sale they still have 25 coats in stock, how many coats did they sell?
Answer:
175 coats
Explanation:
Cheryl’s Department Store have 145 coats in stock and are adding 55 more.
145 + 55 = 200
If at the end of the sale they still have 25 coats in stock,
Number of coats sold = 200 – 25 = 175 coats.

Question 3.
Tracey pedals 16 miles a day on a stationary bicycle. How many miles does she pedal in the month of March? (Remember, March has 31 days.) _______
How many yards does she pedal? ___________
Answer:
496 miles;
872,960 yards.
Explanation:
Tracey pedals 16 miles a day on a stationary bicycle.
How many miles does she pedal in the month of March,
March has 31 days = 31 x 16 = 496 miles,
Number of yards she pedal,
1 mile = 1760
496 miles = 1760 x 496
= 872,960 yards.

Calculate.

Question 4.

Answer:
792
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 5.

Answer:
-649
Explanation:
As we are multiplying -11 with 59,
we get the product as -649 as shown below.

Question 6.

Answer:
2812
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 7.

Answer:
1917
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 8.

Answer:
83
Explanation:

Question 9.

Answer:
21
Explanation:

Question 10.

Answer:
107.118
Explanation:

Question 11.

Answer:
6.2
Explanation:

Question 12.
Bailey bought 11\(\frac{1}{4}\) kilograms of bird feed. On the way home, he spilled 3\(\frac{5}{8}\) kilograms. How much bird feed does he still have left? _____________________________
Answer:
7\(\frac{5}{8}\) kilograms
Explanation:
11\(\frac{1}{4}\)– 3\(\frac{5}{8}\)
= \(\frac{(11 X 4) +1}{4}\)– \(\frac{(3 X 8)+5}{8}\)
= \(\frac{45}{4}\)– \(\frac{29}{8}\)
= \(\frac{90}{8}\)– \(\frac{29}{8}\)
= \(\frac{90 – 29}{8}\)
= \(\frac{61}{8}\)
=7\(\frac{5}{8}\) kilograms

Question 13.
Margaret mixes 1,400 centiliters of grape juice with 5\(\frac{2}{3}\) liters of seltzer and \(\frac{2}{5}\) liters of orange juice: How many liters of punch will this make?
Answer:
7\(\frac{7}{15}\) L
Explanation:
Margaret mixes 1,400 centiliters of grape juice with 5\(\frac{2}{3}\) liters of seltzer and,
\(\frac{2}{5}\) liters of orange juice,
Total liters of punch will this make,
1.4 + 5\(\frac{2}{3}\) + \(\frac{2}{5}\)
= 1.4 +\(\frac{15 + 2}{3}\)+\(\frac{2}{5}\)
= 1.4 + \(\frac{17}{3}\) + \(\frac{2}{5}\)
= \(\frac{1.4 X 15}{15}\) + \(\frac{17 X 5}{15}\)+ \(\frac{2 X 3}{15}\)
= \(\frac{21 + 85 + 6}{15}\)
= \(\frac{112}{15}\)
= 7\(\frac{7}{15}\)

Question 14.
1\(\frac{4}{15}\) + 7\(\frac{2}{5}\) + \(\frac{1}{3}\) = ___________
Answer:
9
Explanation:
1\(\frac{4}{15}\) + 7\(\frac{2}{5}\) + \(\frac{1}{3}\)
= \(\frac{(15 X 1) + 4}{15}\) + \(\frac{(7 X 5) + 2}{5}\) + \(\frac{1}{3}\)
= \(\frac{19}{15}\) + \(\frac{37}{5}\) + \(\frac{1}{3}\)
= \(\frac{19}{15}\) + \(\frac{37 X 3}{5 X 3}\) + \(\frac{1 X 5}{3 X 5}\)
= \(\frac{19}{15}\) + \(\frac{111}{15}\) + \(\frac{5}{15}\)
= \(\frac{19 + 111 + 5}{15}\)
= \(\frac{135}{15}\)
= 9

Question 15.
-9 + 10 – (-8) + 6(-2) + \(\frac{6}{-2}\) =
Answer:
-6
Explanation:
-9 + 10 – (-8) + 6(-2) + \(\frac{6}{-2}\)
= 1 + 8 – 12 + \(\frac{6}{-2}\)
= – 3 – 3
= -6

Question 16.
Solve for x: x — 9 = 18 ______________
Answer:
x = 27
Explanation:
x — 9 = 18
x = 18 + 9
x = 27

Question 17.
Solve for x: 2x + 5 < 15 _____
Answer:
x < 5
Explanation:
2x + 5 < 15
= 2x  < 15 – 5
2x <10
x < 5

Question 18.
What property is represented by the following equation?
4(5 + 6) = 4 × 5 + 4 × 6
______________
Answer:
Distributive Property of Multiplication over Addition.
Explanation:
Distributive Property of Multiplication over Addition.
a x (b x c) = a x b + a x c
4(5 + 6)
= 4 × 5 + 4 × 6
= 20 + 24
= 44

Question 19.
What property is represented by the following equation?
(3 + 6) + 6 = 3 + (6 + 6)
Answer:
Associative Property of Addition.
Explanation:
Associative Property of Addition.
(x + y) + z = x + (y + z)
(3 + 6) + 6 = 3 + (6 + 6)
15 = 15

Question 20.
|—9| + (2 + 3)² — (6 ÷ 3) + 4(8 × 3) + 4(5 — 3) = ___________
Answer:
136
Explanation:
|—9| + (2 + 3)² — (6 ÷ 3) + 4(8 × 3) + 4(5 — 3)
= 9 + 5² — 2 + 96 + 8
= 9 + 25 — 2 + 96 + 8
= 9 + 23 + 96 + 8
= 136

Question 21.
Give the coordinates for the points.
A ___________
B ___________
C ___________
D __________

Answer:
A(2,3); B(-3,5); C(1,-5); D(-3,-3)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.

Question 22.
Restate in exponent form, then solve:
4 × 4 × 4 + 2 × 2 =
_________________
Answer:
= 68
Explanation:
= 4 × 4 × 4 + 2 × 2
= 4³ + 2²  
= 68

Question 23.
What is the area of the rectangle?
__________________

What is the perimeter of the rectangle?
______________
Answer:
Area = 120 sq cm;
Perimeter = 44 cm.
Explanation:
Area of a rectangle = length x width
A = l x w
A = 12 x 10
A = 120 sq cm
Perimeter of  a rectangle P = 2(length + width)
P = 2(L+W)
P = 2(12 + 10)
P = 44 cm

Question 24.
What is the area of the circle? (Use 3.14 for π.)
______________

What is the circumference of the circle?
_______________
Answer:
Area = 19.625 sq cm;
Circumference = 15.75 cm.
Explanation:
Area of circle A = π.r²
A = 3.14 x 2.5²
A = 19.625 sq cm
Circumference = 2 πr
= 2 x 3.14 x 2.5
= 15.75 cm.

Question 25.
Identify the following angles as obtuse, acute, or right.



Answer:



Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If the angle formed between two rays is exactly 90° then it is called a right angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as acute.

Question 26.
Identify the triangles as scalene, isosceles, or equilateral.

_______

_____

__________
Answer:



Explanation:
All angles of a scalene triangle are unequal, all are of different size.
An equilateral triangle is a triangle with all three sides of equal length.
An isosceles triangle is a triangle with two equal sides.

Question 27.
Ramon spends $28.94 a month having pictures developed. He is working on a project that will take 19 months to finish. How much should he plan to spend on developing pictures for the project?
Answer:
$549.86
Explanation:
Ramon spends $28.94 a month having pictures developed.
He is working on a project that will take 19 months to finish.
Total amount he plan to spend on developing pictures for the project,
$28.94 a month x 19 months
28.94 x 19 = 549.86

Question 28.
Restate 3.6 as an improper fraction and a mixed number. ____________
Answer:
3\(\frac{3}{5}\) or \(\frac{18}{5}\)
Explanation:
3\(\frac{3}{5}\) or \(\frac{18}{5}\)
= \(\frac{15 + 3}{5}\)
= \(\frac{18}{5}\)

Question 29.
Restate 4\(\frac{5}{8}\) as a decimal. __________________ ________________
Answer:
4.625
Explanation:
4\(\frac{5}{8}\)
= \(\frac{(4 X 8) +5}{8}\)
= \(\frac{37}{8}\)
= 4.625

Question 30.
Is the following true or false? \(\frac{5}{16}\) = \(\frac{60}{192}\) _______ _______________
Answer:
True
Explanation:
\(\frac{5}{16}\) = \(\frac{60}{192}\)
\(\frac{5 X 12}{16 X 12}\) = \(\frac{60}{192}\)
Thus, equation is TRUE.

Question 31.
\(\sqrt{73}\) is between ____________ and _______________
Answer:
8 and 9
Explanation:
Given, \(\sqrt{73}\)
\( sqrt {64} \) = 8
\( sqrt {81} \) = 9
\( sqrt {73} \) lies between 8 and 9

Question 32.
Drayson deposits $125 in a bank account that earns 4% simple interest. How much money will he have in the account after 1 year? ______
After 2 years ? _____
Answer:
$130 after 1year,
$135.20 after 2 years.
Explanation:
SI = (PTR)/100
SI = 125 x 4 x 1 / 100
SI = 5
Amount after 1 year = 125 + 5 = $130
SI = (PTR)/100
SI = 130 x 4 x 1 / 100
SI = 5.2
Amount after 1 year = 130 + 5.2 = $135.2

Question 33.
What is the mode of the data distribution?

What is the median?
___________
Answer:
Mode = 38
Median = 38
Explanation:
values with respect to the stem leaf data plot is,
{13, 15, 23, 26, 29, 33, 38, 38, 38, 44, 44, 45, 46, 46, 43, 54, 56}
Median is the mid point in the given data.
Mode : frequently occurring or observed value

Question 34.
\(\frac{4}{7}\) × 5\(\frac{4}{9}\) = ______
Answer:
3\(\frac{1}{9}\)
Explanation:
\(\frac{4}{7}\) × 5\(\frac{4}{9}\)
= \(\frac{4}{7}\) × 5\(\frac{9 x 5 + 4}{9}\)
= \(\frac{4}{7}\) × \(\frac{45}{9}\)
= \(\frac{4 X 45}{63}\)
= \(\frac{180}{63}\)
= 3\(\frac{1}{9}\)

Question 35.
What is \(\frac{3}{8}\) of 88%?
Answer:
33%
Explanation:
\(\frac{3}{8}\) of 88%
= \(\frac{3}{8}\) x 88%
= 3 x 11%
= 33%

Question 36.
What is 30% of .675? _______________
Answer:
0.2025
Explanation:
30% x 0.675
(30 x 0.675)/100 = 0.2025

Question 37.

Answer:
1.5667
Explanation:
0.15 x 100 = 15
0.235 x 100 = 23.5

0.235 / 0.15 = 1.5667

Question 38.
latex]\frac{4}{3}[/latex] + latex]\frac{2}{3}[/latex] + latex]\frac{5}{3}[/latex] – latex]\frac{1}{3}[/latex] – latex]\frac{7}{3}[/latex] = _____
Answer:
1
Explanation:
latex]\frac{4}{3}[/latex] + latex]\frac{2}{3}[/latex] + latex]\frac{5}{3}[/latex] – latex]\frac{1}{3}[/latex] – latex]\frac{7}{3}[/latex]
= latex]\frac{4 + 2 + 5 – 1 – 7}{3}[/latex]
= latex]\frac{11 – 8}{3}[/latex]
= latex]\frac{3}{3}[/latex]
=1

Question 39.
Identify each quadrilateral as a square, rectangle, kite, rhombus, or trapezoid.

_____

_____

_____

_____

_____
Answer:





Explanation:
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.
A square is closed, two-dimensional shape with 4 equal sides.
Rhombus is a quadrilateral with all equal sides.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
A Kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.

Question 40.
Identify the following figures.

_____

_____

_____
Answer:



Explanation:
Hexa means six and gona means angles.
A hexagon is a closed two-dimensional polygon with six sides.
Hexagon has 6 vertices and 6 angles.
Penta denotes five and gon denotes angle.
A pentagon is a simple polygon, which has five sides and five angles.
Hepta means seven and gon means sides.
A Heptagon is a polygon with seven sides and seven angles.
It has seven straight sides and seven corners or vertices.

Question 41.
Restate 5\(\frac{6}{13}\) as an improper fraction.
Answer:
\(\frac{71}{13}\)
Explanation:
5\(\frac{6}{13}\)
= 5\(\frac{(5 X 13) + 6}{13}\)
= \(\frac{65 + 6}{13}\)
= \(\frac{71}{13}\)

Question 42.
Restate \(\frac{43}{16}\) as a mixed number.
Answer:
2\(\frac{11}{16}\)
Explanation:
\(\frac{43}{16}\)

2\(\frac{11}{16}\)

Question 43.
What are the chances of choosing a black marker out of a bag containing 3 red markers, 5 blue markers, 3 yellow markers, and 4 black markers? What is the probability of choosing two black markers if the first marker is put back before the second is drawn?
Answer:
\(\frac{4}{15}\); \(\frac{16}{225}\)
Explanation :
Total number of markers = 3 + 5 + 3 + 4 = 15
Probability of choosing black markers
Number of black markers = 4
Probability = black markers ÷ total no of markers
4 ÷ 15 = \(\frac{4}{15}\)
Probability of choosing a black markers again
Number of black markers = 4
remaining number of marbles after choosing a black markers = 4 – 1 + 1 = 4
[the black marker is put back ]
Probability of choosing black markers= black markers ÷ total markers x remaining markers
= 4 ÷ 15 x 15
= \(\frac{4}{225}\)

Question 44.
According to the graph, how many videos did Jamie watch in July?

Answer:
15
Explanation:
According to the graph of Jamie’s Summer Video List
he watched 15 videos July.

Question 45.
During which week did Kelly and Heather swim the same distance?

Answer:
Week 2
Explanation:
According to the graph of Kelly and Heather’s Workout Schedule,
second week they swim the same distance.

Question 46.
What fruit is most preferred by the students?

Answer:
Apples
Explanation:
From the above pie chart of Favorite Fruits,
most preferred fruit by the students are Apples.

Question 47.
Peggy’s score was about 30 pins higher than whose score?

Answer:
Kathy
Explanation:
From the above chart of Bowling Scores,
Peggy’s score was about 30 pins higher than Kathy score.

Question 48.
What is the range of the data in the box-and-whisker plot below?
What is the average (mean) of the data points shown?
________________

Answer:
15; 11.9; 4.12
Explanation:
The range of the data in the box-and-whisker plot is,
R = max – min
R = 20 – 5 = 15
mean average = sum of event / total number of events.
mean average = 5 + 8.5 + 12 + 14 + 20 / 5
mean average = 59.5/5 = 11.9
11.9 – 5 = 6.9
11.9 – 8.5 = 3.4
12 – 11.9 = 0.1
14 – 11.9 = 2.1
20. – 11.9 = 8.1
6.9 + 3.4 + 0.1 + 2.1 + 8.1 = 20.6
average mean = 20.6/5 = 4.12

Question 49.
How much plastic wrap would you need to cover this rectangular solid?

Answer:
94 sq in.
Explanation:
TSA – Total Surface Area to be calculated
the surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA=2lw+2lh+2hw, to find the surface area
TSA = 2(4 x 5 + 5 x 3 + 3 x 4)
TSA = 2(20 + 15 + 12)
TSA = 2 x 47
TSA = 94 sq in

Question 50.
Name two line segments. _____________
Name four rays. ________
Name a line. _________________

Answer:
Line segments:\(\overline{BD}\), \(\overline{DB}\), \(\overline{CA}\), \(\overline{AC}\),\(\overline{HG}\), \(\overline{GH}\), \(\overline{BE}\), \(\overline{EB}\),\(\overline{AB}\), \(\overline{AF}\), \(\overline{FA}\);
Rays: \(\overline{AC}\), \(\overline{BD}\), \(\overline{BE}\),
\(\overline{AF}\), \(\overline{BA}\), \(\overline{AB}\);
Line: \(\overline{AB}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Question 51.
Fill in a Venn Diagram that displays the following data: There are two groups of students, 30 who take the bus to school and 25 who have a younger sibling in the school. There are 10 students who take the bus and who also have a younger sibling in the school.

Answer:

Explanation:
There are two groups of students,
30 who take the bus to school and,
25 who have a younger sibling in the school.
There are 10 students who take the bus and who also have a younger sibling in the school.
who take bus to school 30 – 10 = 20,
who have younger siblings 25 – 10 = 15.

Question 52.
Are the rates in the table below proportional?

Answer:
No,
Explanation:
Car A is going 45 miles per hour and Car b is going 48 miles per hour.
So, they are not proportional to each other.

Question 53.
What is the unit rate for the price of grapes as shown on the graph below?

Answer:
1.50
Explanation :
By observing the graph we can conclude that,
for 6 dollars we get 9 pounds of grapes.
for 1 dollar we get,
9 ÷ 6 = 1.50 pounds of grapes
Hence, 1.5 is the unit rate for the price of grapes.

Question 54.
What is the best way to get a representative sample of the people at a baseball game for a survey about parking at the stadium?
(a) Choose one of the luxury boxes at random and survey all the people in that box.
(b) Survey the first 50 people to walk into the stadium.
(c) Choose 50 seat numbers at random and survey the people in those seats.
Answer:
Option(C)
Explanation :
A representative survey must be done at random.
If we choose to survey the people in luxury boxes,
we can not get a perfect result as they might get a better parking space.
If we choose to survey the first 50 people that walk in,
we can’t get a perfect result,
as the first 50 people are likely to find more empty spots that the people that come in later.

Question No 55.
Complete the probability table below.

Answer:

Explanation:
By looking at the A probability we can say that
Number of wins = 23
Total matches = 90
Line-wise By looking at the C probability we can say that,
probability of a match being a draw = \(\frac{53}{90}\) = 0.59
Number of draws = 53
Therefore number of loses = 90 – 23 + 53
= 13
Probability of losing a match = 13 ÷ 90
= \(\frac{13}{90}\)
= 0.16

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Posttest existing for free of cost.

McGraw-Hill Math Grade 7 Posttest Answer Key

Complete the following test items on pages 156-160.

Question 1.
Restate the number 5,176,802.4539.
Expanded form: ____________________
Written form: ____________________
Answer:
Expanded form:
(5 x 1,000,000) +(1 x 100,000) + (7 x 10,000) + (6 x 1,000) + (5 x 0.01) + (3 x 0.001) + (9 x 0.0001)
Written form :
Five million one hundred seventy-six thousand eight hundred two and four thousand five hundred thirty-nine ten thousandths.
Explanation:
In Expanded form each number is multiplied with their place value, as shown above.
In written form each number is written in word form according to their place values.

Question 2.
Brian’s Bakery is having a sale on cakes. They have 95 cakes and will be baking 23 more before the start of the sale. If at the end of the sale they still have 7 cakes, how many cakes did they sell?
Answer:
111 cakes
Explanation:
Initially they have 95 cakes,
By adding 23 more before the start of the sale ,
the number of cakes are 95 + 23 = 118
They left with 7 cakes at the end of the sale,

Question 3.
Stuart pedals 19 miles a day on his bicycle. How many miles does he pedal in the month of February? (Remember, February has 28 days.)
Answer:
532 miles
Explanation:
pedals 19 miles a day on his bicycle,
He pedal in the month of February which has 28 days.
By multiplying 19 x 28, we get the total number of miles he pedaled in the month of February.

Question 4.

Answer:
-2010
Explanation:

As we are multiplying 134 with -15 which is negative number,
we get the product as -2010 as shown below.

Question 5.

Answer:
5320
Explanation:
As we are multiplying 133 with 40, the product is 5320

Question 6.

Answer:
22032
Explanation:
As we are multiplying -432 with -51, the product is 22032.
Both of the given numbers are negative integers,
So, we get product as positive after multiplication.

Question 7.

Answer:
17617
Explanation:
As we are multiplying 223 with 79, the product is 17,617.

Question 8.

Answer:
28
Explanation:

Question 9.

Answer:
-21
Explanation:
As divisor is negative number, the answer is also with negative sign.

Question 10.

Answer:
19.4166
Explanation:

Question 11.

Answer:
24
Explanation:

Question 12.
Danetta bought 19 \(\frac{3}{8}\) kilograms of gerbil food. On the way home, she spilled 3 \(\frac{4}{5}\) kilograms. How much gerbil food does she still have?
Answer:
15 \(\frac{23}{40}\) kilograms of gerbil food.
Explanation:
19 \(\frac{3}{8}\) – 3\(\frac{4}{5}\)
= \(\frac{155}{8}\) – \(\frac{19}{5}\)
= \(\frac{155 X 5}{8 X 5}\) – \(\frac{19 X 8}{5 X 8}\)
= \(\frac{155 X 5}{8 X 5}\) – \(\frac{19 X 8}{5 X 8}\)
= \(\frac{775 – 152}{40}\)
= \(\frac{623}{40}\)
= 15 \(\frac{23}{40}\)

Question 13.
To make his favorite fruit punch, Ezekiel mixes 1,950 centiliters of juice with 1 \(\frac{4}{9}\) liters of seltzer and \(\frac{3}{8}\) liters of orange juice. How many liters of punch will this make?
Answer:
21 \(\frac{23}{72}\) L
Explanation:
19.50 + 1 \(\frac{4}{9}\) + \(\frac{3}{8}\)
= 19.50 + \(\frac{13}{9}\) + \(\frac{3}{8}\)
= \(\frac{19.50 X 72}{72}\) + \(\frac{13 X 8}{9 X 8}\) + \(\frac{3 X 9}{8 X 9}\)
= \(\frac{1404}{72}\) + \(\frac{104}{72}\) + \(\frac{27}{72}\)
= \(\frac{1404 + 104 + 27}{72}\)
= \(\frac{2714}{72}\)
= \(\frac{1535}{72}\)
= 21 \(\frac{23}{72}\)

Question 14.
3 \(\frac{7}{12}\) + 5 \(\frac{1}{5}\) + \(\frac{1}{4}\) = _____________
Answer:
9 \(\frac{1}{30}\)
Explanation:
3 \(\frac{7}{12}\) + 5 \(\frac{1}{5}\) + \(\frac{1}{4}\)
= \(\frac{43}{12}\) + \(\frac{26}{5}\) + \(\frac{1}{4}\)
= \(\frac{43 x 5}{12 X 5}\) + \(\frac{26 X 12}{5 X 12}\) + \(\frac{1 X 15}{4 X 15}\)
= \(\frac{215}{60}\) + \(\frac{312}{60}\) + \(\frac{15}{60}\)
= \(\frac{216 + 312 + 15}{60}\)
= \(\frac{542}{60}\)
=9 \(\frac{2}{60}\)
=9 \(\frac{1}{30}\)

Question 15.
-5 + |-17| – (-6) + 7(-5) – \(\frac{9}{3}\) = _____________
Answer:
-20
Explanation:
-5 + |-17| – (-6) + 7(-5) – \(\frac{9}{3}\)
= -5 + 17 + 6 + 7(-5) – \(\frac{9}{3}\)
= -5 + 17 + 6 – 35 – \(\frac{9}{3}\)
= 23 – 40 –\(\frac{9}{3}\)
= -17 –\(\frac{9}{3}\)
= -17 x 3 –\(\frac{9}{3}\)
= –\(\frac{51}{3}\) – \(\frac{9}{3}\)
=- \(\frac{51 + 9}{3}\)
= –\(\frac{60}{3}\)
= -20

Question 16.
Solve for x: x – 91 ≥ 13 ___________
Answer:
x ≥ 104
Explanation:
x – 91 ≥ 13
x  ≥ 13 + 91
x  ≥ 104

Question 17.
Solve for x: 4x + 11 = 15 _____________
Answer:
x = 1
Explanation:
4x + 11 = 15
4x = 15 – 11
4x = 4
x = 4/4
x = 1

Question 18.
What property is represented by the following equation?
2(6 + 9) = 2 × 6 + 2 × 9
Answer:
Distributive property of Multiplication over Addition.
Explanation:
a x (b + c) = a x b + a x c
let a = 2, b =6 and c = 9
2(6 + 9) = 2 × 6 + 2 × 9

Question 19.
What property is represented by the following equation?
(4 + 8) + 8 = 4 + (8 + 8)
Answer:
Associative property of Addition
Explanation:
a+ (b + c) = (a + b) + c
let a=4, b=8 c = 8
(4 + 8) + 8 = 4 + (8 + 8)

Question 20.
|-7| + (1 + 3)² – (9 ÷ 3) + 5(8 × 3) + 2(10 – 7) = ______________
Answer:
146
Explanation:
|-7| + (1 + 3)² – (9 ÷ 3) + 5(8 × 3) + 2(10 – 7)
7 + 16 – 3 + 5(24) + 2(3)
= 7 + 13 + 120 + 6
= 20 + 120 + 6
= 146

Question 21.
Give the coordinates for the points.

A _________________
B _________________
C _________________
D _________________
Answer:
A(3,6);
B(-5,2);
C(2,-4);
D(-1,1)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.

Question 22.
Restate in exponent form, then solve:
5 × 5 × 5 + 3 × 3 = _______________
Answer:
134
Explanation:
5 × 5 × 5 + 3 × 3
= 5³ + 3²
= 5³ + 3²
= 125 + 9
= 134

Question 23.
What is the area of the rectangle?

What is the perimeter of the rectangle?
Answer:
Area = 306 sq cm;
Perimeter = 70 cm
Explanation:
The area of the rectangle,
A = length x width
A = 18 x 17 = 306 cm²
the perimeter of the rectangle
P = 2(Length + Width)
P = 2(17 + 18)
= 2 x 35
= 70 cm

Question 24.
What is the area of the circle? (Use 3.14 for π)

What is the circumference of the circle?
Answer:
Area = 63.585 sq cm;
Circumference = 28.26 cm
Explanation:
The area of the circle (Use 3.14 for π)
A = π r²
r = 4.5 cm
A = 3.14 x 4.5 x 4.5
A = 63.585 sq cm
the circumference of the circle,
C = 2πr
C = 2 x 3.14 x 4.5
C = 28.26 cm

Question 25.
Identify the following angles as obtuse, acute, or right.

Answer:
Obtuse Angle; Right Angle; Acute Angle.

Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If the angle formed between two rays is exactly 90° then it is called a right angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as acute.

Question 26.
Identify the triangles as scalene, isosceles, or equilateral.

Answer:
Equilateral; Scalene; Isosceles Triangles.

Explanation:
An equilateral triangle is a triangle with all three sides of equal length.
All angles of a scalene triangle are unequal, all are of different size.
An isosceles triangle is a triangle with two equal sides.

Question 27.
Jackie spends $37.95 a month on art supplies. She is working on a project that will take 19 months to finish. How much should she plan to spend on art supplies for the project?
Answer:
$721.05
Explanation:
Jackie spends $37.95 a month on art supplies.
She is working on a project that will take 19 months to finish.
Total amount she plan to spend on art supplies for the project,
$37.95 x 19 = $721.05

Question 28.
Restate 7.6 as an improper fraction and a mixed number.
Answer:
\(\frac{38}{5}\) or 7 \(\frac{3}{5}\)
Explanation:
\(\frac{76}{10}\)
=\(\frac{38}{5}\)
=7\(\frac{3}{5}\)

Question 29.
\(\sqrt{21}\) is between ___________ and _____________.
Answer:
4 and 5
Explanation:
as we know values of
square of 4 is 16 :: sqrt 16 = 4
square of 5 is 25 :: sqrt 25 = 5
sqrt 21 lies between 4 and 5
sqrt 16 < sqrt 21 < sqrt 25

Question 30.
Is the following true or false? \(\frac{4}{11}\) = \(\frac{68}{187}\) _________________
Answer:
True
Explanation:
\(\frac{4}{11}\) = \(\frac{68}{187}\)
\(\frac{4 X 17}{11 X 17}\) = \(\frac{68}{187}\)

Question 31.
Put the following numbers in order from least to greatest:
1.141, 1.014, 1.044, 1.004, 1.9, 1.996, 1.89, .9 ______________
Answer:
0.9; 1.004, 1.014; 1.044; 1.141; 1.89; 1.9; 1.996
Explanation:
Arrange all the given numbers in ascending order by placing whole numbers first,
then decimals number with the least digit according to their place values.

Question 32.
Juliette deposits $295 in a bank account that earns 6% simple interest. How much money will she have in the account after 1 year?
______________ After 2 years? ________________
Answer:
$312.70; $330.40
Explanation:
Juliette deposits $295 in a bank account that earns 6% simple interest
SI = PRT/100
SI = (295 x 6 x 1)/100
SI = $17.7
Amount = $ 295 +$ 17.7 = $ 312.70 after one year
Amount = $ 312.70 + $ 17.7 = $ 330.40 after two years

Question 33.
What is the mode of the data distribution?

What is the median?
Answer:
Mode = 36
Median = 36
Explanation:
The mode is the number or numbers that occur the most frequently.
Given numbers [14, 16, 22, 25, 27, 31, 36, 36, 36, 43, 43, 45, 47, 47, 52, 55, 56]
Put the numbers in numerical order from smallest to largest.
Mode = 36
 First, arrange the given data in ascending order.
Median = Given data [14, 16, 22, 25, 27, 31, 36, 36, 36, 43, 43, 45, 47, 47, 52, 55, 56]
Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 36

Question 34.
\(\frac{2}{7}\) × 2 \(\frac{5}{22}\) = _____________
Answer:
\(\frac{7}{11}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{2}{7}\) × 2\(\frac{5}{22}\)
= \(\frac{2}{7}\) × \(\frac{220}{22}\)
= \(\frac{2 X 220}{7 X 22}\)
= \(\frac{440}{154}\)
= \(\frac{2}{11}\)
= 4\(\frac{2}{3}\)

Question 35.
What is \(\frac{5}{8}\) of 75%? _____________
Answer:
46.875%
Explanation:
\(\frac{5}{8}\) of 75%
\(\frac{5 X 75}{8}\) %
46.875 %

Question 36.
What is 25% of .525?
Answer:
0.13125
Explanation:
25% of .525
\(\frac{25}{100}\) x 0.525
= \(\frac{25 X 0.525}{100}\)
= \(\frac{13.125}{100}\)
= 0.13125

Question 37.

Answer:
2350
Explanation:
While dividing the divisor with the decimal dividend,
multiply the divisor and divided with 100.

Question 38.
\(\frac{5}{4}\) + \(\frac{7}{4}\) + \(\frac{15}{4}\) – \(\frac{9}{4}\) – \(\frac{17}{4}\) = ____________
Answer:
\(\frac{1}{4}\)
Explanation:
\(\frac{5}{4}\) + \(\frac{7}{4}\) + \(\frac{15}{4}\) – \(\frac{9}{4}\) – \(\frac{17}{4}\) =
= \(\frac{5 + 7 + 15 – 9 – 17}{4}\)
= \(\frac{27 – 26}{4}\)
= \(\frac{1}{4}\)

Question 39.
Identify each quadrilateral as a square, rectangle, kite, rhombus, or trapezoid.

Answer:
Trapezoid; Square; Rhombus; Rectangle and Kite.

Explanation:
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.
A square is closed, two-dimensional shape with 4 equal sides.
Rhombus is a quadrilateral with all equal sides.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
A kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.

Question 40.
Identify the following figures.

Answer:
Hexagon; Pentagon; Heptagon.

Explanation:
Hexa means six and gona means angles.
A hexagon is a closed two-dimensional polygon with six sides.
Hexagon has 6 vertices and 6 angles.
Penta denotes five and gon denotes angle.
A pentagon is a simple polygon, which has five sides and five angles.
Hepta means seven and gon means sides.
A Heptagon is a polygon with seven sides and seven angles.
It has seven straight sides and seven corners or vertices.

Question 41.
Restate 9 \(\frac{11}{13}\) as an improper fraction.
Answer:
\(\frac{128}{13}\)
Explanation:
9 \(\frac{11}{13}\)
= \(\frac{9 x 13 + 11}{13}\)
=  \(\frac{117 + 11}{13}\)
=  \(\frac{128}{13}\)

Question 42.
Restate \(\frac{72}{13}\) as a mixed number.
Answer:
5\(\frac{7}{13}\)
Explanation:
=  \(\frac{72}{13}\)
= \(\frac{5 x 13 + 7}{13}\)
=  \(\frac{72}{13}\)

Question 43.
What are the chances of choosing a blue marble out of a bag containing 7 red marbles, 6 green marbles, 11 yellow marbles, and 4 blue marbles?
What is the probability of choosing a blue marble, not replacing it, and then choosing a green marble?
Answer:
\(\frac{1}{7}\) and \(\frac{6}{189}\)
Explanation:
Total number of marbles = 7 + 6 + 11 + 4 = 28
Probability of choosing blue marbles
Number of blue marbles = 4
Probability = marbles ÷ total no of marbles
4 ÷ 28 = \(\frac{1}{7}\)
Probability of choosing a green marble
Number of green marbles = 6
remaining number of marbles after choosing a blue marble = 28 – 1 = 27
Probability of choosing green marbles = marbles ÷ total marbles x remaining marbles
= 6 ÷ 27 x 28
= \(\frac{6}{189}\)

Question 44.
According to the graph, how many miles did Janice swim in September?

Answer:
10 miles
Explanation:
From the above graph of Janice’s Swimming Chart,
he swims 10 miles in september.

Question 45.
During which week did Brian and Ray run the same distance?

Answer:
week 2
Explanation:
From the given chart of Brain nd Ray’s Running Schedule,
they both run same distance in second week.

Question 46.
Which vegetable is most preferred by the students?

Answer:
Cauliflower
Explanation:
From the above pie chart of Favorite vegetables Of The Students,
Cauliflower is preferred by many of the students.

Question 47.
Dean’s score was about 20 points higher than whose score?

Answer:
Joe’s
Explanation:
From the above Dart Scores,
Dean scored the highest and also 20 points more than Joe.

Question 48.
What is the range of the data in the box-and-whisker plot below?

What is the average (mean) of the data points shown? ____________
What is the mean absolute deviation of the data points shown? ___________
Answer:
15; 12.4; 4.72
Explanation:
Range of the data is the difference between max – min
Range = 20 – 5 = 15
mean = \(\frac{5 + 8 + 13 + 16 + 20}{5}\)
mean =\(\frac{62}{5}\)
mean  =12.4
the mean absolute deviation of the data points
I 12.4 – 5 I = 7.4
I 12.4 – 8 I = 4.4
I 12.4 – 13 I = 0.6
I 12.4 – 16 I = 3.6
I 12.4 – 20 I = 7.6
mean absolute deviation( MAD )= \(\frac{7.4 + 4.4 + 0.6 + 3.6 + 7.6}{5}\)
MAD=\(\frac{23.6}{5}\)
MAD  = 4.72

Question 49.
How much plastic wrap would you need to cover this rectangular solid?

Answer:
318 sq in.
Explanation:
TSA – Total Surface Area to be calculated
the surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA=2lw+2lh+2hw, to find the surface area
TSA = 2(7 x 6 + 6 x 9 + 9 x 7)
TSA = 2(42 + 54 + 63)
TSA = 2 x 159
TSA = 318 sq in

Question 50.
Name two line segments.

Name 4 rays. _______________
Name a line. ___________
Answer:
Line segments:
\(\overline{YS}\), \(\overline{XT}\), \(\overline{XR}\), \(\overline{YZ}\),\(\overline{LM}\), \(\overline{ML}\), \(\overline{XY}\), \(\overline{TX}\),\(\overline{RX}\), \(\overline{SY}\), \(\overline{ZY}\);
Rays:
\(\overline{XR}\), \(\overline{XT}\), \(\overline{YS}\), \(\overline{YZ}\),
\(\overline{XY}\), \(\overline{YX}\);
Line:
\(\overline{XY}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Question 51.
Fill in a Venn Diagram that displays the following data:

There are two groups of students, 25 who are in the drama club and 15 who enjoy math. There are 8 students who are in the drama club who also enjoy math.
Answer:

Explanation:
There are two groups of students,
25 who are in the drama club and 15 who enjoy math.
There are 8 students who are in the drama club who also enjoy math.
Number of students in Drama Club = 25 – 8 = 17
Number of students enjoy Math = 15 – 8 = 7

Question 52.
Are the rates in the table below proportional?

Answer:
Yes, Both are $2.50 per pound.
Explanation:
Lets write them in the form of ratio
$5.00 : 2 pounds
$1.25 : 0.5 pounds
according to proportion,
product of means = product of extremes
5 : 2 = 1.25 : 0.5
product of means :
= 2 x 1.25 = 2.5
product of extremes :
= 2 x 0.5 = 2.5
product of means = product of extremes = 2.5
Hence ; both of them are proportioanal

Question 53.
What is the unit rate for the speed of the car shown on the graph below?

Answer:
\(\frac{1}{2}\)
Explanation :
By observing the graph we can see that
it took 6 seconds to travel 4 miles
that means the distance traveled in 1 second = \(\frac{1}{2}\)

Question 54.
Ebony asked four of her female friends if they liked wearing sandals better than wearing boots. All four said yes. Ebony concluded that none of the girls her age like boots. Is her conclusion valid? Did she use a representative sample for her survey?
Answer:
No
Explanation:
The Conclusion is based on too small a sample,
A representative sample is a sample from a larger group,
that accurately represents the characteristics of a larger population.
It’s known as a representative sample because the answers obtained from it,
accurately reflect the results you would achieve by interviewing the entire population.
The sample is not representative since she only asked her friends.

Question 55.
Create a probability table for choosing a marble out of a bag of 14 white, 18 black, and 6 red marbles.

Answer:

Explanation:
Total number of marbles = 14+ 18 + 6 = 38
Probability of choosing white marble,
number of white marbles = 14
probability = no of marbles ÷ total number of marbles
= 14 ÷ 38
= \(\frac{14}{38}\)
= 0.37
Probability of choosing black marble,
number of black marbles = 18
probability = no of marbles ÷ total number of marbles
= 18 ÷ 38
= \(\frac{18}{38}\)
= 0.47
Probability of choosing red marble,
number of red marbles = 6
probability = no of marbles ÷ total number of marbles
= 6 ÷ 38
= \(\frac{6}{38}\)
= 0.16

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.4 Comparing and Ordering Decimals existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.4 Comparing and Ordering Decimals

Exercises Compare

Each problem will have three numbers: a lowest, middle, and largest number.
You will be told which of the three to select: lowest, middle or largest.

Question 1.
4, 5, and 10 Lowest
_______________
Answer:
4
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
4, 5 and 10 Lowest,
4 is the lowest number in the given numbers above.

Question 2.
10.01, 10.10, and 10.11 Middle
____________
Answer:
10.10
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
10.01, 10.10 and 10.11 Middle,
10.10 is middle among the numbers given above.

Question 3.
.567, .5677, and .56 Largest
____________
Answer:
0.5677
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
0.56, 0.567 and 0.5677 Largest,
0.5677 is the largest among the numbers given above.

Question 4.
45.45, 45.449, and 45.4449 Middle
____________
Answer:
45.449
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
45.4449, 45.449, and 45.45 Middle,
45.449 is the middle among the numbers given above.

Question 5.
14.125, 14.0126, and 14.00126 Lowest
Answer:
14.00126
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
14.00126, 14.0126 and 14.125 Lowest,
14.00126 is the lowest among the numbers given above.

Question 6.
21.21, 21.211, and 21.2121 Lowest
Answer:
21.21
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
21.21, 21.211 and 21.2121 Lowest,
21.21 is the lowest among the numbers given above.

Question 7.
11.1, 11.11, and 11.111 Largest
Answer:
11.111
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
11.1, 11.11 and 11.111 largest,
11.111 is the largest among the numbers given above.

Question 8.
12.12, 12.102, and 12.1023 Middle
Answer:
12.1023
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
12.102, 12.1023 and 12.12 Middle,
12.1023 is the middle among the numbers given above.

Question 9.
166.66, 166.60, and 166.6607 Middle
Answer:
166.66
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
166.60, 166.66 and 166.6607 Middle,
166.66 is the middle among the numbers given above.

Question 10.
144.32, 14.432, and 1.4432 Largest
Answer:
144.32
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
1.4432, 14.432 and 144.32 Largest,
144.32 is the largest among the numbers given above.

Question 11.
25.025, 25.205, and 25.502 Middle
Answer:
25.205
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
25.025, 25.205, and 25.502 Middle,
25.205 is the middle among the numbers given above.

Question 12.
156.12, 157.01, and 158.32 Lowest
Answer:
156.12
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
156.12, 157.01, and 158.32 Lowest,
156.12 is the lowest among the numbers given above.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.3 Changing Decimals to Fractions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.3 Changing Decimals to Fractions

Exercises Change Decimals To Fractions

Question 1.
.85
Answer:
\(\frac{17}{20}\)
Explanation:
Given, .85
\(\frac{85}{100}\)
dividing both the numerator and denominator with 5
17 x 5 = 85
20 x 5 = 100
\(\frac{17}{20}\)

Question 2.
.77
Answer:
\(\frac{77}{100}\)
Explanation:
Given, 0.77
multiplying both the numerator and denominator with 100
\(\frac{77}{100}\)

Question 3.
.888
Answer:
\(\frac{111}{125}\)
Explanation:
Given, 0.888
\(\frac{888}{1000}\)
dividing both the numerator and denominator with 8
111 x 8 = 888
125 x 8 = 1000
\(\frac{111}{125}\)

Question 4.
.0125
Answer:
\(\frac{1}{80}\)
Explanation:
Given, 0.125
\(\frac{125}{10000}\)
dividing both the numerator and denominator with 125
1 x 125 = 125
80 x 125 = 10000
\(\frac{1}{80}\)

Question 5.
.678
Answer:
\(\frac{339}{500}\)
Explanation:
Given, 0.678
\(\frac{678}{1000}\)
dividing both the numerator and denominator with 2
339 x 2 = 678
500 x 2 = 1000
\(\frac{339}{500}\)

Question 6.
.6255
Answer:
\(\frac{1251}{2000}\)
Explanation:
Given, 0.6255
\(\frac{6255}{10000}\)
dividing both the numerator and denominator with 5
1251 x 5 = 6255
2000 x 5 = 10000
\(\frac{1251}{2000}\)

Question 7.
.331
Answer:
\(\frac{331}{1000}\)
Explanation:
Given, 0.331
multiplying both the numerator and denominator with 1000
\(\frac{331}{1000}\)

Question 8.
.4545
Answer:
\(\frac{909}{2000}\)
Explanation:
Given, 0.4545
\(\frac{4545}{10000}\)
dividing both the numerator and denominator with 5
909 x 5 = 4545
2000 x 5 = 10000
\(\frac{909}{2000}\)

Question 9.
.876
Answer:
\(\frac{219}{250}\)
Explanation:
Given, 0.87
\(\frac{876}{1000}\)
dividing both the numerator and denominator with 4
219 x 4 = 876
250 x 4 = 1000
\(\frac{219}{250}\)

Question 10.
.3125
Answer:
\(\frac{5}{16}\)
Explanation:
Given, 0.3125
\(\frac{3125}{10000}\)
dividing both the numerator and denominator with 625
5 x 625 = 3125
16 x 625 = 10000
\(\frac{5}{16}\)

Question 11.
.3435
Answer:
\(\frac{687}{2000}\)
Explanation:
\(\frac{3435}{10000}\)
dividing both the numerator and denominator with 5
687 x 5 = 3435
2000 x 5 = 10000
\(\frac{687}{2000}\)

Question 12.
.7007
Answer:
\(\frac{7007}{10000}\)
Explanation:
Given 0.7007
multiplying both the numerator and denominator with 10000
\(\frac{7007}{10000}\)

Question 13.
.336
Answer:
\(\frac{42}{125}\)
Explanation:
Given, 0.336
\(\frac{336}{1000}\)
dividing both the numerator and denominator with 8
42 x 8 = 336
125 x 8 = 1000
\(\frac{42}{125}\)

Question 14.
.2141
Answer:
\(\frac{2141}{10000}\)
Explanation:
Given, 0.2141
multiplying both the numerator and denominator with 10000
\(\frac{2141}{10000}\)

Question 15.
.56
Answer:
\(\frac{14}{25}\)
Explanation:
Given, 0.56
\(\frac{56}{100}\)
dividing both the numerator and denominator with 4
14 x 4 = 56
25 x 4 = 100
\(\frac{14}{25}\)

Question 16.
.0055
Answer:
Given, 0.0055
\(\frac{11}{2000}\)
Explanation:
\(\frac{55}{10000}\)
dividing both the numerator and denominator with 5
11 x 5 = 55
2000 x 5 = 10000
\(\frac{11}{2000}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.2 Changing Fractions to Decimals existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.2 Changing Fractions to Decimals

Exercises Change Fractions To Decimals
Round to the nearest ten-thousandth.

Question 1.
\(\frac{5}{16}\)
Answer:
0.3125
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{5}{16}\) = 5 ÷ 16 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 2.
\(\frac{4}{7}\)
Answer:
0.5714
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{4}{7}\) = 4 ÷ 7 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 3.
\(\frac{15}{31}\)
Answer:
0.4839
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{15}{31}\) = 15 ÷ 31 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 4.
\(\frac{3}{5}\)
Answer:
0.6000
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{3}{5}\) = 3 ÷ 5 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 5.
\(\frac{5}{212}\)
Answer:
0.0236
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{5}{212}\) = 5 ÷ 212 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 6.
\(\frac{31}{33}\)
Answer:
0.9394
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{31}{33}\) = 31 ÷ 33 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 7.
\(\frac{45}{157}\)
Answer:
0.2866
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{45}{157}\) = 45 ÷ 157 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 8.
\(\frac{12}{13}\)
Answer:
0.9231
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{12}{13}\) = 12 ÷ 13 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 9.
\(\frac{1}{2001}\)
Answer:
0.0005
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{5}{16}\) = 1 ÷ 2001 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 10.
\(\frac{23}{76}\)
Answer:
0.3026
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{23}{76}\) = 23 ÷ 76 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 11.
\(\frac{3}{32}\)
Answer:
0.0938
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{3}{32}\) = 3 ÷ 32 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 12.
\(\frac{55}{66}\)
Answer:
0.8333
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{55}{66}\) = 55 ÷ 66 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 13.
\(\frac{12}{47}\)
Answer:
0.2553
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{12}{47}\) = 12 ÷ 47 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 14.
\(\frac{7}{8}\)
Answer:
0.8750
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{7}{8}\) = 7 ÷ 8 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 15.
\(\frac{13}{15}\)
Answer:
0.8667
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{13}{15}\) = 13 ÷ 15 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 16.
\(\frac{13}{17}\)
Answer:
0.7647
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{13}{17}\) = 13 ÷ 17 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.