# Prasanna

## Texas Go Math Grade 3 Lesson 9.5 Answer Key Multiply 2-Digit by 1-Digit Numbers

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 9.5 Answer Key Multiply 2-Digit by 1-Digit Numbers.

## Texas Go Math Grade 3 Lesson 9.5 Answer Key Multiply 2-Digit by 1-Digit Numbers

Essential Question
How can you use strategies to multiply a 2-digit number by a 1-digit number?
Multiply the 1 digits together first. Cross-multiply by multiplying diagonal digits, then add the two sums together. Multiply the 2-digit numbers.

Explanation:
Here is one way that you can speed up the process of 2-digit by 1-digit multiplication:
Multiply the 1 digits together first. Cross-multiply by multiplying diagonal digits, then add the two sums together. Multiply the 2-digit numbers.

Unlock the Problem
A Thoroughbred racehorse can run at speeds of up to 60 feet per second. During practice, Celiaâ€™s horse runs at a speed of 36 feet per second. How far does her horse run in 3 seconds?

• Underline important information.
• Is there information you will not use? If so, cross out the information.

Example 1.
Multiply. 3 Ã— 36

So, Celiaâ€™s racehorse runs ___ feet in 3 seconds.
So, Celiaâ€™s racehorse runs 108 feet in 3 seconds.

Explanation:
Number of feet Celiaâ€™s horse runs per second = 36.
Distance her horse runs in 3 seconds = 3 Ã— Number of feet Celiaâ€™s horse runs per second
= 3 Ã— 36
= (3 Ã— 10) + (3 Ã— 10) + (3 Ã— 10) + (3 Ã— 6)
= 30 + 30 + 30 + 18
= 60 + 30 + 18
= 90 + 18
= 108 feet.

Math Talk
Mathematical Processes
Look at Step 1. Explain how the blocks show the regrouping of the 18 ones.

Example 2.
Multiply. 8 Ã— 22

So, 8 Ã— 22 = ____.

Math talk
Mathematical Processes
Why is 8 Ã— 2 tens recorded as 160 and not as 16?
8 Ã— 2 tens is recorded as 160 and not as 16 because 8 Ã— 2 tens = 8 Ã— 20 = 160 not 16.

Explanation:
8 Ã— 2 tens = 8 Ã— (2 Ã— 10)
= 8 Ã— 20
Multiply tens and ones place.
= 160.

Share and Show
Question 1.
Use the model to find the product.

Explanation:
2 Ã— 36 = (2 Ã— 3 tens) + (2 Ã— 6 ones)
= [2 Ã—(3 Ã— 10)]+ [2 Ã— (6 Ã— 1)]
= (2 Ã— 30) + (2 Ã— 6)
= 60 + 12
= 72.

Find the product. Tell which strategy you used.
Question 2.

Strategy used is multiplication and addition to find the product.

Explanation:
42 Ã— 4 = (40 Ã— 4) + (2 Ã— 4)
= 160 + 8
= 168.

Strategy used is multiplication and addition to find the product.

Explanation:
32 Ã— 6 = (30 Ã— 6) + (2 Ã— 6)
= 180 + 12
= 192.

Question 4.

Strategy used is multiplication and addition to find the product.

Explanation:
85 Ã— 3 = (80 Ã— 3) + (5 Ã— 3)
= 240 + 15
= 255.

Question 5.

Strategy used is multiplication and addition to find the product.

Explanation:
$63 Ã— 7 = ($60 Ã— 7) + ($3 Ã— 7) =$420 + $21 =$441.

Math Talk
Mathematical Processes
Describe the steps for using place value and regrouping to find 3 Ã— 78.
Steps for using place value and regrouping to find 3 Ã— 78:
1. Multiply the tens place and record the value.
2. Multiply the ones place and record the value.
3. Do add the both vales.
3 Ã— 78 = 234.

Explanation:
Steps for using place value and regrouping to find 3 Ã— 78:
1. Multiply the tens place and record the value:
3 Ã— 70 = 210.
2. Multiply the ones place and record the value:
3 Ã— 8 = 24.
3. Do add the both vales:
=> (3 Ã— 70) + (3 Ã— 8)
= 210 + 24
= 234.

Problem Solving
Use the table for 6-8.
Question 6.
How far can a desert cottontail run in 9 seconds?

Distance desert cottontail runs 9 seconds = 198 feet.

Explanation:
Distance desert cottontail runs per second = 22 feet.
Distance desert cottontail runs 9 seconds = 9 Ã— Distance desert cottontail runs per second
= 9 Ã— 22
= (9 Ã— 10) + (9 Ã— 10) + (9 Ã— 2)
= 90 + 90 + 18
= 180 + 18
= 198 feet.

Analyze A black-tailed jackrabbit hops about 7 feet in a single hop. How far can it hop in 5 seconds?

Distance black-tailed jackrabbit hops in a 5 seconds = 35 feet.

Explanation:
Distance black-tailed jackrabbit hops in a single hopÂ  per second = 7 feet.
Distance black-tailed jackrabbit hops in a 5 seconds = 5 Ã— Distance black-tailed jackrabbit hops in a single hopÂ  per second
= 5 Ã— 7
= 35 feet.

Question 8.
H.O.T. Multi-Step At the speeds shown, how much farther could a black-tailed jackrabbit run than a desert cottontail in 7 seconds?
203 feet farther a black-tailed jackrabbit run than a desert cottontail in 7 seconds.

Explanation:
Distance a black-tailed jackrabbit run in a second = 51.
Distance a black-tailed jackrabbit run in 7 seconds = 7 Ã— Distance a black-tailed jackrabbit run in a second
= 7 Ã— 51
= (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 1)
= 70 + 70 + 70 + 70Â  + 70 + 7
= 140 + 70 + 70Â  + 70 + 7
= 210 + 70Â  + 70 + 7
= 280 + 70 + 7
= 350 + 7
= 357 feet.
Distance a desert cottontail run in a second = 22.
Distance a desert cottontail run in 7 seconds = 7 Ã— Distance a desert cottontail run in a second
= 7 Ã— 22
=(7 Ã— 10) + (7 Ã— 10) +(7 Ã— 2)
= 70 + 70 + 14
= 140 + 14
= 154 feet.
Difference:
Distance a black-tailed jackrabbit run in 7 seconds – Distance a desert cottontail run in 7 seconds
= 357 – 154
= 203 feet.

Question 9.
Multi-Step Mr. Wright bought a 3-pound bag of cat food and a 5 pound bag of dog food, There are 16 ounces in each pound. How many ounces of pet food did Mr. Wright buy?
Number of ounces of pet food Mr. Wright buy = 128.

Explanation:
Number of pounds bag of cat food Mr. Wright bought = 3.
Number of pounds bag of dog food Mr. Wright bought = 5.
Number of ounces in each pound = 16.
Number of ounces are in bag of cat food Mr. Wright bought = Number of pounds bag of cat food Mr. Wright bought Ã—Number of ounces in each pound
= 3 Ã— 16
=(3 Ã— 10 + (3 Ã— 6)
= 30 + 18
= 48.
Number of ounces are in bag of dog food Mr. Wright bought = Number of pounds bag of dog food Mr. Wright bought Ã— Number of ounces in each pound
= 5 Ã— 16
=(5 Ã— 10) + (5 Ã— 6)
= 50 + 30
= 80.
Number of ounces of pet food Mr. Wright buy = Number of ounces are in bag of cat food Mr. Wright bought + Number of ounces are in bag of dog food Mr. Wright bought
= 48 + 80
= 128.

Question 10.
H.O.T. Reasoning The sum of two numbers is 31. The product of the two numbers is 150. What are the numbers?
The numbers are 6 and 25.

Explanation:
The sum of two numbers is 31.
The product of the two numbers is 150.
Let the numbers be X and Y.
Multiples of 150:
3 Ã— 50 = 150. => 3 + 50 = 53.
5 Ã— 30 = 150. => 5 + 30 = 35.
6 Ã— 25 = 150. => 6 + 25 = 31.
10 Ã— 15 = 150. => 10 + 15 = 25.

Question 11.
Write Math 6 Ã— 87 is greater than 5 Ã— 87. How much greater? Explain how you know without multiplying.
Difference = 87.
Without multiply:
(6 Ã— 87) – (5 Ã— 87) = difference of multiple (6 – 5) Ã— 87 = 1 Ã— 87 = 87.

Explanation:
Product of 6 Ã— 87 = (6 Ã— 10) + ( 6 Ã— 10) + (6 Ã— 10) + ( 6 Ã— 10) +Â (6 Ã— 10) + ( 6 Ã— 10) + (6 Ã— 10) + ( 6 Ã— 10) + (6 Ã— 7)
= 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 42
= 120 + 60 + 60 + 60 + 60 + 60 + 60 + 42
= 180 + 60 + 60 + 60 + 60 + 60 + 42
= 240 + 60 + 60 + 60 + 60 + 42
= 300 + 60 + 60 + 60 + 42
= 360 + 60 + 60 + 42
= 420 + 60 + 42
= 480 + 42
= 522.
Product of 5 Ã— 87 = (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 7)
= 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 35
= 100 + 50 + 50 + 50 + 50 + 50 + 50 + 35
= 150 + 50 + 50 + 50 + 50 + 50 + 35
= 200 + 50 + 50 + 50 + 50 + 35
= 250 + 50 + 50 + 50 + 35
= 300 + 50 + 50 + 35
= 350 + 50 + 35
= 400 + 35
= 435.
Difference:
Product of 6 Ã— 87 – Product of 5 Ã— 87
= 522 – 435
= 87.

Without multiply:
(6 Ã— 87) – (5 Ã— 87) = difference of multiple (6 – 5) Ã— 87 = 1 Ã— 87 = 87.

Fill in the bubble for the correct answer. Use a strategy to solve.
Question 12.
Clayton bought 7 boxes of markers for an art project. There are 12 markers in each box. How many markers did he buy?
(A) 84
(B) 14
(C) 19
(D) 74
Number of markers he buy = 84.
(A) 84.

Explanation:
Number of boxes of markers for an art project Clayton bought = 7.
Number of markers in each box = 12.
Number of markers he buy = Number of boxes of markers for an art project Clayton boughtÂ  Ã— Number of markers in each box
= 7 Ã— 12
= (7 Ã— 10) + ( 7 Ã— 2)
= 70 + 14
= 84.

Question 13.
Apply Alana has been on the swim team for 3 years. She practices 26 weeks a year. How many weeks has she practiced?
(A) 68
(B) 618
(C) 78
(D) 6,018
Number of weeks she practiced = 78.
(C) 78.

Explanation:
Number of years Alana has been on the swim team = 3.
Number of weeks a year she practices = 26.
Number of weeks she practiced = Number of years Alana has been on the swim team Ã— Number of weeks a year she practices
= 3 Ã— 26
= (3 Ã— 10) + (3 Ã— 10) +(3 Ã— 6)
= 30 + 30 + 18
= 60 + 18
= 78.

Question 14.
Multi-Step At Huff and Puff Day Care, the art teachers have 5 sets of 16 paints for morning classes and 4 sets of 12 paints for afternoon classes. How many paints do the art teachers have?
(A) 80
(B) 128
(C) 48
(D) 20
Total number of paints the art teachers have = 128.
(B) 128.

Explanation:
Number of sets of paints the art teachers have for morning classes= 5.
Number of paints for morning classes = 16.
Total Number of paints the art teachers have for morning classes = Number of sets of paints the art teachers have for morning classes Ã— Number of paints for morning classes
= 5 Ã— 16
= (5 Ã— 10) + (5 Ã— 6)
= 50 + 30
= 80.
Number of sets of paints the art teachers have for afternoon classes = 4.
Number of paints for afternoon classes = 12.
Total Number of paints the art teachers have for afternoon classes = Number of sets of paints the art teachers have for afternoon classes Ã— Number of paints for afternoon classes
= 4 Ã— 12
= (4 Ã— 10) + (4 Ã— 2)
= 40 + 8
= 48.
Total number of paints the art teachers have = Total Number of paints the art teachers have for morning classes + Total Number of paints the art teachers have for afternoon classes
= 80 + 48
= 128.

Texas Test Prep
Question 15.
Mrs. Sawyer bought a book for $25 and 3 toys for$13 each. How much change should she get back from a $100 bill? (A)$46
(B) $36 (C)$26
(D) $64 Answer: Amount of change Mrs. Sawyer gets back =$36.
(B) $36. Explanation: Cost of a book Mrs. Sawyer bought =$25.
Cost ofÂ  a toy Mrs. Sawyer bought each = $13. Number of toys Mrs. Sawyer bought = 3. Amount of bill =$100.
Total cost of toys Mrs. Sawyer bought = Cost ofÂ  a toy Mrs. Sawyer bought each Ã— Number of toys Mrs. Sawyer bought
= $13 Ã— 3 = ($10 Ã— 3) + ($3 Ã— 3) =$30 + $9 =$39.
Total amount of a book and 3 toys Mrs. Sawyer bought = Cost of a book Mrs. Sawyer boughtÂ  + Total cost of toys Mrs. Sawyer bought
= $25 +$39
= $64. Amount of change Mrs. Sawyer gets back = Amount of bill – Total amount of a book and 3 toys Mrs. Sawyer bought =$100 – $64 =$36.

### Texas Go Math Grade 3 Lesson 9.5 Homework and Practice Answer Key

Find the product. Tell which strategy you used.

Question 1.

Explanation:
Strategy used is multiplication and addition to find the product.
53 Ã— 4 = (50 Ã— 4) + (3 Ã— 4)
= 200 + 12
= 212.

Go Math Grade 3 Practice and Homework Lesson 9.5 Answer Key Question 2.

Strategy used is multiplication and addition to find the product.

Explanation:
64 Ã— 6 = (60 Ã— 6) + (4 Ã— 6)
= 360 + 24
= 384.

Question 13.

Strategy used is multiplication and addition to find the product.

Explanation:
47 Ã— 9 = (40 Ã— 9) + (7 Ã— 9)
= 360 + 63
= 423.

Question 14.

Strategy used is multiplication and addition to find the product.

Explanation:
82 Ã— 3 = (80 Ã— 3) + (2 Ã— 3)
= 240 + 6
= 246.

Problem Solving
Use the table for 5-7.
Question 5.
The mayor of a town buys 4 packages of balloons for a street festival. How many balloons did the mayor buy?

Total number of balloons the mayor buy = 232.

Explanation:
Number of packages of balloons for a street festival the mayor of a town buys = 4.
Number of balloons in each package = 58.
Total number of balloons the mayor buy = Number of packages of balloons for a street festival the mayor of a town buys Ã— Number of balloons in each package
= 4 Ã— 58
= (4 Ã— 50) + ( 4 Ã— 8)
= 200 + 32
= 232.

Question 6.
Roberto buys 4 packages of noisemakers and 3 packages of hats. Does he have more hats or more noisemakers? Explain.
He has 7 more hats than noisemakers.

Explanation:
Number of packages of noisemakers Roberto buys = 4.
Number of noisemakersÂ  in each package = 17.
Total number of noisemakers Roberto buys = Number of packages of noisemakers Roberto buysÂ  Ã— Number of noisemakersÂ  in each package
= 4 Ã— 17
= (4 Ã— 10) + (4 Ã— 7)
= 40 + 28
= 68.
Number of packages of hats Roberto buys = 3.
Number of hats in each package =Â  25.
Total number of hats Roberto buys = Number of packages of hats Roberto buys Ã— Number of hats in each package
= 3 Ã— 25
= (3 Ã— 20) + (3 Ã— 5)
= 60 + 15
= 75.
Difference:
Total number of hats Roberto buys – Total number of noisemakers Roberto buys
= 75 – 68
= 7.

Nan buys 3 packages of party favors, If she has 100 people coming to a party, does she have enough favors? Explain.
No, she will not have enough favors to give to the people coming to a party.

Explanation:
Number of packages of party favors Nan buys = 3.
Number of favors in each package = 32.
Total number of favors Nan buysÂ  = Number of packages of party favors Nan buys Ã— Number of favors in each package
= 3 Ã— 32
= (3 Ã— 30) + (3 Ã— 2)
= 90 + 6
= 96.
Number of people coming to a party = 100.
Difference:
Number of people coming to a party – Total number of favors Nan buys
= 100 – 96
= 4.

Question 8.
Erika has 6 boxes of buttons. Each box holds 28 buttons. Explain how Erika can use place value and regrouping to find how many buttons there are.
Total number of buttons Erika has = 168.

Explanation:
Number of boxes of buttons Erika has = 6.
Number of buttons each box holds = 28.
Total number of buttons Erika has =Â  Number of boxes of buttons Erika has Ã— Number of buttons each box holds
= 6 Ã— 28
Multiply 6 with the place value of 2 = 2 tens (2 Ã—10 = 20) and add to place value of 8 = ones (8 Ã—1 = 8)
= (6 Ã— 20) + (6 Ã— 8)
= 120 + 48
= 168.

Lesson Check
Texas Test Prep
Question 9.
It takes a train 42 minutes to ride â€˜from Coltsville to Newburgh. If the train makes 8 trips in one day, how many minutes does it travel?
(A) 336 minutes
(B) 236 minutes
(C) 322 minutes
(D) 412 minutes
Number of minutes it travels = 336.
(A) 336 minutes.

Explanation:
Number of minutes a train takes to ride â€˜from Coltsville to Newburgh = 42.
Number of trips a train takes in one day = 8.
Number of minutes it travels = Number of minutes a train takes to ride â€˜from Coltsville to NewburghÂ  Ã— Number of trips a train takes in one day
= 42 Ã— 8
= (40 Ã— 8) + (2 Ã— 8)
= 320 + 16
= 336.

Question 10.
Charlie puts together boxes of model cars at a factory. If he packs 18 boxes in one hour, how many boxes does he pack in 7 hours?
(A) 187
(B) 156
(C) 76
(D) 126
Number of boxes he pack in 7 hours = 126.
(D) 126.

Explanation:
Number of boxes he packs in one hour = 18.
Number of boxes he pack in 7 hours = 7 Ã— Number of boxes he packs in one hour
= 7 Ã— 18
= (7 Ã— 10) + (7 Ã— 8)
= 70 + 56
= 126.

Question 11.
A bookstore has 6 shelves of art books. There are 27 books on each shelf. how many art hooks are in the bookstore?
(A) 33
(B) 44
(C) 112
(D) 162
Number of art books are in the bookstore = 162.
(D) 162.

Explanation:
Number of shelves of art books aÂ bookstore has = 6.
Number of books on each shelf = 27.
Number ofÂ art books are in the bookstore = Number of shelves of art books a bookstore has Ã— Number of books on each shelf
= 6 Ã— 27
= (6 Ã— 20) + (6 Ã— 7)
= 120 + 42
= 162.

Question 12.
A deli has 6 boxes of soup cans. Each box holds 14 cans. How many soup cans does the deli have?
(A) 64
(B) 20
(C) 84
(D) 24
Number of soup cans the deli have = 84.
(C) 84.

Explanation:
Number of boxes of soup cans aÂ deli has = 6.
Number of cans each box holds = 14.
Number of soup cans the deli have = Number of boxes of soup cans a deli has Ã— Number of cans each box holds
= 6 Ã— 14
= (6 Ã— 10) + (6 Ã— 4)
= 60 + 24
= 84.

Multi-Step Ashley has 4 bags each of red marbles and yellow marbles. Each bag holds 14 marbles. How many marbles does Ashley have?
(A) 56
(B) 112
(C) 39
(D) 92
Number of marbles Ashley have = 112.
(B) 112.

Explanation:
Number of bags of each red marbles and yellow marbles Ashley has = 4.
Number of marbles each bag holds = 14.
Number of marbles Ashley have = (2 Ã— Number of bags of each red marbles and yellow marbles Ashley has ) Ã— Number of marbles each bag holds
= (2 Ã— 4) Ã— 14
= 8 Ã— 14
= (8 Ã— 10) + (8 Ã— 4)
= 80 + 32
= 112.

Question 14.
Multi-Step Devon collects 23 bottles and 4 boxes of 16 cans on recycling day. His goal is to collect 100 items. How many more items does Devon need to reach his goal?
(A) 43
(B) 39
(C) 87
(D) 13
Number of more items Devon needs to reach his goal = 13.
(D) 13.

Explanation:
Number of bottles Devon collectsÂ  = 23.
Number of boxes Devon collectsÂ  = 4.
Number of cans he collects = 16.
Number of items to collect his goal = 100.
Number of items he collected on recycling day = Number of bottles Devon collects + (Number of boxes Devon collects Ã— Number of cans he collects)
= 23 + (4 Ã— 16)
= 23 + 64
= 87.
Number of more items Devon needs to reach his goal = Number of items to collect his goal – Number of items he collected on recycling day
= 100 – 87
= 13.

## Texas Go Math Grade 3 Lesson 11.2 Answer Key Division Rules for 1 and 0

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 11.2 Answer Key Division Rules for 1 and 0.

## Texas Go Math Grade 3 Lesson 11.2 Answer Key Division Rules for 1 and 0

Essential Question
What are the rules for dividing with 1 and 0?
A Number Divided by 1 a1=a Just like multiplying by 1,
dividing any number by 1 doesn’t change the number at all.
0 Divided by a Number 0a=0 Dividing 0 by any number gives us a zero.
Zero will never change when multiplyingÂ or dividing any number by it.

Unlock the Problem

What rules for division can help you divide with 1 and 0?
Any number divided by 0 is not defined.
Any number (except 0) divided by itself equals 1.
Any number divided by 1 equals that number.
Explanation:
For Example:
35 Ã· 1 = 35
35 Ã· 0 = 0

If there is only 1 fishbowl, then all the fish must go in that fishbowl.

Try This! There are 3 fish and 1 fishbowl. Draw a quick picture to show the fish in the fishbowl.

Write the equation your picture shows.

3 Ã· 1 = 3

Rule A: Any number divided by 1 equals that number.

Math Talk
Mathematical processes
Explain how Rule A is related to the Identity Property of Multiplication.

If there is the same number of fish and fishbowls, then 1 fish goes in each fishbowl.

Try This There are 3 fish and 3 fishbowls. Draw a quick picture to show the fish divided equally among the fishbowls.

Write the equation your picture shows.
3 Ã·3 = 1

Rule B: Any number (except 0) divided by itself equals 1.

If there are 0 fish and 4 fishbowls, there will not be any fish in the fishbowls.

Try This! There are 0 fish and 3 fishbowls. Draw a quick picture to show the fishbowls.

Write the equation your picture shows.
___ Ã· ___ = ____
0 Ã· 4 = 0
Rule C: Zero divided by any number (except 0) equals 0.

If there are 0 fish bowls, then you cannot separate the fish equally into fishbowls Dividing by 0 is not possible.

Rule D: You cannot divide by 0.

Share and Show

Math Talk
Mathematical Processes
Explain what happens when you divide a number (except 0) by itself.

Question 1.
Use the picture to find 2 Ã· 2. ___

Explanation:
Rule B: Any number (except 0) divided by itself equals 1.
2 Ã· 2 = 1

Find the quotient.

Texas Go Math Grade 3 Answer Key Pdf Lesson 11.2 Question 2.
7 Ã· 1 = ___

Rule A: Any number divided by 1 equals that number.
7 Ã· 1 = 7

Question 3.
8 Ã· 8 = ___

8 Ã· 8 = 1
Explanation:
Rule A: Any number divided by 1 equals that number.

Question 4.
0 Ã· 5 = ___

0 Ã· 5 = 0
Explanation:
Rule C: Zero divided by any number (except 0) equals 0.

Question 5.
6 Ã· 6 = ___

Explanation:
Rule A: Any number divided by 1 equals that number.

Question 6.

0 Ã· 5 = 0
Explanation:
Rule C: Zero divided by any number (except 0) equals 0.

Question 7.

9 Ã· 1 = 9
Explanation:
Rule A: Any number divided by 1 equals that number

Question 8.

7 Ã· 7 = 1
Explanation:
Rule A: Any number divided by 1 equals that number.

Question 9.

10 Ã· 1 =10
Explanation:
Rule A: Any number divided by 1 equals that number

Problem Solving

Question 10.
Multi-Step Claire has 7 parakeets. She puts 4 of them in a cage. She divides the other parakeets equally among 3 friends to hold. How many parakeets does each friend get to hold?

Explanation:
Claire has 7 parakeets.
She puts 4 of them in a cage.
7 – 4 = 3
She divides the other parakeets equally among 3 friends to hold.
Number of parakeets each friend get to hold
3 Ã· 3 = 1

Write Math Pose a Problem Look back at Problem 10. Change the number of parakeets and friends so you can use the equation 6 Ã· 6 = 1. Then solve your problem.
Claire has 10 parakeets. She puts 4 of them in a cage. She divides the other parakeets equally among 6 friends to hold. How many parakeets does each friend get to hold?
Explanation:
Claire has 10 parakeets.
She puts 4 of them in a cage.
10 – 4 = 6
She divides the other parakeets equally among 6 friends to hold.
Number of parakeets each friend get to hold
6 Ã· 6 = 1

Question 12.
Lily has some parrots. She gives each parrot 1 grape. If Lily gives out 5 grapes, how many parrots does she have?
Explanation:
Lily has some parrots.
She gives each parrot 1 grape.
If Lily gives out 5 grapes,
Total parrots she have
5 Ã· 5 = 1

Question 13.
H.O.T. Use Math Language Suppose a pet store has 21 birds that are in 21 cages. Use what you know about division rules to find the number of birds in each cage. Explain your answer.
21 Ã· 21 = 1
Any number divides by itself equals to 1
Explanation:
A pet store has 21 birds that are in 21 cages.
Division equation to find the number of birds in each cage.
21 Ã· 21 = 1

Fill in the bubble for the correct answer choice.

Question 14.
There are 18 people waiting in line to ride the Texas Giant roller coaster. There are 0 seats available and 6 roller coaster cars. Which division equation describes how many people can move from the line to a car?
(A) 0 Ã— 6 = 0
(B) 6 Ã· 6 = 1
(C) 0 Ã· 6 = 0
(D) 6 Ã· 1 = 6
Option(C)
Explanation:
There are 18 people waiting in line to ride the Texas Giant roller coaster.
There are 0 seats available and 6 roller coaster cars.
Division equation 0 Ã· 6 = 0 describes number of people can move from the line to a car

Question 15.
Kai has some cats. Each cat has its own food bowl. There are 4 food bowls. How many cats does Kai have?
(A) 1
(B) 4
(C) 8
(D) 0
Option(B)
Explanation:
There are 4 food bowls.
Each cat has its own food bowl.
Number of cats Kai has 4 Ã· 1 = 4

Analyze Multi-Step Taylor has 6 juice boxes in her refrigerator. She leaves 2 juice boxes in the refrigerator and divides the rest equally among 3 friends and herself. How many juice boxes is each person given?
(A) 4
(B) 2
(C) 1
(D) 3
Option(C)
Explanation:
Taylor has 6 juice boxes in her refrigerator.
She leaves 2 juice boxes in the refrigerator
6 – 2 = 4
and divides the rest equally among 3 friends and herself.
Number of juice boxes each person get
4 Ã· 4 = 1

Texas Test Prep

Question 17.
Jude has 6 horses. Two horses are in the pasture, and he puts each of the rest of the horses in its own stall. How many stalls does Jude use?
(A) 2
(B) 1
(C) 0
(D) 4
Option(D)
Explanation:
Jude has 6 horses.
Two horses are in the pasture,
6 – 2 = 4
and he puts each of the rest of the horses in its own stall.
Number of stalls Jude use
4 Ã· 1 = 4

### Texas Go Math Grade 3 Lesson 11.2 Homework and Practice Answer Key

Question 1.
Use the picture to find 3 Ã· 1. ___

3 Ã· 1 = 3
Explanation:
Rule A: Any number divided by 1 equals that number.

Question 2.
Use the picture to find 3 Ã· 3.

3 Ã· 3 = 1
Explanation;
Rule B: Any number (except 0) divided by itself equals 1.

Find the quotient.

Question 3.
8 Ã· 1 = ___
8 Â Ã· 1 = 8
Explanation:
Rule A: Any number divided by 1 equals that number.

Question 4.
5 Ã· 5 = ___
5 Ã· 5 = 1
Explanation:
Rule B: Any number (except 0) divided by itself equals 1.

Question 5.
0 Ã· 9 = ___
0 Ã· 9 = 0
Explanation:
Rule C: Zero divided by any number (except 0) equals 0.

Go Math Grade 3 Practice and Homework Lesson 11.2 Answer Key Question 6.
2 Ã· 2 = ___
Explanation:
Rule B: Any number (except 0) divided by itself equals 1.

Question 7.
0 Ã· 6 = ___
Explanation:
Rule C: Zero divided by any number (except 0) equals 0.

Question 8.
4 Ã· 1 = ___
Explanation:
Rule A: Any number divided by 1 equals that number.

Problem Solving

Question 9.
Angie has 8 muffins. She wraps up 4 muffins. She divides the other muffins among 3 friends and herself. How many muffins does each person get?
Each person get 1 muffin.
Explanation:
Angie has 8 muffins.
She wraps up 4 muffins.
8 – 4 = 4
She divides the other muffins among 3 friends and herself.
Number of muffins each person get
Rule B: Any number (except 0) divided by itself equals 1.
4 Ã· 4 = 1

Question 10.
Walt has 5 vases. He has no flowers to put in the vases. Write a division sentence to show how many flowers he can put in each vase.
0 Ã· 5 = 0
Explanation:
Walt has 5 vases.
He has no flowers to put in the vases.
Division equation 0 Ã· 5 = 0 show number of flowers he can put in each vase.

Question 11.
Look back at Problem 10. Change the number of flowers and vases so you can use the equation 7 Ã· 7 = 1.
Walt has 7 vases. He has 7 flowers to put in the vases. Write a division sentence to show how many flowers he can put in each vase.
Explanation:
Walt has 7 vases.
He has 7 flowers to put in the vases.
Division equation 7 Ã· 7 = 1 number of flowers he can put in each vase.

Texas Test Prep

Lesson Checks

Question 12.
There are 10 people waiting for the bus. There are no seats left on the bus. Which division equation describes how many people can get on the bus?
(A) 10 Ã· 10 = 1
(B) 10 Ã— o = o
(C) 10 Ã· 1 = 10
(D) o Ã· 10 = o
Option(D)
Explanation:
There are 10 people waiting for the bus.
There are no seats left on the bus.
Division equation 0 Ã· 10 = 0 describes number of people that can get on the bus.
As, we know any that divided by 0 is 0.

Question 13.
A group of 9 people are going on a trip. The van can seat 6 people. Which division equation shows how many people can get on the van?
(A) 9 Ã— 1 = 9
(B) 6 Ã— 1 = 6
(C) 9 + 9 = 1
(D) 6 Ã· 1 = 6
Option(D)
Explanation:
A group of 9 people are going on a trip.
The van can seat 6 people.
Division equation 6 Ã· 1 = 6 shows number of people that can get on the van.
As, the seating capacity of the van is 6.

Question 14.
There are some students on the playground. Each student has a seat on the swings. There are 6 swing seats. How many students are on the swings?
(A) 0
(B) 6
(C) 1
(D) 12
Option(B)
Explanation:
There are 6 swing seats.
Each student has a seat on the swing.
Number of students on the swings
6 Ã· 1 = 6

A daycare center has some babies. Each baby has a bottle. There are 8 bottles. How many babies are in the daycare center?
(A) 16
(B) 0
(C) 1
(D) 8
Option(D)
Explanation:
A daycare center has some babies.
Each baby has a bottle.
There are 8 bottles.
Total babies in the daycare center
8 Ã· 1 = 8

Question 16.
Multi-Step Len has a box of 8 granola bars. He leaves 5 bars in the box and divides the rest among 2 friends and himself. How many granola bars does each person get?
(A) 1
(B) 5
(C) 2
(D) 8
Option(A)
Explanation:
Len has a box of 8 granola bars.
He leaves 5 bars in the box
8 – 5 = 3
and divides the rest among 2 friends and himself.
Number of granola bars each person gets
3 Ã· 3 = 1

Question 17.
Multi-Step Sonya has a pack of 12 crayons. She leaves 0 crayons in the box and divides the rest equally among 11 students and herself. How many crayons is each student given?
(A) 0
(B) 1
(C) 12
(D) 11
Option(B)
Explanation:
Sonya has a pack of 12 crayons.
She leaves 0 crayons in the box and divides the rest equally among 11 students and herself.
Number of crayons each student given
12 Ã· 12 = 1

## Texas Go Math Grade 1 Lesson 13.1 Answer Key Record Related Facts

Refer to our Texas Go Math Grade 1 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 1 Lesson 13.1 Answer Key Record Related Facts.

## Texas Go Math Grade 1 Lesson 13.1 Answer Key Record Related Facts

Explore

Listen to the problem. Model with . Draw . Write the number sentence.
________ + _________ = __________
________ – _________ = __________

FOR THE TEACHER â€¢ Read the following problem for the left box. Colin has 7 crackers. He sets 1 more cracker. How many crackers does Colin have now? Then read the following for the right box. Colin has 8 crackers. He gives one to Jacob. How many crackers does Colin have now?

Math Talk
Mathematical Processes

Model and Draw

Share and Show

Use . Add or subtract. Complete the related facts.

Question 1.
8 + _________ = 15
7 + 8 = _________

15 – 7 = __________
_________ – _________ = __________
8 + 7 = 15
7 + 8 = 15
15 – 7 = 8
15 – 8 = 7

Question 2.
________ + 9 = 14
9 + 5 = ___________

14 – __________ = 5
_________ – _________ = __________
5 + 9 = 14
9 + 5 = 14
14 – 9 = 5
14 – 5 = 9

Question 3.
7 + _________ = 13
6 + 7 = ____________

13 – 6 = __________
_________ – _________ = __________
7 + 6 = 13
6 + 7 = 13
13 – 6 = 7
13 – 7 = 6

Problem Solving

Use . Add or subtract. Complete the related facts.

Question 4.
________ + 8 = 13
8 + 5 = ____________

13 – __________ = 5
_________ – _________ = __________
5 + 8 = 13
8 + 5 = 13
13 – 8 = 5
13 – 5 = 8

Question 5.
H.O.T. Circle the number sentence that has a mistake. Correct it to complete the related facts.

7 + 9 = 16
16 + 9 = 7

9 + 7 = 16
16 – 7 = 9

Question 6.
H.O.T. Multi-Step Choose three numbers to make related facts. Choose numbers between 0 and 18. Write your numbers. Write the related facts.

Question 7.
Use to count.
Aunt Kay makes 6 instruments. Matt and Karen give her 3 more. Which completes the related facts?
6 + 3 = 9
3 + 6 = 9

9 – 6 = 3
___________
(A) 9 + 3 = 12
(B) 9 – 3 = 6
(C) 6 + 6 = 12
9 – 3 = 6

Question 8.
Analyze Pete has 13 pencils. One day he uses 8 pencils. Another day he uses the rest. Which completes the related facts?
13 – __________ = 8
________ + 8 = 13

13 – 8 = __________
8 + __________ = 13
(A) 6
(B) 8
(C) 5
Given that
The total number of pencils near pete = 13
one day he use pencils = 8
pencils used in another day =13 – 8 = 5
The correct answer is option – C
13 – 5 = 8
5 + 8 = 13
13 – 8 = 5

Question 9.
Texas Test Prep Which completes the related facts?
9 + 8 = 17
8 + 9 = 17

17 – 8 = 9
__________
(A) 9 + 9 = 18
(B) 9 – 6 = 3
(C) 17 – 9 = 8
The correct answer is option – C
9 + 8 = 17
8 + 9 = 17
17 – 8 = 9
17 – 9 = 8

TAKE HOME ACTIVITY â€¢ Write an addition fact. Ask your child to write three other related facts.

### Texas Go Math Grade 1 Lesson 13.1 Homework and Practice Answer Key

Question 1.
_______ + 5 = 11
5 + 6 = ________

11 – _________ = 6
__________ – __________ = __________
6 + 5 = 11
5 + 6 = 11
11 – 5 = 6
11 – 6 = 5

Problem Solving

Circle the number sentence that has a mistake. Correct it to complete the related facts.

Question 2.
6 + 8 = 14
14 – 6 = 8

8 – 6 = 14
14 – 8 = 6

Lesson Check

Question 3.
Which completes the related facts?
8 + 4 = 12
4 + 8 = 12

12 – 8 = 4
__________
(A) 12 + 4 = 14
(B) 12 – 4 = 8
(C) 4 + 4 = 8
12 – 4 = 8 is the related fact.
Option B is the correct answer.

Question 4.
Which completes the related facts?
15 – 7 = __________
7 + __________ = 15

15 – ________ = 7
________ + 7 = 15
(A) 8
(B) 9
(C) 7
Number 8 is related to the fact.
Option A is the correct answer.

Question 5.
Multi-Step Write the related facts you can make with these 3 numbers: 5, 14, and 9.

## Texas Go Math Grade 4 Lesson 17.1 Answer Key Frequency Tables

Refer to our Texas Go Math Grade 4 Answer Key Pdf to score good marks in the exams. Test yourself by practising the problems from Texas Go Math Grade 4 Lesson 17.1 Answer Key Frequency Tables.

## Texas Go Math Grade 4 Lesson 17.1 Answer Key Frequency Tables

Essential Question

How do you make a frequency table from data that is given to you?
Answer: Frequency tables are used to collect a wide range of numbers in a data set. TheÂ frequency of a particular data value is the number of times the data value occurs.
For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4.Â  The frequency of a data value is often represented byÂ f.
AÂ frequency tableÂ is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.
Example:
The marks awarded for an assignment set for a Year 8 class of 20 students were as follows:
6Â Â Â Â  7Â Â Â Â  5Â Â Â Â  7Â Â Â Â  7Â Â Â Â  8Â Â Â Â  7Â Â Â Â  6Â Â Â Â  9Â Â Â Â  7
4Â Â Â Â  10Â Â  6Â Â Â Â  8Â Â Â Â  8Â Â Â Â  9Â Â Â Â  5Â Â Â Â  6Â Â Â Â  4Â Â Â Â  8
Present this information in a frequency table:
Solution:
To construct a frequency table, we proceed as follows:
Step 1:
Construct a table with three columns.Â  The first column shows what is being arranged in ascending order (i.e. the marks).Â  The lowest mark is 4.Â  So, start from 4 in the first column as shown below.

Step 2:
Go through the list of marks.Â  The first mark in the list is 6, so put a tally mark against 6 in the second column.Â  The second mark in the list is 7, so put a tally mark against 7 in the second column.Â  The third mark in the list is 5, so put a tally mark against 5 in the third column as shown below.

We continue this process until all marks in the list are tallied.
Step 3:
Count the number of tally marks for each mark and write it in the third column.Â  The finished frequency table is as follows:

Unlock the Problem

A frequency table is a table that uses numbers to record data about how often something happens. The frequency is the number of times the data occurs.

Example 1

Tony kept a table of the number of minutes he read during a 15 day period. He wants to represent this data in a frequency table. Make a frequency table using the data from the table.

Make a frequency table.

STEP 1
List the number of minutes from Tonyâ€™s Reading Times table in the Minutes column of the frequency table.
Construct a table with three columns.Â  The first column shows what is being arranged in ascending order (i.e. the minutes).Â  The lowest minute is 30.Â  So, start from 30 in the first column as shown below.

STEP 2
Go through the minutes. The first minute in the list is 30, so put a tally mark against 30 in the first column.Â  The second minute in the list is 60, so put a tally mark against 7 in the second column.Â  The third minute in the list is 90, so put a tally mark against 90 in the third column as shown below. Record the frequency of the number of minutes from Tonyâ€™s Reading Table in the Frequency column.

Complete the frequency table.

How would the data in Tonyâ€™s table change if he recorded the number of minutes he read during a 20 day period instead of a 15 day period?

Explain how the frequency table would change to show the new data Tony recorded during the 20 day period.
Answer: The minute’s column will stay the same but the frequency column will change. This will be shown below:

Math Talk

Mathematical Processes
Explain how you used the data in Tonyâ€™s table to record the numbers in the frequency Column.
To complete the frequency column, go through the list of data values and place one tally mark at the appropriate place in the second column for every data value. Count the number of tally marks for each data value and write it in the third column.

Example 2

Jasmine went for a walk each day. She recorded the distance she walked in a table. Use the data in the table to make a frequency table.

Make a frequency table to represent the data.

STEP 1
List the distances that Jasmine walked in the Distance column of the frequency table.
Construct a table with three columns.Â  The first column shows what is being arranged in ascending order (i.e. the distance).Â  The lowest distance is 1/4.Â  So, start from 1/4 in the first column as shown below.

STEP 2
Record the frequency of each distance from the Distance Walked table in the Frequency column.
Complete the frequency table.

Explain how creating a frequency table whose data is infractions is similar to creating a frequency table where the data is in whole numbers.
Using fractions does not change anything. because fractions are a way of expressing a division of a quantity into parts.
First, we need to know the definition of whole numbers.
Whole numbers are part of real numbers including all the positive integers and zero, but not the fractions, decimals, or negative numbers.
To convert a fraction into a whole number: Divide the numerator by the denominator, only if the numerator is a multiple of the denominator.
A fraction can be written as a whole number only if the numerator is a multiple of the denominator.
For example, convert 4/2 into a whole number.
Since 4 is a multiple of 2, we can write 4/2 = 2

Share and Show

Use the data on the table to complete the frequency table.

STEP 1: The title of the frequency
table is __________________
The two column titles are ___________ and ____________ .
The title of the frequency table is Time Spent Doing Homework(minutes)
The two column titles are minutes and frequency.

STEP 2: List the number of minutes in the Minutes column:
________, ________, ________, ________, ________

The number of minutes in the minute column is:
15, 30, 45, 60, 90.
Construct a table with two columns.Â  The first column shows what is being arranged in ascending order (i.e. the minutes).Â  The lowest minute is 15.Â  So, start from 15 in the first column as shown below.

STEP 3: List the frequency of the amount of time in the Frequency table:
________, ________, ________, ________, ________

The frequency of the amount of time in the Frequency table:
4, 4, 3, 2, 1
Count the number for each minute and write it in the frequency column.Â  The finished frequency table is as follows:

Question 2.
Make a frequency table using the data in the table.

Step 1:
The title of the frequency table is Time Spent Studying(hour)
The two-column titles are hour and frequency.
Step 2:
The number of hours in the hour’s column is:
1/4, 1/2, 3/4, 1.
Construct a table with two columns.Â  The first column shows what is being arranged in ascending order (i.e. the minutes).Â  The lowest hour is 1/4.Â  So, start from 1/4 in the first column as shown below.

Step 3:
The frequency of the amount of time in the Frequency table: 3, 4, 2, 1
Count the number for each hour and write it in the frequency column.Â  The finished frequency table is as follows:

Make a frequency table using the data in the table.

Step 1:
The title of the frequency table is Distance Traveled On Bike(km)
The two-column titles are Kilometre and frequency.
Step 2:
The number of hours in the hour’s column is:
3, 4, 7, 9, 11
Construct a table with two columns. The first column shows what is being arranged in ascending order (i.e. the minutes). The lowest km is 3. So, start from 3 in the first column as shown below.

Step 3:
The frequency of the amount of time in the Frequency table: 3, 4, 4, 2, 2.
Count the number for each hour and write it in the frequency column.Â  The finished frequency table is as follows:

Problem Solving

Question 4.

H.O.T. Multi-Step Gloria likes to hike every Saturday. She records the number of miles she hikes each day. Use the data in the Distance Hiked table to make a frequency table.

Step 1:
The title of the frequency table is Distance Hiked (miles).
The two-column titles are miles and frequency.
Step 2:
Write the miles in the miles column is:
7, 8, 12, 15.
Construct a table with two columns. The first column shows what is being arranged in ascending order (i.e. the miles). The lowest mile is 7. So, start from 7 in the first column as shown below.

Step 3:
The frequency of the amount of time in the Frequency table: 3, 6, 3, 4
Count the number for each mile and write it in the frequency column.Â  The finished frequency table is as follows:

Question 5.
H.O.T. Explain how you would use the data in the table to make a frequency table. Then represent the data in a frequency table.

Step 1:
The title of the frequency table is Amount Of Pizza Left.
The two-column titles are amount and frequency.
Step 2:
Write the amount in the Amount column is:
1/8, 1/4, 1/2, 3/8.
Construct a table with two columns. The first column shows what is being arranged in ascending order (i.e. the miles). The lowest amount is 1/8. So, start from 1/8 in the first column as shown below.

Step 3:
The frequency of the amount of time in the Frequency table: 3, 4, 3, 2
Count the number for each mile and write it in the frequency column.Â  The finished frequency table is as follows:

Question 6.
Joe made a table to show the length of time he walked.
If Joe were to create a frequency table from this data, what number would he use to show the number of times he walked 45 minutes?

(A) 2
(B) 4
(C) 3
(D) 5

Explanation:
In the table given the time Joe walked. The question asked was the number of times Joe walked 45 minutes. Count the number 45 in the table and write the frequency. In the table there are five 45’s. So the frequency is 5.

Use the table at the right for 7-8.

Jennie has 4 different routes that she goes on when she walks her dog. She made a table to show when she took each of the 4 routes.

Go Math Grade 4 Lesson 17.1 Frequency Table Question 7.
If Jennie was going to make a frequency table from this data, what number would she put to show the number of times she took the 1$$\frac{3}{4}$$ route?

(A) 3
(B) 5
(C) 2
(D) 4

Explanation:
At the table given, Jennie walked with the dog in miles. The question asked was the number would she put to show the number of times she took the 1$$\frac{3}{4}$$ route. Count the number 1$$\frac{3}{4}$$ in the table and write the frequency. In the table, there are three 1$$\frac{3}{4}$$. So the frequency is 3.

Question 8.
What number would Jennie put for the frequency of $$\frac{1}{2}$$?
(A) 2
(B) 3
(C) 4
(D) 5

Explanation:
Now asked the number would Jennie put for the frequency of $$\frac{1}{2}$$. Count the number would Jennie put for the frequency of $$\frac{1}{2}$$ (1/2). The frequency is 3.
Formula: $\frac{1} {a}$ = 1/a

TEXAS Test Prep

Question 9.
During a fund-raiser, several students were asked to sell soda during a baseball game; Danny made a table to keep track of the number of sodas students sold.

If Danny were to create a frequency table from this data, what number would he use to show the number of students who sold 10 sodas?

(A) 3
(B) 5
(C) 10
(D) 7

Explanation:
In the table given the number of sodas Danny sold. The question asked was the number would he use to show the number of students who sold 10 sodas. Count the number 10’s in the table and write the frequency. In the table there are seven 10’s. So the frequency is 7.

### Texas Go Math Grade 4 Lesson 17.1 Homework and Practice Answer Key

Question 1.
Make a frequency table using the data in the table.

Step 1:
The title of the frequency table is Books Checked Out
The two-column titles are the Number of books and frequency.
Step 2:
The number of books in the books column is:
2, 3, 5, 6, 7.
Construct a table with two columns.Â  The first column shows what is being arranged in ascending order (i.e. the books).Â  The lowest hour is 2.Â  So, start from 2 in the first column as shown below.

Step 3:
The frequency of the number of books in the Frequency table: 4, 5, 2, 3, 1
Count the number for each book and write it in the frequency column.Â  The finished frequency table is as follows:

Question 2.
Make a frequency table using the data in the table.

Step 1:
The title of the frequency table is Number Of Laps Run.
The two-column titles are the Number and frequency.
Step 2:
The number of books in the books column is:
1, 2, 3, 4, 5.
Construct a table with two columns.Â  The first column shows what is being arranged in ascending order (i.e. the number).Â  The lowest number is 1.Â  So, start from 1 in the first column as shown below.

Step 3:
The frequency of the number of laps run in the Frequency table: 1, 2, 5, 4, 3.
Count the number for each lap run and write it in the frequency column.Â  The finished frequency table is as follows:

Problem-Solving

Question 3.
Paul made a table to show how many hits each baseball player got in 2 games. Use the data from the table to make a frequency table.

Step 1:
The title of the frequency table is Number Of Hits.
The two-column titles are the Number and frequency.
Step 2:
The number of hits in the number column is:
0,1, 2, 3, 4.
Construct a table with two columns.Â  The first column shows what is being arranged in ascending order (i.e. the number).Â  The lowest number is 0.Â  So, start from 0 in the first column as shown below.

Step 3:
The frequency of the number of hits in the Frequency table: 3, 6, 4, 3, 2.
Count the number for each hit and write it in the frequency column.Â  The finished frequency table is as follows:

Sahara made a table to show how many cans were left in the recycle bin each day. Use the data from the table to make a frequency table.

Step 1:
The title of the frequency table is Cans Left in Recycling Bin.
The two-column titles are the number and frequency.
Step 2:
The number of cans in the number column is:
10, 12, 13, 14, 18.
Construct a table with two columns.Â  The first column shows what is being arranged in ascending order (i.e. the number).Â  The lowest number is 10.Â  So, start from 10 in the first column as shown below.

Step 3:
The frequency of the number of cans left in the Frequency table: 4, 2, 1, 3, 5.
Count the number for each can and write it in the frequency column.Â  The finished frequency table is as follows:

Lesson Check

Question 5.

If Greg were to make a frequency table from this data, what number would he use to show the number of times he made 14 baskets?
(A) 5
(B) 0
(C) 3
(D) 4

Explanation:
In the table given the number of baskets made. The question asked was the number would he use to show the number of times he made 14 baskets. Count the number 14’s in the table and write the frequency. In the table there are three 14’s. So the frequency is 3.

Question 6.
Lacy made a table to show the number of miles she walked.

If Lacy were to make a frequency table from this data, what number would she use to show the number of times she walked $$\frac{1}{2}$$ mile?
(A) 4
(B) 2
(C) 1
(D) 3

Explanation:
Now asked the number would Lacy put for the frequency of $$\frac{1}{2}$$. Count the number would Jennie put for the frequency of $$\frac{1}{2}$$ (1/2). The frequency is 3.
Formula: $\frac{1} {a}$ = 1/a

Use the table at right for 7 – 8.

Ellen is training to run a marathon. She made a table to show how many miles she runs each day she trains.

Question 7.
Multi-Step Ellen made a frequency table from this data. Which mileage will have the greatest frequency?
(A) 12
(B) 13
(C) 9
(D) 10

Explanation:
Ellen already made a frequency table. Here asked which mileage has a higher frequency. We need to count each mileage and circle the mileage which has the highest.

Question 8.
Multi-Step Which statement about the frequency table Ellen made is NOT true?
(A) Ellen ran the same number of 9 and 10 mile days.
(B) Ellen ran more 12 mile days than 10 mile days.
(C) Ellen ran four 9, 10, and 13 mile days.
(D) Ellen ran fewer 9 mile days than 8 mile days.

Explanation:
Ellen ran 4 nine miles and 3 eight miles. In option D fewer 9 miles than 8 miles are given.

## Texas Go Math Grade 3 Lesson 10.5 Answer Key Model with Arrays

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 10.5 Answer Key Model with Arrays.

## Texas Go Math Grade 3 Lesson 10.5 Answer Key Model with Arrays

Essential Question
How can you use arrays to solve division problems?
An arrangement of objects, pictures, or numbers in columns and rows is called an array, and division of the objects or pictures in equal group solve the problem.

Investigate
Materials square tiles
You can use arrays to model division and find equal groups.

A. Count out 30 tiles. Make an array to find how many rows of 5 are in 30.

6 rows

Explanation:
30 tiles are grouped 5 of 6 rows
30Ã·5 = 6

B. Make a row of 5 tiles.

Explanation:
The array contains 30 tiles which are grouped 5 of 6 rows.
30Ã·5 = 6

C. Continue to make as many rows of 5 tiles as you can.
How many rows of 5 did you make? ____

6 rows
Explanation:
30Ã·5 = 6
So, we can make 6 rows.

Make Connections
You can write a division equation to show how many rows of 5 are in 30. Show the array you made in Investigate by completing the drawing below.

30 Ã· 5 = ___
There are ___ rows of 5 tiles in 30.
So, 30 Ã· 5 = _____
completing the drawing:

30 Ã· 5 = 6
There are 6 rows of 5 tiles in 30.
So, 30 Ã· 5 = 6

Math Idea
You can divide to find the number of equal rows or to find the number in each row.
n x n
1 x 1
2 x 2
3 x 3

Share and Show

Use square tiles to make an array. Solve.

Question 1.
How many rows of 3 are in 18?
6 rows

Explanation:
Array has 18 tiles arranged in rows.
Each row has 3 tiles.
Total rows in array
18 Ã· 3 = 6

How many rows of 6 are in 12?
2 rows

Explanation:
Array has 12 tiles arranged in rows.
Each row has 6 tiles.
Total rows in array
18 Ã· 6 = 2

Question 3.
How many rows of 7 are in 21?
3 rows

Explanation:
Array has 21 tiles arranged in rows.
Each row has 7 tiles.
Total rows in array
21 Ã· 7 = 3

Question 4.
How many rows of 8 are in 32?
4 rows

Explanation:
Array has 32 tiles arranged in rows.
Each row has 8 tiles.
Total rows in array
32 Ã· 8 = 4

Make an array. Then write a division equation.

Question 5.
25 tiles in 5 rows
5 tiles in a row
25Ã·5 = 5

Explanation:
Array has 25 tiles arranged in rows.
Total 5 rows in array
Each row has 25 Ã· 5 = 5

Question 6.
14 tiles in 2 rows
7 tiles in a row
14Ã·2 = 7

Explanation:
Array has 14 tiles arranged in rows.
Each row has 7 tiles
Total rows in array 14 Ã· 2 = 7

Question 7.
28 tiles in 4 rows
7 tiles in a row
28Ã·4 = 7

Explanation:
Array has 28 tiles arranged in rows.
Total 4 rows in array
Each row has 28 Ã· 7 = 7

27 tiles in 9 rows
3 tiles in a row
27Ã·9=3

Explanation:
Array has 27 tiles arranged in rows.
Total 9 rows in array
Each row has 27 Ã· 9 = 3

Question 9.
How many rows of 3 are in 15?
5 rows
15 Ã· 5 = 3

Explanation:
Array has 15 tiles arranged in rows.
Each row has 3 tiles
Total rows in array 27 Ã· 9 = 3

Question 10.
How many rows of 8 are in 24?
3 rows
24 Ã· 8 = 3

Explanation:
Array has 24 tiles arranged in rows.
Each row has 8 tiles
Total rows in array 24 Ã· 8 = 3

Math Talk
Mathematical Processes
Explain when you Count the number of rows to find the answer and when you count the number of tiles in each row to find the answer.
To find the number of tiles in a row,Â  total tiles Ã· number of row is calculated.
To find the number of rows,Â  total tiles Ã· number of tiles in row is calculated.

Question 11.
Write Math Show two ways you could make an array with tiles for 18 Ã· 6. Shade squares on the grid to record the arrays.

18 Ã· 6 = 3
6 rows of 3 tiles
or
3 rows of 6 tiles
Explanation:
count the number of tiles on the grid and shade as,
6 rows of 3 tiles
3 rows of 6 tiles

Problem Solving

Question 12.
Thomas has 28 tomato seedlings to plant in his garden. He wants to plant 7 seedlings in each row. How many rows of tomato seedlings will Thomas plant?
4 rows of tomato seedlings.
Explanation:
Thomas has 28 tomato seedlings to plant in his garden.
He wants to plant 7 seedlings in each row.
Total rows of tomato seedlings Thomas plant
28 Ã· 7 = 4

Question 13.
H.O.T. Use Math Language Tell how to use an array to find how many rows of 8 are in 40.

An array is an orderly arrangement (often in rows, columns or a matrix) that is most commonly used as a visual tool for demonstrating multiplication and division .
40Â Ã· 8 = 5
Explanation:
An array refers to a set of numbers or objects that will follow a specific pattern.
40Â Ã· 8 = 5

Faith plants 36 flowers in 6 equal rows. How many flowers are in each row?
6 flowers in each row.
Explanation:
Faith plants 36 flowers in 6 equal rows.
Total flowers in each row
36 Ã· 6 = 6

Question 15.
H.O.T. Multi-Step There were 20 plants sold at a store on Saturday and 30 plants sold at the store on Sunday. Customers bought 5 plants each. How many customers in all bought the plants?
10 customers bought the plants.
Explanation:
There were 20 plants sold at a store on Saturday and
30 plants sold at the store on Sunday.
Total plants sold on both days 20 + 30 = 50
Customers bought 5 plants each.
Number of customers bought the plants
50 Ã· 5 =10

Question 16.
H.O.T. Multi-Step Lionel made an array with 24 tiles. The number of rows is 5 more than the number of tiles in each row. How many rows are in Lionelâ€™s array?
3 rows
Explanation:

Lionel made an array with 24 tiles.
The number of rows is 5 more than the number of tiles in each row.
Number of rows in Lionel’s array is 3

Fill in the bubble for the correct answer choice.
You may use objects or models to solve.

Question 17.
Multi-Step Mrs. Weston is baking 24 oatmeal raisin cookies. There will be 4 rows of cookies on the cookie tray. She has already put one row of cookies on the tray. How many more cookies does she have left to put on the tray?
(A) 6
(B) 20
(C) 18
(D) 3
Mrs. Weston is baking 24 oatmeal raisin cookies.
24 Ã· 4 = 6
4 – 1 = 3 rows left
3 x 6 = 18
18 more cookies she have left to put on the tray.

Question 18.
Representations Which division equation is shown by the array?

(A) 24 Ã· 3 = 8
(B) 24 Ã· 4 = 6
(C) 24 Ã· 2 = 12
(D) 21 Ã· 3 = 7
Option (A)
Explanation:
The array contains 24 tiles,
arranged as 3 rows of 8 tiles.

Question 19.
Multi-Step Hajune finds 9 black rocks one week and 9 black rocks the next week. He wants to keep the rocks in a box with 3 rows. How many black rocks can he put in each row?
(A) 18
(B) 6
(C) 12
(D) 3
6 black rocks in a box.
Explanation:
Hajune finds 9 black rocks one week and 9 black rocks the next week.
Total black rocks 9 + 9 = 18
He wants to keep the rocks in a box with 3 rows.
Total black rocks he put in each row
18 Ã· 3 = 6

Texas Test Prep

Question 20.
Sally makes an array using 36 coins. If she puts 4 coins in each row, how many rows does she make?
(A) 40
(B) 32
(C) 8
(D) 9
Option(D)
Explanation:
Sally makes an array using 36 coins.
If she puts 4 coins in each row,
Total rows she make
36 Ã· 4 = 9

### Texas Go Math Grade 3 Lesson 10.5 Homework and Practice Answer Key

Make an array. Then write a division equation.

Question 1.
21 tiles in 3 rows
7 tiles in each row

21 Ã· 3 = 7
Explanation:
Array has 21 tiles arranged in 3 rows.
Each row has 27 Ã· 9 = 3 tiles

Question 2.
36 tiles in 6 rows
6 tiles in each row

36 Ã· 6 = 6
Explanation:
Array has 36 tiles arranged in 6 rows.
Each row has 36 Ã· 6 = 6 tiles
Question 3.
16 tiles in 8 rows
2 tiles in each row

16 Ã· 8 = 2
Explanation:
Array has 16 tiles arranged in 8 rows.
Each row has 16 Ã· 8 = 2 tiles

Question 4.
18 tiles in 3 rows
6 tiles in each row
18 Ã· 3 = 6

Explanation:
Array has 18 tiles arranged in 3 rows.
Each row has 18 Ã· 3 = 6 tiles

Question 5.
How many rows of 4 are in 32?
8 tiles in each row
32 Ã· 4 = 8

Explanation:
Array has 21 tiles arranged.
Each row has 4 tiles
number of rows 27 Ã· 9 = 3

Question 6.
How many rows of 4 are in 16?
4 tiles in each row
16 Ã· 4 = 4

Explanation:
Array has 21 tiles arranged.
Each row has 4 tiles
number of rows 27 Ã· 9 = 3

Problem Solving

Question 7.
Hannah has a collection of 27 seashells. She wants to put 9 shells on each shelf. How many shelves does Hannah need?
3 shelves
27 Ã· 9 = 3
Explanation:
Hannah has a collection of 27 seashells.
She wants to put 9 shells on each shelf.
Number of shelves Hannah needs
27 Ã· 9 = 3

Go Math Grade 3 Practice and Homework Lesson 10.5 Answer Key Question 8.
Dexter buys 18 fish. He wants to put an equal number of fish into 3 fishbowls. How many fish will he put in each fishbowl?
6 fish in each bowl.
Explanation:
He wants to put an equal number of fish into 3 fishbowls.
Number of fish he put in each fishbowl
18 Ã· 3 = 6

Question 9.
Quentin is making a tile design with 35 tiles. He wants to put the tiles in rows. How can he set up the tiles so there are an equal number of tiles in each row?
35Ã·7 =5 or
35Ã·5 =7
Explanation:
Quentin is making a tile design with 35 tiles.
He wants to put the tiles in rows.
He can set up the tiles in 2 ways, an equal number of tiles in each row
35Ã·7 =5 or 35Ã·5 =7

Texas Test Prep

Lesson Check

Question 10.
Marla makes this array.

What division equation can she write?
(A) 14 Ã· 3 = 7
(B) 14 Ã· 2 = 7
(C) 2 Ã— 7 = 14
(D) 7 + 7 = 14
Option(B)
Explanation:
Marla makes array of 14 tiles, arranged in 2 equal rows.
Number of tiles in each row
14 Ã· 2 = 7

Question 11.
Claude makes this array.

What division equation can he write?
(A) 24 Ã· 4 = 6
(B) 24 Ã· 3 = 8
(C) 4 Ã— 6 = 24
(D) 6 Ã— 4 = 20
Option(A)
Explanation:
Claude makes array of 24 tiles.
Each row contains 4 tiles.
Total tiles arranged in equal rows
24Â Ã· 4 = 6

Question 12.
Sondra runs for 32 minutes. If she runs 4 miles, how many minutes does it take her to run one mile?
(A) 6 minutes
(B) 7 minutes
(C) 8 minutes
(D) 28 minutes
Option(C)
Explanation:
Sondra runs for 32 minutes.
If she runs 4 miles,
Total minutes it take her to run one mile
32 Ã· 4 = 8

Question 13.
There are 25 students on the playground. The students are in teams of 5. How many teams are on the playground?
(A) 6
(B) 5
(C) 4
(D) 7
Option(B)
Explanation:
There are 25 students on the playground.
The students are in teams of 5.
Total teams on the playground
25 Ã·Â  5 = 5

Question 14.
Multi-Step Jennifer collects 9 animal cards and 21 nature cards. She wants to arrange them on a bulletin board in 6 rows. How many cards will be in each row?
(A) 5
(B) 2
(C) 3
(D) 7
Option(A)
Explanation:
Jennifer collects 9 animal cards and 21 nature cards.
9 + 21 = 30
She wants to arrange them on a bulletin board in 6 rows.
Number of cards in each row
30 Ã· 6 = 5

Question 15.
Multi-Step Zach is planting a garden of 27 tomato plants. He puts the plants into rows of 9. If he has already planted one row, how many more rows does he need to plant?
(A) 3
(B) 2
(C) 18
(D) 4
Explanation:
Option (B)
Zach is planting a garden of 27 tomato plants.
He puts the plants into rows of 9.
27 Ã· 9 = 3
If he has already planted one row, 3 – 1 = 2
2 more rows he need to plant

## Texas Go Math Grade 3 Lesson 9.1 Answer Key Use the Distributive Property

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 9.1 Answer Key Use the Distributive Property.

## Texas Go Math Grade 3 Lesson 9.1 Answer Key Use the Distributive Property

Essential Question
How can you use the strategy draw a diagram to multiply with multiples of 10?

Unlock the Problem
The school assembly room has 10 rows of chairs with 20 chairs in each row. If the third-grade classes fill 3 rows
of chairs, how many third graders are at the assembly?

What do I need to find?
I need to find how many ___ are at the assembly.

What information am I given?
There are ___ chairs in each row.
The third graders fill __ rows of chairs.

Plan
What is my plan or strategy?
The Distributive Property tells me
I can ___ the factor 20 to multiply.
3 Ã— 20 = 3 Ã— (10 + ___)

Solve
Draw a diagram. Finish the shading to show 3 rows of 20 chairs.

I can use the sum of the products of the smaller rectangles to find how many third graders are at the assembly.
3 Ã— 10 = ___ 3 Ã— 10 = __
___ + ___ = ____
3 Ã— 20 = ___
So, __ third graders are at the assembly.

Question 1.
Explain how breaking apart the factor 20 makes finding the product easier.
Breaking apart the factor 20 makes finding the product easier because its helps to manipulate the numbers in different easy ways to get the end result in an quick and understandable way.

Explanation:
Breaking apart an addend is a mental math. This strategy involves breaking up one addend in an equation into more manageable parts. Like many other mental math strategies, this strategy encourages students to think flexibly and to manipulate numbers in different ways.

Try Another Problem
Megan is watching a marching band practice. The band marches by with 4 rows of people playing instruments. She counts 30 people in each row. How many people are marching in the band?

What do I need to find?

What information am I given?

Plan
What is my plan or strategy?

Solve
Record the steps you used to solve the problem

Explain how you can use the Distributive Property to help you find a product.
Distributive property helps us in finding the product as it allows you to split a large multiplication problem into two smaller ones and add the results to get the answer in an easy, simplified, and understanding way.

Explanation:
The distributive property tells us how to solve expressions in the form of a(b + c). Â The distributive property is sometimes called the distributive law of multiplication and division.

Math talk
Mathematical Processes
Explain how you can check to see if your answer is reasonable.

Share and Show
Unlock the Problem Tips
âœ“ Use the Problem Solving MathBoard.
âœ“ Underline important facts.
âœ“ Choose a strategy you know.

Question 1.
The front section of a theater has 6 rows with 40 seats in each row. In the front section, 24 seats are reserved. How many seats in the front section of the theater are not reserved?

Step 1.
Write the problem you need to solve. ____
Draw and label a diagram to break apart the problem.

There are __ seats in the front section of the theater.

Step 2.
Find the difference. 240 â€” ___ = ___
So, there are ____ seats in the front section that are not reserved.
Total number of seats in the front section in the theatre = 240.

Explanation:
Number of seats in the front section in the theatre = ???
Total number of rows in the theatre = 6.
Number of seats in each row in the theatre = 40.
Total number of seats in the front section in the theatre = Total number of rows in the theatre Ã— Number of seats in each row in the theatre
= 6 Ã— 40
= 6 Ã— (10 + 10 + 10 + 10)
= (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10)
= 60 + 60 + 60 + 60
= 120 + 60 + 60
= 180 + 60
= 240.

Question 2.
What if seats are added to the front section of the theater so that there are 6 rows with 50 seats in each row? How many seats are in the front section?
Total number of seats in the front section in the theatre = 300.

Explanation:
If seats are added to the front section of the theater so that there are 6 rows with 50 seats in each row:
Total number of seats in the front section in the theatre = ???
Total number of rows in the theatre = 6.
Number of seats in each row in the theatre = 50.
Total number of seats in the front section in the theatre = Total number of rows in the theatre Ã— Number of seats in each row in the theatre
= 6 Ã— 50
= 6 Ã— (10 + 10 + 10 + 10 + 10)
= (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10)
= 60 + 60 + 60 + 60 + 60
= 120 + 60 + 60 + 60
= 180 + 60 + 60
= 240 + 60
= 300.

Problem Solving

H.O.T. Multi-Step Tova sewed 60 pieces of blue ribbon together to make a costume. Each piece of ribbon was 2 meters long. She also sewed 40 pieces of red ribbon together that were each 3 meters long. Did Tova use more blue ribbon or red ribbon? Explain.

No, Tova did not use more blue ribbon nor red ribbon because she used both ribbons same amount of length.

Explanation:
Number of pieces of blue ribbon Tova sewed = 60.
Length of each piece of blue ribbon = 2 meters.
Total length of piece of blue ribbon Tova sewed = Number of pieces of blue ribbon Tova sewedÂ  Ã— Length of each piece of blue ribbon
= 60 Ã— 2
= 120meters.
Number of pieces of red ribbon Tova sewed = 40.
Length of each piece of red ribbon = 3 meters.
Total length of piece of red ribbon Tova sewed = Number of pieces of red ribbon Tova sewedÂ  Ã— Length of each piece of red ribbon
= 40 Ã— 3
= 120 meters.

Fill in the bubble for the correct answer choice.
Question 4.
Apply A zoo gives 8 tubs of food to the male gorillas. Each tub has 40 pounds of food. How much food do the male gorillas eat each day?
(A) 270 pounds
(B) 180 pounds
(C) 320 pounds
(D) 90 pounds
Total weight of the tubs of food to the male gorillas Apply A zoo gives = 320 pounds.
(C) 320 pounds.

Explanation:
Number of tubs of food to the male gorillas Apply A zoo gives = 8.
Weight of each tub of food has = 40 pounds.
Total weight of the tubs of food to the male gorillas Apply A zoo gives = Number of tubs of food to the male gorillas Apply A zoo gives Ã— Weight of each tub of food has
= 8 Ã— 40
= (8 Ã— 10) + (8 Ã— 10) + (8 Ã— 10) + (8 Ã— 10)
= 80 + 80 + 80 + 80
= 160 + 80 + 80
= 240 + 80
= 320 pounds.

Question 5.
Marcus will make 20 omelets. Each omelet takes 3 eggs. How many eggs will Marcus use?
(A) 23
(B) 17
(C) 60
(D) 50
Total number of eggs will Marcus use = 60.
(C) 60.

Explanation:
Number of omelets Marcus will make = 20.
Number of eggs each omelet takes = 3.
Total number of eggs will Marcus use = Number of omelets Marcus will make Ã— Number of eggs each omelet takes
= 20 Ã— 3
= 60.

Question 6.
Multi-Step Shania makes a scrapbook about her trip to the state capitol. She makes 2 sections about the history and 4 sections about what she saw. Each history section has 30 pages and each section about what she saw has 20 pages. How many pages does Shania’s scrapbook have?
(A) 140
(B) 300
(C) 80
(D) 60
Total number of pages Shania scrapbooks has = 140.
(A) 140.

Explanation:
Number of sections about the history Shania makes = 2.
Number of pages each history section has = 30.
Number of pages about history Shania makes = Number of sections about the history Shania makesÂ  Ã— Number of pages each history section has
= 2 Ã— 30
= (2 Ã— 10) + (2 Ã— 10)Â  + (2 Ã— 10)
= 20 + 20 + 20
= 40 + 20
= 60.
Number of sections about what she saw Shania makes = 4.
Number of pages each what she saw section has = 20.
Number of pages about what she saw Shania makes = Number of sections about what she saw Shania makes Ã— Number of pages each what she saw section has
= 4 Ã— 20
= 80.
Total number of pages Shania scrapbooks has = Number of pages about history Shania makes + Number of pages about what she saw Shania makes
= 60 + 80
= 140.

Texas Test Prep

Stefan orders theater tickets for each of the 5 members of his family. If each ticket costs $20, what is the total cost for the tickets? (A)$70
(B) $30 (C)$25
(D) $100 Answer: Total cost for the tickets =$100.
(D) $100. Explanation: Number of members in the family of Stefan = 5. Cost of each ticket =$20.
Total cost for the tickets = Number of members in the family of Stefan Ã— Cost of each ticket
= 5 Ã— $20 =$100.

### Texas Go Math Grade 3 Lesson 9.1 Homework and Practice Answer Key

Draw and label the diagram to solve.

Question 1.
The Morgan family buys 7 booklets of tickets at the carnival. Each booklet has 30 tickets. Of all the tickets bought, 21 tickets are for rides. How many tickets are not for rides?

Step 2
Find the differences. 210 – ___ = ___
So, there are __ tickets that are not for rides.
Number of tickets are not for rides = 189.

Explanation:
Number of booklets of tickets at the carnival the Morgan family buys = 7.
Number of tickets each booklet has = 30.
Total number of tickets booklet has = Number of booklets of tickets at the carnival the Morgan family buys Ã— Number of tickets each booklet has
= 7 Ã— 30
= (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10)
= 70 + 70 + 70
= 140 + 70
= 210.
Number of tickets are for rides = 21.
Number of tickets are not for rides = Total number of tickets booklet has – Number of tickets are for rides
= 210 – 21
= 21( 10 – 1)
= 21 Ã— 9
= 189.

Problem Solving
Question 2.
The roller coaster ride costs 8 tickets. If 30 people ride the roller coaster, how many tickets are collected?
___ Ã— ___ = ____
Number of tickets are collected = 240.
8 Ã— 30 = 240.

Explanation:
Number of tickets the roller coaster ride costs = 8.
Number of people ride the roller coaster = 30.
Number of tickets are collected = Number of tickets the roller coaster ride costs Ã— Number of people ride the roller coaster
= 8 Ã— 30
= (8 Ã— 10) + (8 Ã— 10) + (8 Ã— 10)
= 80 + 80 + 80
= 160 + 80
= 240.

The giant swing ride costs 6 tickets. If 50 people ride the giant swing ride, how many tickets are collected?
___ Ã— ___ = ____
Number of tickets are collected = 300.
6 Ã— 50 = 300.

Explanation:
Number of tickets the giant swing ride costs = 6.
Number of people ride the giant swing ride = 50.
Number of tickets are collected = Number of tickets the giant swing ride costs Ã— Number of people ride the giant swing ride
= 6 Ã— 50
= (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10) + (6 Ã— 10)
= 60 + 60 + 60 + 60 + 60
= 120 + 60 + 60 + 60
= 180 + 60 + 60
= 240 + 60
= 300.

Texas Test Prep
Lesson Check

Question 4.
An has a rock collection. He puts 20 rocks into each of 8 boxes. How many rocks does An have in his collection?
(A) 160
(B) 28
(C) 16
(D) 140
Number of rocks An have in his collection = 160.
(A) 160.

Explanation:
Number of rocks An has in his rock collection = 20.
Number of boxes = 8.
Number of rocks An have in his collection = Number of rocks An has in his rock collection Ã— Number of boxes
= 20 Ã— 8
= (10 Ã— 8) + (10 Ã— 8)
= 80 + 80
= 160.

Question 5.
At the town picnic, there are 7 stacks of paper cups on a shelf. Each stack holds 60 cups. How many cups are on the shelf?
(A) 490
(B) 420
(C) 670
(D) 67
Number of cups are on the shelf = 420.
(B) 420.

Explanation:
Number of stacks of paper cups on a shelf = 7.
Number of cups each stack holds = 60.
Number of cups are on the shelf = Number of stacks of paper cups on a shelfÂ  Ã— Number of cups each stack holds
= 7 Ã— 60
= (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10)
= 70 + 70 + 70 + 70 + 70 + 70
= 140 + 70 + 70Â  + 70 + 70
= 210 + 70 + 70Â  + 70
= 280 + 70 + 70
= 350 + 70
= 420.

Go Math Lesson 9.1 Distributive Property Third Grade Question 6.
Mr. Franz buys 4 bags of forks. There are 30 forks in each bag. Which number sentence shows how many forks are there in all?
(A) 4 + 30 = 34
(B) 4 Ã— 30 = 120
(C) 4 + 30 = 120
(D) 40 + 30 = 70
Number of forks are there in all = 120.
(B) 4 Ã— 30 = 120.

Explanation:
Number of bags of forks Mr. Franz buys = 4.
Number of forks in each bag = 30.
Number of forks are there in all = Number of bags of forks Mr. Franz buysÂ  Ã— Number of forks in each bag
= 4 Ã— 30
= (4 Ã— 10) + (4 Ã— 10) + (4 Ã— 10)
= 40 + 40 + 40
= 80 + 40
= 120.

Question 7.
Valerie buys 5 sticker books. Each book has 80 stickers. Which number sentence shows how many stickers Valerie buys?
(A) 5 Ã— 80 = 40
(B) 8 + 50 = 58
(C) 5 Ã— 80 = 400
(D) 5 Ã— 80 = 450
Number of stickers Valerie buys = 400.
(C) 5 Ã— 80 = 400.

Explanation:
Number of sticker books Valerie buys = 5.
Number of stickers each book has = 80.
Number of stickers Valerie buys = Number of sticker books Valerie buysÂ  Ã— Number of stickers each book has
= 5 Ã— 80
= (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) +(5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10) + (5 Ã— 10)
= 50 + 50 + 50 + 50Â  + 50 + 50Â  + 50 + 50
= 100 + 50 + 50Â  + 50 + 50Â  + 50 + 50
= 150 + 50 + 50Â  + 50 + 50 + 50
= 200 + 50 + 50Â  + 50 + 50
= 250 + 50 + 50Â  + 50
= 300 + 50 + 50
= 350 + 50
= 400.

Question 8.
Multi-Step A farm stand has 4 bushels of apples. Each bushel has 40 red apples. There are also 7 bushels of 30 green apples. How many apples are there in all?
(A) 490
(B) 370
(C) 280
(D) 160
Total number of apples in all = 370.
(B) 370

Explanation:
Number of bushels of apples aÂ farm stand has = 4.
Number of red apples in each bushel has = 40.
Total number of red apples = Number of bushels of apples a farm stand has Ã— Number of red apples in each bushel has
= 4 Ã— 40
= (4 Ã— 10) + (4 Ã— 10) + (4 Ã— 10)Â  + (4 Ã— 10)
= 40 + 40 + 40 + 40
= 80 + 40 + 40
= 120 + 40
= 160.
Number of bushels of green apples a farm stand has = 7.
Number of green apples in each bushel has = 30.
Total number of green apples = Number of bushels ofÂ  green apples a farm stand has Ã— Number of green apples in each bushel has
= 7 Ã— 30
= (7 Ã— 10) + (7 Ã— 10) + (7 Ã— 10)
= 70 + 70 + 70
= 140 + 70
= 210.
Total number of apples in all = Total number of red apples + Total number of green apples =
= 160 + 210
= 370.

Lesson 9.1 Distributive Property 3rd Grade Go Math Question 9.
Multi-Step Marcel buys 3 large boxes of cherries. Each box holds 40 cherries. He also buys 8 small boxes. Each small box holds 20 cherries. How many cherries does Marcel buy?
(A) 280
(B) 120
(C) 480
(D) 160
Total number of cherries in all he buys = 280.
(A) 280.

Explanation:
Number of large boxes of cherries Marcel buys = 3.
Number of cherries each box holds = 40.
Total number of cherries in large boxes = Number of large boxes of cherries Marcel buysÂ  Ã— Number of cherries each box holds
= 3 Ã— 40
= (3 Ã— 10) + (3 Ã— 10) + (3 Ã— 10) + (3 Ã— 10)
= 30 + 30 + 30 + 30
= 60 + 30 + 30
= 90 + 30
= 120.
Number of small boxes of cherries Marcel buys = 8.
Number of cherries each box holds = 20.
Total number of cherries in small boxes = Number of small boxes of cherries Marcel buysÂ  Ã— Number of cherries each box holds
= 8 Ã— 20
= (8 Ã— 10) + (8 Ã— 10)
= 80 + 80
= 160.
Total number of cherries in all he buys = Total number of cherries in large boxes + Total number of cherries in small boxes
= 120 + 160
= 280.

## Texas Go Math Grade 7 Lesson 5.4 Answer Key Making Predictions with Experimental Probability

Refer to ourÂ Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 5.4 Answer Key Making Predictions with Experimental Probability.

## Texas Go Math Grade 7 Lesson 5.4 Answer Key Making Predictions with Experimental Probability

Making Predictions from Probability Results Worksheet Answer Key Question 1.
A car rental company sells accident insurance to 24% of its customers. Out of 550 customers, how many customers are predicted to purchase insurance?.
Find 24% of 550.
Write 24% as a fraction. The percent equation will be
x = $$\frac{24}{1000}$$ âˆ™ 550 Write fraction as decimal.
= 0.24 âˆ™ 550 Multiply.
= 132
About 132 customers of 550 are predicted to purchase insurance.

Example 2

A doctor’s office records data and concludes that, on average, 11% of patients call to reschedule their appointments per week. The office manager predicts that 23 appointments will be rescheduled out of the 240 total appointments during next week. Explain whether the prediction is reasonable.

Method 1: Use a proportion.

Method 2: Use a percent equation.
0.11 âˆ™ 240 = x Find 11% of 240.
26.4 = x Solve for x
The prediction of 23 is reasonable but a little low, because 23 is a little less than 26.4.

Reflect

Question 2.
Does 26.4 make sense for the number of patients? Explain.
36.4 is the solution of the equation for finding the average number of patients that would call to reschedule.
But, we can not divide people, so we need to round the solution of the equation to a smaller whole number, hence, about 26 people would call to reschedule.

In emails to monthly readers of a newsletter 3% of the emails come back undelivered. The editor predicts that if he sends out 12,372 emails, he will receive 437 notices for undelivered emails. Do you agree with his prediction? Explain.
Find 3% of 12, 372.
Write 3% as a fraction. The percent equation will be
x = $$\frac{3}{100}$$ âˆ™ 12, 372 Write fraction as decimal.
= 0.03 âˆ™ 12. 372 Multiply.
= 371.16
We need to round the solution of the equation to a smaller whole number, hence, about 371 of 12, 372 emails are predicted to come back undelivered.
The prediction of 437 isnâ€™t reasonable, because 371 is way Less than 437.

Question 4.
On average, 24% of customers who buy shoes in a particular store buy two or more pairs. One weekend, 350 customers purchased shoes. How many can be predicted to buy two or more pairs? If 107 customers buy more than two pairs, did more customers than normal buy two or more pairs?
Find 24% of 350.
Write 24% as a fraction. The percent equation will. be
x = $$\frac{24}{100}$$ âˆ™ 350 Write fraction as decimal
= 0.24 âˆ™ 350 Multiply.
= 84
84 is average number of customers that buy two or more pairs of shoes.
If 107 customers buy more than two pairs of shoes, this is more than normal customers who buy two or more pairs, because 107 > 84.

Question 1.
A baseball player reaches first base 30% of the times he is at bat. Out of 50 times at bat, about how many times will the player reach first base? (Example 1)
Find 30% of 50.
Write 30% as a fraction. The percent equation will be
x = $$\frac{30}{100}$$ âˆ™ 50 Write fraction as decimal.
= 0.3 âˆ™ 50 Multiply
=15
About 15 times will the player reach first base.

The experimental probability that it will rain on any given day in Houston, Texas, is about 15%. Out of 365 days, about how many days can residents predict rain? (Example 1)
Find 15% of 365.
Write 15% as a fraction. The percent equation will be
x = $$\frac{15}{100}$$ âˆ™ 365 Write fraction as decimal.
= 0.15 âˆ™ 365 Multiply.
= 54.75
We need to round the solution of the equation to a smaller whole number, hence, about 54 of 365 days residents predict rain in Houston in Texas.

Question 3.
A catalog store has 6% of its orders returned for a refund. The owner predicts that a new candle will have 812 returns out of the 16,824 sold. Do you agree with this prediction? Explain. (Example 2)
Find 6% of 16,824.
Write 6% as a fraction. The percent equation will be
x = $$\frac{6}{100}$$ âˆ™ 824 Write fraction as decimal
= 0.06 âˆ™ 16, 824 Multiply.
= 1009.44
We need to round the solution of the equation to a smaller whole number, hence, about 1009 of 16,824 orders will return for a refund.

The prediction of 812 is reasonable, but a lot low, because 1009 is a lot greater than 812.

Question 4.
On a toy assembly line, 3% of the toys are found to be defective. The quality control officer predicts that 872 toys will be found defective out of 24,850 toys made. Do you agree with this prediction? Explain. (Example 2)
Find 3% of 24, 850.
Write 3% as a fraction. The percent equation will be
x = $$\frac{3}{100}$$ âˆ™ 24,850 Write fraction as decimal
= 0.03 âˆ™ 24. 850 Multiply.
= 745.5
We need to round the solution of the equation to a smaller whole number, hence, about 745 of 24, 850 toys will be defective.

The prediction of 872 isnâ€™t reasonable, because 872 is a lot greater than the predicted number of defective toys.

A light-rail service claims to be on time 98% of the time. If Jeanette takes the light-rail 40 times a month, how many times can she predict she will be on time? Is the light-railâ€™s claim accurate if she is late 6 times? (Example 3)
Find 98% of 40.
Write 98% as a fraction. The percent equation will be
x = $$\frac{98}{100}$$ âˆ™ 40 Write fraction as decimal
= 0.98 âˆ™ 40 Multiply.
= 39.2
We need to round the solution of the equation to a smaller whole number, hence, about 39 of 40 times she will be on time.
Only once she will be late.

Question 6.
On average, a college claims to accept 18% of its applicants. If the college has 5,000 applicants, predict how many will be accepted. If 885 applicants are accepted, is the collegeâ€™s claim accurate? (Example 3)
Find 18% of 5000.
Write 18% as a fraction. The percent equation will be
x = $$\frac{18}{100}$$ âˆ™ 5000 Write fraction as decimal.
= 0.18 âˆ™ 5000 Multiply.
= 900
About 900 of 5000 applicants will be accepted.
The claim is correct because 885 is less than the number of predicted applicants.

Essential Question Check-In

Question 7.
How do you make predictions using experimental probability?
We can equalize the probability with a fraction that has an unknown number in numerator, white in denominator is a number of times how many times the experiment was repeated.

The table shows the number of students in a middle school at the beginning of the year and the percentage that can be expected to move out of the area by the end of the year.

Question 8.
How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th grade students move than expected? Justify your answer.
Find 4% of 200.
Write 4% as a fraction. The percent equation will be
x = $$\frac{4}{100}$$ âˆ™ 200 Write fraction as decimal.
= 0.04 âˆ™ 200 Multiply.
=8
About 8 7th grade students will move by the end of the year.
12 > 7, hence, more than the predicted number of 7th-grade students moved by the end of the year.

Critique Reasoning The middle school will lose some of its funding if 50 or more students move away in any year. The principal claims he only loses about 30 students a year. Do the values in the table support his claim? Explain.
Find how many students of all grades are expected to move by the end of the year.
Find 2% of 250.
Write 2% as a fraction. The percent equation will be
x1 = $$\frac{2}{100}$$ âˆ™ 250 Write fraction as decimal.
= 0.02 âˆ™ 250 Multiply.
= 5
About 5 6th grade students will move by the end of the year.

Find 4% of 200.
Write 4% as a fraction. The percent equation will be
x2 = $$\frac{4}{100}$$ âˆ™ 200 Write fraction as decimal.
= 0.04 âˆ™ 200 Multiply.
= 8
About 8 7th grade students will move by the end of the year.

Find 8% of 150.
Write 8% as a fraction. The percent equation will be
x3 = $$\frac{8}{100}$$ âˆ™ 150 Write fraction as decimal.
= 0.08 âˆ™ 150 Multiply.
= 12
About 12 8th grade students will move by the end of the year.

x1 + x2 + x3 = 5 + 8 + 12 = 25
About 25 students of all grades will move by the end of the year.
Principal claim is correct, because 30 students is less than the predicted number of student who will move by the end of the year.

Question 10.
Represent Real-World Problems An airline knows that, on average, the probability that a passenger will not show up for a flight is 6%. If an airplane is fully booked and holds 300 passengers, how many seats are expected to be empty? If the airline overbooked the flight by 10 passengers, about how many passengers are expected to show up for the flight? Justify your answer.
Find 6% of 300.
Write 6% as a fraction. The percent equation will be
x = $$\frac{6}{100}$$ âˆ™ 300 Write fraction as decimal
= 0.06 âˆ™ 300 Multiply.
=18
About 18 of 300 passengers will not show up for a flight if the airplane is fully booked, hence, about 18 seats will be empty.

If the airline overbooked the flight by 10 passengers, we have to add 10 to 300 and then find 4% of that sum.
Write 6% as a fraction. The percent equation will be
x = $$\frac{6}{100}$$ âˆ™ 310 Write fraction as decimal.
= 0.06 âˆ™ 310 Multiply.
= 18.6
We need to round the solution of the equation to a smaller whole number, hence, about 18 of 310 passengers will not show up for a flight.
Hence, about 310 – 18 = 292 passengers will show up for the flight.

Draw Conclusions In a doctor’s office, an average of 94% of the clients pay on the day of the appointment. If the office has 600 clients per month, how many are expected not to pay on the day of the appointment? If 40 clients do not pay on the day of their appointment in a month, did more or fewer than the average not pay?
Find 94% of 600.
Write 94% as a fraction. The percent equation will be
x = $$\frac{94}{100}$$ âˆ™ 600 Write fraction as decimal.
= 0.94 âˆ™ 600 Multiply.
= 564
About 564 of 600 clients will. pay on the day of the appointment in a month.
Hence, about 600 – 564 = 36 clients who will not pay on the day of the appointment.
40 clients is more than expected number of clients who donâ€™t pay on the day of their appointment in a month.

Question 12.
Counterexamples The soccer coach claimed that, on average, only 80% of the team comes to practice each day. The table shows the number of students that came to practice for 8 days. If the team has 20 members, how many team members should come to practice to uphold the coach’s claim? Was the coach’s claim accurate? Explain your reasoning.

Find 80% of 20.
Write 80% as a fraction. The percent equation will be
x = $$\frac{20}{100}$$ âˆ™ 80 Write fraction as decimal.
= 0.2 âˆ™ 80 Multiply.
= 16
About 16 students of 20 should practice each day to uphold the coachâ€™s claim.
From the table, we have to find the average number of students that come to practice each day and compare it with the coachâ€™s claim.
To find the average number of students that come to practice each day, we have to sum the number of students that come every day, and then divide that sum by the number of days.
x = $$\frac{18+15+18+17+17+19+20+20}{8}=\frac{144}{8}$$ = 18
About 18 students come to practice each day, hence, the coachâ€™s claim is correct

Question 13.
What’s the Error? Ronnie misses the school bus 1 out of every 30 school days. He sets up the proportion $$\frac{1}{30}$$ = $$\frac{180}{x}$$ to predict how many days he will miss the bus in the 180-day school year. What is Ronnie’s error?
He writes 1 of 30 is 180 out of how many, instead of 1 of 30 is how many out of 180 because he wants to predict how many days of 180 he will miss the bus.
The right proportion is
$$\frac{1}{30}$$ = $$\frac{x}{180}$$

H.O.T. Focus on Higher Order Thinking

Question 14.
Persevere in Problem-Solving A gas pump machine rejects 12% of credit card transactions. If this is twice the normal rejection rate for a normal gas pump, how many out of 500 credit card transactions would a normal gas pump machine reject?
Find 12% of 500.
Write 12% as a fraction. The percent equation will be
x = $$\frac{12}{100}$$ âˆ™ 500 Write fraction as decimal
= 0.12 âˆ™ 500 Multiply.
= 60
About 60 of 500 credit card transactions will, be rejected by a gas pump machine.
Since 60 is twice the normal rejection number for a normal gas pump, a normal gas pump machine wilt reject half of 60, hence, 30 credit card transactions.

Make Predictions An airline’s weekly flight data showed a 98% probability of being on time. If this airline has 15,000 flights in a year, how many flights would you predict to arrive on time? Explain whether you can use the data to predict whether a specific flight with this airline will be on time.
P (flight arrive on time) = $$\frac{98}{100}$$ = $$\frac{49}{50}$$
Use proportion.

In order to determine the probability of a particular flight, we need to know how many of the 15,000 flights arrived in time.

Question 16.
Draw Conclusions An average response rate for a marketing letter is 4%, meaning that 4% of the people who receive the letter respond to it. A company writes a new type of marketing letter, sends out 2,400 of them, and gets 65 responses. Explain whether the new type of letter would be considered to be a success.
Find 4% of 2400.
Write 4% as a fraction. The percent equation will be
x = $$\frac{4}{100}$$ âˆ™ 2400 Write fraction as decimal.
= 0.04 âˆ™ 2400 Multiply.
= 96
About 96 of 2400 letters get responses.
If a company sends out 2400 new types of marketing Letters and gets 65 responses, the new type of marketing letters arenâ€™t successful because the average number of letters with responses is 96, and 65 is way less than 96.

## Texas Go Math Grade 8 Lesson 1.1 Answer Key Rational and Irrational Numbers

Refer to ourÂ Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 1.1 Answer Key Rational and Irrational Numbers.

## Texas Go Math Grade 8 Lesson 1.1 Answer Key Rational and Irrational Numbers

Write each fraction as a decimal.

Question 1.
$$\frac{5}{11}$$__________
To write $$\frac{5}{11}$$ as a decimal, we divide the numerator by the denominator until the remainder is zero or until the digits in the quotient begin to repeat.
We add as many zeros after the decimal point in the dividend as needed

When a decimal has one or more digits that repeat indefinitely, we write the decimal with a bar over the repeating digit(s). In our case, 45 repeats indefinitely.
$$\frac{5}{11}$$ = $$0 . \overline{45}$$

Rational and Irrational Numbers Answer Key Question 2.
$$\frac{1}{8}$$ __________
To write $$\frac{1}{8}$$ as a decimal, we divide the numerator by the denominator until the remainder is zero or until the digits in the quotient begin to repeat.
We add as many zeros after the decimal point in the dividend as needed

$$\frac{1}{8}$$ = 0.125

Question 3.
2$$\frac{1}{3}$$ _______
First, we convert the mixed number to an improper fraction:
2$$\frac{1}{3}$$ = 2 + $$\frac{1}{3}$$
= $$\frac{6}{3}$$ + $$\frac{1}{3}$$
= $$\frac{7}{3}$$
To write $$\frac{7}{3}$$ as a decimal, we divide the numerator by the denominator until the remainder is zero or until the digits in the quotient begin to repeat.
We add as many zeros after the decimal point in the dividend as needed.

When a decimal has one or more digits that repeat indefinitely, we write the decimal with a bar over the repeating digit(s). In our case, 3 represents indefinitely.
2$$\frac{1}{3}$$ = $$2 . \overline{3}$$

Reflect

Question 4.
Analyze Relationships How are the two square roots of a positive number related? Which is the principal square root?
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb. The principal square root of b is the positive square root, denoted âˆšb

Question 5.
Is the principal square root of 2 a whole number? What types of numbers have whole number square roots?
Because âˆš2 is not an integer (2 is not a perfect square), âˆš2 must thereforeÂ be irrational. Numbers whose square roots are whole numbers, (or more accurately positive integers) are calledÂ perfect square numbers. Numbers with decimals aren’t perfect square roots.

Find the two square roots of each number.

Question 6.
64 ____
The given number is: 64
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
So,
$$\sqrt{64}$$ = Â±8
Hence, from the above,
We can conclude that
$$\sqrt{64}$$ = 8
$$\sqrt{64}$$ = -8

Question 7.
100 _________
The given number is: 100
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
So,
$$\sqrt{100}$$ = Â±10
Hence, from the above,
We can conclude that
$$\sqrt{100}$$ = 10
$$\sqrt{100}$$ = -10

Lesson 1.1 Define Rational Numbers Answer Key Question 8.
$$\frac{1}{9}$$ _________
The given number is: $$\frac{1}{9}$$
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
Now,
We know that,
$$\sqrt{\frac{a}{b}}$$ = $$\frac{\sqrt{a}}{\sqrt{b}}$$
So,
$$\sqrt{\frac{1}{9}}$$ = $$\frac{\sqrt{1}}{\sqrt{9}}$$
= Â±$$\frac{1}{3}$$
Hence, from the above,
We can conclude that
$$\sqrt{\frac{1}{9}}$$ = $$\frac{1}{3}$$
$$\sqrt{\frac{1}{9}}$$ = –$$\frac{1}{3}$$

Question 9.
A square garden has an area of 144 square feet. How long is each side?
It is given that
A square garden has an area of 144 square feet
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 144
$$\sqrt{SideÂ²}$$ = $$\sqrt{144}$$
Side = Â± 12
But,
We know that,
The side of a square will not be negative
So,
The side of a square field is: 12 feet
Hence, from the above,
We can conclude that
The side of a square field is: 12 feet

Explore Activity 1
Estimating Irrational Numbers
Irrational numbers are numbers that are not rational. in other words, they cannot be written in the form $$\frac{a}{b}$$ where a and b are integers and b is not 0.

Estimate the value of $$\sqrt{2}$$.

A. Since 2 is not a perfect square, $$\sqrt{2}$$ is irrational.
B. To estimate $$\sqrt{2}$$, first find two consecutive perfect squares that 2 is between. Complete the inequality by writing these perfect squares in the boxes.
1 < 2 < 9
C. Now take the square root of each number.
$$\sqrt{1}$$ < $$\sqrt{2}$$ < $$\sqrt{9}$$
D. Simplify the square roots of perfect squares.
$$\sqrt{2}$$ is between _____ and ___.
1 < $$\sqrt{2}$$ < 3
E. Estimate that $$\sqrt{2}$$ â‰ˆ 1.5.
F. To find a better estimate, first, choose some numbers between 1 and 2 and square them. For example, choose 1.3, 1.4, and 1.5.
1.32 = 1.69
1.42 = 1.96
1.52 = 2.25
Is $$\sqrt{2}$$ between 1.3 and 1.4? How do you know?
From the above,
We can observe that
The estimation of $$\sqrt{2}$$ is: 1.5
Now,
From part (f),
We can observe that
The squares of the numbers 1.3, 1.4, and 1.5
Hence, from the above,
We can observe that
$$\sqrt{2}$$ is not between 1.3 and 1.4

Is $$\sqrt{2}$$ between 1.4 and 1.5? How do you know?
From the above,
We can observe that
The estimation of $$\sqrt{2}$$ is: 1.5
Now,
From part (f),
We can observe that
The squares of the numbers 1.3, 1.4, and 1.5
Hence, from the above,
We can observe that
$$\sqrt{2}$$ is not between 1.4 and 1.5
So,
$$\sqrt{2}$$ is between 1.4 and 1.5.
So,
$$\sqrt{2}$$ â‰ˆ 1.5
G. Locate and label this value on the number line.

Reflect

Question 10.
How could you find an even better estimate of $$\sqrt{2}$$?
The given number is: $$\sqrt{2}$$
Now,
Find the perfect squares that is between $$\sqrt{2}$$
So,
1 < $$\sqrt{2}$$ < 3
We know that,
$$\sqrt{2}$$ â‰ˆ 1.414
So,
The value of $$\sqrt{2}$$ lies closer to: 1.4
Hence, from the above,
We can conclude that
The better estimate of $$\sqrt{2}$$ is: 1.4

Question 11.
Find a better estimate of $$\sqrt{2}$$. Draw a number line and locate and label your estimate.

$$\sqrt{2}$$ is between _____ and _____, so $$\sqrt{2}$$ â‰ˆ ___
The given number is: $$\sqrt{2}$$
Now,
Find the perfect squares that is between $$\sqrt{2}$$
So,
1 < $$\sqrt{2}$$ < 3
So,
The value of $$\sqrt{2}$$ lies between 1.4 and 1.5
Now,
We know that,
$$\sqrt{2}$$ â‰ˆ 1.414
So,
The value of $$\sqrt{2}$$ lies closer to: 1.4
Now,
The representation of the value of $$\sqrt{2}$$ on a number line is:

Hence, from the above,
We can conclude that
$$\sqrt{2}$$ is between 1.4 and 1.5,
So,
$$\sqrt{2}$$ â‰ˆ 1.5

Question 12.
Estimate the value of $$\sqrt{7}$$ to the nearest 0.05. Draw a number line and locate and label your estimate.

$$\sqrt{7}$$ is between and _____, so $$\sqrt{7}$$ â‰ˆ ___.
The given number is: $$\sqrt{7}$$
Now,
Find the perfect squares that lies between 7
So,
4 < 7 < 9
$$\sqrt{4}$$ < $$\sqrt{7}$$ < $$\sqrt{9}$$
2 < $$\sqrt{7}$$ < 3
Now,
2.1Â² = 4.41
2.5Â²= 6.25
2.6Â² = 6.76
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{7}$$ is approximately equal to: 6.76
Now,
The representation of $$\sqrt{7}$$ on a number line is:

Hence, from the above,
We can conclude that
$$\sqrt{7}$$ is between 2.5 and 2.6
So,
$$\sqrt{7}$$ â‰ˆ 2.6

Explore Activity 2
Approximating Ï€
The number Ï€, the ratio of the circumference of a circle to its diameter, is an irrational number. It cannot be written as the ratio of two integers.

In this activity, you will explore the relationship between the diameter and circumference of a circle.
A. Use a tape measure to measure the circumference and the diameter of four circular objects using metric measurements. To measure the circumference, wrap the tape measure tightly around the object and determine the mark where the tape starts to overlap the beginning of the tape. When measuring the diameter, be sure to measure the distance across the object at its widest point.
The examples of the four circular objects are:
a. CD
b. Bottle lid
c. Frisbee
d. Bowl

B. Record the circumference and diameter of each object in the table.

C. Divide the circumference by the diameter for each object. Round each answer to the nearest hundredth and record it in the table.

D. Describe what you notice about the ratio of circumference to diameter.
From part (b),
The complete table is:

Now,
From the above table,
We can observe that
The ratio of the circumference to diameter is approximately equal to 3
Hence, from the above,
We can conclude that
The point we noticed is that
The ratio of the circumference to diameter is approximately equal to 3

Reflect

Lesson 1.1 Rational Numbers as Decimals Answer Key Question 13.
What does the fact that Ï€ is irrational indicate about its decimal equivalent?
Ï€ is an irrational number because its decimal expansion is a “Non-Terminating Non-Recurring decimal”

Question 14.
Plot Ï€ on the number line.

We know that,
The value of Ï€ is: 3.14
Hence, from the above,
We can conclude that
The representation of Ï€ on the number line is:

Question 15.
Explain Why A CD and a DVD have the same diameter. Explain why they have the same circumference.
It is given that
A CD and a DVD have the same diameter
Now,
We know that,
The shapes of CD and DVDs are in circular shape
Now,
We know that,
The circumference of a circle (C) = Ï€d
Where,
d is the diameter
It is given that
The diameter is the same for both CD and DVD
So,
The circumference will also be the same since the value of Ï€ is constant
Hence, from the above,
We can conclude that
The CD and DVD have the same circumference since the values of diameter and Ï€ are constant

Question 1.
Vocabulary Square roots of numbers that are not perfect squares are ____________
We know that,
The square roots of numbers that are not perfect squares are called “Irrational Numbers”
Hence, from the above,
We can conclude that
The term that best suits the given statement is: irrational Numbers

Write each fraction as a decimal. (Example 1)

$$\frac{7}{8}$$ ____
The given fraction is: $$\frac{7}{8}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{7}{8}$$ as a decimal is: 0.87

Question 3.
$$\frac{17}{20}$$ ________
The given fraction is: $$\frac{17}{20}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{17}{20}$$ as a decimal is: 0.85

Question 4.
$$\frac{18}{25}$$ ________
The given fraction is: $$\frac{18}{25}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{18}{25}$$ as a decimal is: 0.72

Go Math Grade 8 Lesson 1.1 Question 5.
2$$\frac{3}{8}$$ ________
The given mixed number is: 2$$\frac{3}{8}$$
Now,
The representation of the given mixed number in the form of a fraction is: $$\frac{19}{8}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{19}{8}$$ as a decimal is: 0.42

Question 6.
5$$\frac{2}{3}$$ ________
The given mixed number is: 5$$\frac{2}{3}$$
Now,
The representation of the given mixed number in the form of a fraction is: $$\frac{17}{3}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{17}{3}$$ as a decimal is: 0.17

Question 7.
2$$\frac{4}{5}$$ ________
The given mixed number is: 2$$\frac{4}{5}$$
Now,
The representation of the given mixed number in the form of a fraction is: $$\frac{14}{5}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{14}{5}$$ as a decimal is: 0.35

Find the two square roots of each number. (Example 2)

Question 8.
49 ______________
The given number is: 49
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
So,
$$\sqrt{49}$$ = Â±7
Hence, from the above,
We can conclude that
$$\sqrt{49}$$ = 7
$$\sqrt{49}$$ = -7

Go Math Grade 8 Chapter 1 Lesson 1.1 Question 9.
144 _____________
The given number is: 144
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b.
It is a number that when multiplied by itself gives you b.
Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
So,
$$\sqrt{144}$$ = Â±12
Hence, from the above,
We can conclude that
$$\sqrt{144}$$ = 12
$$\sqrt{144}$$ = -12

Question 10.
400 _________
The given number is: 400
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
So,
$$\sqrt{400}$$ = Â±20
Hence, from the above,
We can conclude that
$$\sqrt{400}$$ = 20
$$\sqrt{400}$$ = -20

Question 11.
$$\frac{1}{16}$$ ________
The given number is: $$\frac{1}{16}$$
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
Now,
We know that,
$$\sqrt{\frac{a}{b}}$$ = $$\frac{\sqrt{a}}{\sqrt{b}}$$
So,
$$\sqrt{\frac{1}{16}}$$ = $$\frac{\sqrt{1}}{\sqrt{16}}$$
= Â±$$\frac{1}{4}$$
Hence, from the above,
We can conclude that
$$\sqrt{\frac{1}{16}}$$ = $$\frac{1}{4}$$
$$\sqrt{\frac{1}{16}}$$ = –$$\frac{1}{4}$$

$$\frac{4}{9}$$ ________
The given number is: $$\frac{4}{9}$$
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
Now,
We know that,
$$\sqrt{\frac{a}{b}}$$ = $$\frac{\sqrt{a}}{\sqrt{b}}$$
So,
$$\sqrt{\frac{4}{9}}$$ = $$\frac{\sqrt{4}}{\sqrt{9}}$$
= Â±$$\frac{2}{3}$$
Hence, from the above,
We can conclude that
$$\sqrt{\frac{4}{9}}$$ = $$\frac{2}{3}$$
$$\sqrt{\frac{4}{9}}$$ = –$$\frac{2}{3}$$

Question 13.
$$\frac{9}{4}$$ ________
The given number is: $$\frac{9}{4}$$
Now,
We know that,
A square root of a number b is the solution of the equation xÂ²=b. It is a number that when multiplied by itself gives you b. Every positive number b has two square roots, denoted âˆšb and âˆ’âˆšb
So,
âˆšx = Â±b
Now,
We know that,
$$\sqrt{\frac{a}{b}}$$ = $$\frac{\sqrt{a}}{\sqrt{b}}$$
So,
$$\sqrt{\frac{9}{4}}$$ = $$\frac{\sqrt{9}}{\sqrt{4}}$$
= Â±$$\frac{3}{2}$$
Hence, from the above,
We can conclude that
$$\sqrt{\frac{9}{4}}$$ = $$\frac{3}{2}$$
$$\sqrt{\frac{9}{4}}$$ = –$$\frac{3}{2}$$

Approximate each irrational number to the nearest 0.05 without using a calculator. (Explore Activity 1)

Question 14.
$$\sqrt{34}$$ ________
The given number is: $$\sqrt{34}$$
Now,
Find the perfect squares that lie between 34
So,
25 < 34 < 36
$$\sqrt{25}$$ < $$\sqrt{34}$$ < $$\sqrt{36}$$
5 < $$\sqrt{34}$$ < 6
Now,
5.5Â² = 30.25
5.9Â²= 34.81
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{34}$$ is approximately equal to: 5.9
Hence, from the above,
We can conclude that
$$\sqrt{34}$$ is between 5.8 and 5.9
So,
$$\sqrt{34}$$ â‰ˆ 5.9

Question 15.
$$\sqrt{82}$$ ________
The given number is: $$\sqrt{82}$$
Now,
Find the perfect squares that lie between 82
So,
81 < 82 < 100
$$\sqrt{81}$$ < $$\sqrt{82}$$ < $$\sqrt{100}$$
9 < $$\sqrt{82}$$ < 10
Now,
9.1Â² = 82.81
8.9Â²= 79.21
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{81}$$ is approximately equal to: 9.1
Hence, from the above,
We can conclude that
$$\sqrt{82}$$ is between 8.9 and 9.1
So,
$$\sqrt{82}$$ â‰ˆ 9.1

Question 16.
$$\sqrt{45}$$ ________
The given number is: $$\sqrt{45}$$
Now,
Find the perfect squares that lie between 45
So,
36 < 45 < 49
$$\sqrt{36}$$ < $$\sqrt{45}$$ < $$\sqrt{49}$$
6 < $$\sqrt{45}$$ < 7
Now,
6.5Â² = 42.25
6.7Â²= 44.89
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{45}$$ is approximately equal to: 6.7
Hence, from the above,
We can conclude that
$$\sqrt{45}$$ is between 6.7 and 6.8
So, $$\sqrt{45}$$ â‰ˆ 6.7

$$\sqrt{104}$$ ________
The given number is: $$\sqrt{104}$$
Now,
Find the perfect squares that lie between 104
So,
100 < 104 < 121
$$\sqrt{100}$$ < $$\sqrt{104}$$ < $$\sqrt{121}$$
10 < $$\sqrt{104}$$ < 11
Now,
10.5Â² = 110.25
10.1Â²= 102.01
10.2Â² = 104.04
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{104}$$ is approximately equal to: 10.2
Hence, from the above,
We can conclude that
$$\sqrt{104}$$ is between 10.1 and 10.2
So,
$$\sqrt{104}$$ â‰ˆ 10.2

Question 18.
–$$\sqrt{71}$$ ________
The given number is: –$$\sqrt{71}$$
Now,
Find the perfect squares that lie between 71
So,
64 < 71 < 81
$$\sqrt{64}$$ < $$\sqrt{71}$$ < $$\sqrt{81}$$
8 < $$\sqrt{71}$$ < 9
Now,
8.5Â² = 56.25
8.4Â²= 70.56
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{71}$$ is approximately equal to: 8.4
Hence, from the above,
We can conclude that
$$\sqrt{71}$$ is between 8.4 and 8.5
So,
–$$\sqrt{71}$$ â‰ˆ -8.4

Question 19.
–$$\sqrt{19}$$ ________
The given number is: $$\sqrt{19}$$
Now,
Find the perfect squares that lies between 19
So,
16 < 19 < 25
$$\sqrt{16}$$ < $$\sqrt{19}$$ < $$\sqrt{25}$$
4 < $$\sqrt{19}$$ < 5
Now,
4.5Â² = 20.25
4.3Â²= 18.49
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{19}$$ is approximately equal to: 4.3
Hence, from the above,
We can conclude that
$$\sqrt{19}$$ is between 4.3 and 4.4
So,
–$$\sqrt{19}$$ â‰ˆ -4.3

Divide Multi-Digit Numbers Lesson 1.1 Question 20.
Measurement Complete the table for the measurements to estimate the value of Ï€. Round to the nearest tenth. (Explore Activity 2)

Describe what you notice about the ratio of circumference to diameter.
The given table is:

Now,
We know that,
Circumference (C) = Ï€d
Where,
d is the diameter
So,
Ï€ = $$\frac{C}{d}$$
Now,
We know that,
The value of Ï€ is 3.141
Now,
The complete table is:

Now,
From the above table,
We can observe that
The values of Ï€ are approximately equal to 3
Hence, from the above,
We can conclude that
The approximate value of the ratio of the circumference to diameter is: 3

Essential Question Check-In

Question 21.
Describe how to approximate the value of an irrational number.
“Irrational numbers” cannot be written in the form $$\frac{a}{b}$$ as it is a non-terminating, non-repeating decimal. Students should know the perfect squares(1 to 15) in order to approximate the value of irrational numbers. Irrational numbers would include Ï€, as well as square roots of numbers that are no larger than 225.

Question 22.
A $$\frac{7}{16}$$-inchlong bolt is used in a machine. What is the length of the bolt written as a decimal?
It is given that
A $$\frac{7}{16}$$-inchlong bolt is used in a machine
Now,
The given fraction is: $$\frac{7}{16}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The length of the bolt in the form of a decimal is: 0.43

Question 23.
Astronomy The weight of an object on the moon is $$\frac{1}{6}$$ of its weight on Earth. Write $$\frac{1}{6}$$ as a decimal.
It is given that
The weight of an object on the moon is $$\frac{1}{6}$$ of its weight on Earth
Now,
The given fraction is: $$\frac{1}{6}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of $$\frac{1}{6}$$ in the form of a decimal is: 0.16

Lesson 1.1 Rational Numbers as Decimals Answer Key Question 24.
The distance to the nearest gas station is 2$$\frac{3}{4}$$ miles. What is this distance written as a decimal?
It is given that
The distance to the nearest gas station is 2$$\frac{3}{4}$$ miles
Now,
The given mixed number is: 2$$\frac{3}{4}$$
Now,
The representation of the given mixed number in the form of a fraction is: $$\frac{11}{4}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of the distance in the form of a decimal is: 2.75

Question 25.
A pitcher on a baseball team has pitched 98$$\frac{2}{3}$$ innings. What is the number of innings written as a decimal?
It is given that
A pitcher on a baseball team has pitched 98$$\frac{2}{3}$$ innings
Now,
The given mixed number is: 98$$\frac{2}{3}$$
Now,
The representation of the given mixed number in the form of a fraction is: $$\frac{296}{3}$$
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of the number of innings in the form of a decimal number is: 98.66

Question 26.
A Coast Guard ship patrols an area of 125 square miles. The area the ship patrols is a square. About how long is each side of the square? Round your answer to the nearest mile.
It is given that
A Coast Guard ship patrols an area of 125 square miles. The area the ship patrols is a square
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 125
Side = $$\sqrt{125}$$
Now,
We know that,
125 is not a perfect square
Now,
Find the perfect squares that lie between 125
So,
121 < 125 < 144
$$\sqrt{121}$$ < $$\sqrt{125}$$ < $$\sqrt{144}$$
11 < $$\sqrt{125}$$ < 12
Now,
11Â² = 121
12Â²= 144
Now,
From the above,
We can observe that
The Estimate of $$\sqrt{125}$$ is approximately equal to: 11
Hence, from the above,
We can conclude that
The length of each side of the square is about 11 miles

Question 27.
Each square on Oliviaâ€™s chessboard Is 11 square centimeters. A chessboard has 8 squares on each side. To the nearest tenth, what is the width of Oliviaâ€™s chessboard?
It is given that
Each square on Oliviaâ€™s chessboard Is 11 square centimeters. A chessboard has 8 squares on each side
Now,
The total area of the chessboard = 8 Ã— 11
= 88 square centimeters
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 88
Side = Â±$$\sqrt{88}$$
Now,
Find the squares that lie between 88
So,
81 < 88 < 100
So,
9 < $$\sqrt{88}$$ < 10
So,
The approximate value of $$\sqrt{88}$$ is: 9
Hence, from the above,
We can conclude that
The width of Olivia’s chessboard is about 9 centimeters

Go Math 8th Grade Lesson 1.1 Question 28.
The thickness of a surfboard relates to the weight of the surfer. A surfboard is 21$$\frac{3}{16}$$ inches wide and 2$$\frac{3}{8}$$ inches thick. Write each dimension as a decimal.
It is given that
The thickness of a surfboard relates to the weight of the surfer. A surfboard is 21$$\frac{3}{16}$$ inches wide and 2$$\frac{3}{8}$$ inches thick.
Now,
The given mixed numbers are: 21$$\frac{3}{16}$$ and 2$$\frac{3}{8}$$
Now,
The representation of the given mixed numbers in the form of fractions are: $$\frac{339}{16}$$ and $$\frac{19}{8}$$
Now,
The representation of the width of the surfboard in the form of a fraction is: $$\frac{339}{16}$$ inches
The representation of the thickness of the surfboard in the form of a fraction is: $$\frac{19}{8}$$ inches
Now,
By using the Long Division,

Hence, from the above,
We can conclude that
The representation of the width of the surfboard in the form of a decimal is: 21.18
The representation of the thickness of the surfboard in the form of a decimal is: 2.37

Question 29.
A gallon of stain can cover a square deck with an area of 300 square feet. About how long is each side of the deck? Round your answer to the nearest foot.

It is given that
A gallon of stain can cover a square deck with an area of 300 square feet
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 300
Side = Â±$$\sqrt{300}$$
Now,
Find the squares that lie between 300
So,
289 < 300 < 324
So,
17 < $$\sqrt{300}$$ < 18
So,
The approximate value of $$\sqrt{300}$$ is: 18
Hence, from the above,
We can conclude that
The length of each side of the deck is: 18 feet

Lesson 1.1 Rational Numbers as Decimals Question 30.
The area of a square field is 200 square feet. What is the approximate length of each side of the field? Round your answer to the nearest foot.
It is given that
The area of a square field is 200 square feet.
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 200
Side = $$\sqrt{200}$$
Now,
Find the squares that lie between 200
So,
196 < 200 < 225
So,
14 < $$\sqrt{200}$$ < 15
So,
The approximate value of $$\sqrt{200}$$ is: 14
Hence, from the above,
We can conclude that
The length of each side of the field is: 14 feet

Question 31.
Measurement A ruler is marked at every $$\frac{3}{16}$$ inches. Do the labeled measurements convert to terminating or repeating decimals?
It is given that
A ruler is marked at every $$\frac{3}{16}$$ inches.
Now,
By using the Long Division,

Now,
From the above Long Division,
We can observe that
The given fraction is a non-terminating decimal
Hence, from the above,
We can conclude that
$$\frac{3}{16}$$ is a non-terminating decimal

Question 32.
Multistep A couple wants to install a square mirror that has an area of 500 square inches. To the nearest tenth of an inch, what length of wood trim is needed to go around the mirror?
It is given that
A couple wants to install a square mirror that has an area of 500 square inches
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 500
Side = $$\sqrt{500}$$
Now,
Find the squares that lie between 500
So,
484 < 500 < 625
So,
24 < $$\sqrt{500}$$ < 25
So,
The approximate value of $$\sqrt{500}$$ is: 24
Hence, from the above,
We can conclude that
The length of wood trim that is needed to go around the mirror is: 24 inches

Rational and Irrational Numbers Grade 8 Question 33.
Multistep A square photo-display board is made up of 60 rows of 60 photos each. The area of each square photo is 4 square inches. How long is each side of the display board?

It is given that
A square photo-display board is made up of 60 rows of 60 photos each. The area of each square photo is 4 square inches
Now,
The number of photos in each row = (The number of rows) Ã· (The number of photos)
= $$\frac{60}{60}$$
= 1 photo per row
Now,
We know that,
The area of a square = SideÂ²
So,
SideÂ² = 60 Ã— 4
SideÂ² = 240
Side = $$\sqrt{240}$$
Now,
Find the squares that lie between 240
So,
225 < 240 < 256
So,
15 < $$\sqrt{240}$$ < 16
So,
The approximate value of $$\sqrt{500}$$ is: 16
Hence, from the above,
We can conclude that
The length of each side of the display board is: 16 inches

Approximate each irrational number to the nearest 0.05 without using a calculator. Then plot each number on a number line.

Question 34.

The given number is: $$\sqrt{24}$$
Now,
Find the perfect squares that is between $$\sqrt{24}$$
So,
4 < $$\sqrt{24}$$ < 5
So,
The value of $$\sqrt{24}$$ lies between 4 and 5
Now,
We know that,
$$\sqrt{24}$$ â‰ˆ 5
So,
The value of $$\sqrt{24}$$ lies closer to: 5
Now,
The representation of the value of $$\sqrt{24}$$ on a number line is:

Hence, from the above,
We can conclude that
$$\sqrt{24}$$ is between 4 and 5
So,
$$\sqrt{24}$$ â‰ˆ 5

The given number is: $$\sqrt{41}$$
Now,
Find the perfect squares that is between $$\sqrt{41}$$
So,
6 < $$\sqrt{41}$$ < 7
So,
The value of $$\sqrt{41}$$ lies between 6 and 7
Now,
We know that,
$$\sqrt{41}$$ â‰ˆ 6
So,
The value of $$\sqrt{41}$$ lies closer to: 6
Now,
The representation of the value of $$\sqrt{41}$$ on a number line is:

Hence, from the above,
We can conclude that
$$\sqrt{41}$$ is between 6 and 7
So,
$$\sqrt{41}$$ â‰ˆ 6

Question 36.
Represent Real-World Problems If every positive number has two square roots and you can find the length of the side of a square window by finding a square root of the area, why is there only one answer for the length of a side?
We know that,
The two square roots of a positive number are:
a) one positive square root
b) one negative square root.
Now,
As long as you’re doing math, on paper, you can work with both of them. But as soon as you start talking about windows or other physical things, it’s pretty silly to talk about a negative length.Â  When you’re working with real physical things, you usually just ignore the negative square root.
Hence,
There is only one answer for the length of the side

Question 37.
Make a Prediction To find $$\sqrt{5}$$, Beau found 22 = 4 and 32 = 9. He said that since 5 is between 4 and 9, $$\sqrt{5}$$ is between 2 and 3. Beau thinks a good estimate for is $$\sqrt{5}$$ is $$\frac{2+3}{2}$$ = 2.5. Is his estimate high or low? How do you know?
It is given that
To find $$\sqrt{5}$$, Beau found 22 = 4 and 32 = 9. He said that since 5 is between 4 and 9, $$\sqrt{5}$$ is between 2 and 3. Beau thinks a good estimate for is $$\sqrt{5}$$ is $$\frac{2+3}{2}$$ = 2.5
Now,
From the above,
We can observe that
5 is very close to 4
So,
The estimate of $$\sqrt{5}$$ is also close to 2 but not to 3
So,
The estimate of $$\sqrt{5}$$ should be less than 2.5 and greater than 2. i.e.,
2 < Estimate < 2.5
Hence, from the above,
We can conclude that
The Estimate of Beau is high

Texas Go Math Grade 8 Lesson 1.1 H.O.T. Focus On Higher Order Thinking Answer KeyÂ

Question 38.
Multistep On a baseball field, the infield area created by the baselines is a square. In a youth baseball league, this area is 3600 square feet. A pony league of younger children uses a smaller baseball field with a distance between each base that is 20 feet less than the youth league. What is the distance between each base for the pony league?
It is given that
On a baseball field, the infield area created by the baselines is a square. In a youth baseball league, this area is 3600 square feet. A pony league of younger children uses a smaller baseball field with a distance between each base that is 20 feet less than the youth league
Now,
We know that,
The area of a square = SideÂ²
So,
The length of each side in a youth baseball league’s field is:
SideÂ² = 3600
Side = $$\sqrt{3600}$$
Side = 60 feet
Now,
The length of each side in a smaller baseball field = 60 – 20
= 40 feet
Hence, from the above,
We can conclude that
The distance between each base for the pony league is: 40 feet

Question 39.
Problem Solving The difference between the square roots of a number is 30. What is the number? Show that your answer is correct.
It is given that
The difference between the square roots of a number is 30
Now,
Let the square root of a number be: x
Now,
We know that,
The square root of a number has 2 numbers. i.e., 1 positive number and 1 negative number
So,
According to the above information,
x – (-x) = 30
x + x = 30
2x = 30
x = $$\frac{30}{2}$$
x = 15
So,
The required number = xÂ²
= 15Â²
= 225
Hence, from the above,
We can conclude that
The required number is: 225

Lesson 1.1 Write Rational Numbers in Equivalent Forms Answer Key Question 40.
Analyze Relationships If the ratio of the circumference of a circle to its diameter is Ï€, what is the relationship of the circumference to the radius of the circle? Explain.
It is given that
The ratio of the circumference of a circle to its diameter is Ï€
Now,
According to the given information,
$$\frac{Circumference}{Diameter}$$ = Ï€
Now,
We know that,
So,
$$\frac{Circumference}{2 Ã— Radius}$$ = Ï€
$$\frac{Circumference}{Radius}$$ = 2Ï€
Hence, from the above,
We can conclude that
The relationship of the circumference to the radius of the circle is: 2Ï€

Refer to our Texas Go Math Grade 5 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 5 Lesson 8.2 Answer Key Addition and Subtraction Equations.

Unlock the Problem

Yara is going camping in the Everglades National Park. Her backpack with camping gear weighs 17 pounds. When she adds her camera gear, the total weight of her backpack is 25 pounds. How much does Yara’s camera gear weigh?
â€¢ What does the backpack weigh without the camera gear?
________________
â€¢ What do you need to find?
_________________
The backpack weigh without the camera gear is 17 pounds.
We need to find out the camera gear weigh.

Write a related equation.
The problem describes a part-part-whole relationship. A strip diagram can help you understand this relationship and write an equation. Let c represent the weight (in pounds) of the camera gear.

STEP 1: Use the strip diagram to write an equation

STEP 2: Write a subtraction equation that is related to the addition equation.
Equation: _______________
Subtract: c = _______________
So, Yaraâ€™s camera gear weighs _______________ pounds.
Equation: 17 + c = 25
Subtract: c = 25 – 17 = 8
So, Yaraâ€™s camera gear weighs 8 pounds.

What if Yara’s backpack with camping gear weighs 15 pounds and the camera gear weighs 6 pounds? How much does her backpack with camping gear and camera gear weigh? How would the strip diagram above change?

15 pounds + 6 pounds = 21 pounds
Yara’s backpack with camping gear and camera gear weigh is 21 pounds.
Explanation:
Yara’s backpack with camping gear weighs 15 pounds and the camera gear weighs 6 pounds. Add 15 pounds with 6 pounds the sum is 21 pounds. Yara’s backpack with camping gear and camera gear weigh is 21 pounds.

Math Talk
Mathematical Processes

Explain how you can tell that your solution to an equation is true.

Example

Use a related equation.
Kent has a collection of CDs. He gives 5 CDs to his brother. He then has 8 CDs left in his collection. How many CDs did Kent have before he gave some to his brother?
â€¢ How many CDs did Kent give away?
_________________
â€¢ What operation will you use to show the CDs that Kent gave away?
___________________
Kent gave 5 CDs to his brother.
I will use subtraction operation to show the CDs that Kent gave away.

STEP 1: Draw a strip diagram.
â€¢ Write the missing labels in the strip diagram, where c is the number of CDs in Kent’s collection before he gave some away.
â€¢ Use the model to write the equation.

STEP 2: Use the strip diagram to write a related addition equation. Then add to solve.
Equation: _______________
So, Kent had _______________ CDs before he gave some away.

Equation: c – 5 = 8
Add: c = 8 + 5 = 13
So, Kent had 13 CDs before he gave some away.
Explanation:
Kent has a collection of CDs. He gives 5 CDs to his brother. He then has 8 CDs left in his collection. First write the equation c – 5 = 8. Where c is the number of CDs in Kent’s collection before he gave some away. By using above strip diagram we can write the related addition equation. The addition equation is c = 8 + 5. Add 8 with 5 the sum is 13. So, Kent had 13 CDs before he gave some away.

Share and Show

Use the strip diagram to write an equation. Then solve.

Question 1.
Janine went to the beach 22 times during July and August. Six of those times were in August. how many times did she go in July?

Equation: ____________ ________ = d

Equation:
6 + d = 22
d = 22 – 6
d = 16
Janine went to the beach 16 times in July.
Explanation:
Janine went to the beach 22 times during July and August. Six of those times were in August. The equation is
6 + d = 22. Perform a subtraction operation to find the d value. Subtract 6 from 22 the difference is 16. Janine went to the beach 16 times in July.

Go Math Lesson 8.2 5th Grade Question 2.
Ariana has some crayons and her friend has 7 fewer crayons. If her friend has 15 crayons, how many crayons, c, does Ariana have?

Equation: _____________ c = _________

Equation:
c – 7 = 15
c = 15 + 7
c = 22
Ariana have 22 crayons.
Explanation:
Ariana has some crayons and her friend has 7 fewer crayons. Which means Ariana have more crayons than her friend. If her friend has 15 crayons then we have to calculate the Ariana crayons. The equation is c – 7 = 15. Perform addition operation to calculate the c value. Add 15 with 7 the sum is 22. So, Ariana have 22 crayons.

Question 3.
Explain how a strip diagram helps you understand the problem and write an equation.
In the above problem strip diagram is used to understand the problem and helped to writ the equation. First Ariana friend have 15 crayons. Ariana has some crayons and her friend has 7 fewer crayons. Which means 7 crayons are less than Ariana. So the equation is c – 7 = 15. Where c is Ariana’s crayons. Add 15 with 7 the sum is 22. So, Ariana have 22 crayons.

Problem Solving.

Use the bar graph to solve 4-6. Draw a strip diagram to write each equation. Then solve.

Question 4.
H.O.T. Multi-Step Taking a shower uses about 13 fewer gallons of water than taking a bath. About how many gallons of water are used for taking a bath?
In your equation, let b represent the number of gallons of water needed for a bath.

H.O.T. Multi-Step Stephan did some chores before heading to practice. He washed the dishes and washed a load of laundry. He used about 44 gallons of water in all. How many gallons of water did he use to wash a load of laundry?

Question 6.
H.O.T. Multi-Step You use 2 fewer gallons of water to brush your teeth than to wash your hands. How much water do you use to wash your hands?
In your equation, let h represent the number of gallons of water used to wash your hands.

Question 7.
Apply Wes had some money in his wallet and $39 in his pocket. He had$76 in all. He could represent his money by using the equation 39 + m = 76. How much did Wes have in his wallet?
$39 + m =$76
m = $76 –$39
m = $37 Wes have$37 in his wallet.
Explanation:
Wes had some money in his wallet and $39 in his pocket. He had$76 in all. He represented his money by using the equation 39 + m = 76. Perform subtraction operation. Subtract 39 from 76 the difference is $37. Wes have$37 in his wallet.

Question 8.
Stan spent $18 on giant carrots at the Giant Vegetable Store. He also bought a bag of giant peas, but the bag had no price tag. Stan was charged a total of$23. Which equation can help you find the cost of the peas?
(A) 18 + 23 = p
(B) 18 – 23 = p
(C) 18 + p = 23
(D) 23 + p = 18

The equation 18 + p = 23 is used to find the cost of the peas.
So, option C is correct.
Explanation:
Stan spent $18 on giant carrots at the Giant Vegetable Store. He also bought a bag of giant peas, but the bag had no price tag. Stan was charged a total of$23. So, the equation 18 + p = 23 is used to find the cost of the peas.
So, option C is correct.

Question 9.
Representations Morgan has 28 pieces of jewelry, 10 of which are necklaces. The rest of the jewelry pieces are bracelets. Which equation can you use to find the number of bracelets, b, she has?
(A) b = 10 – 28
(B) b = 28 – 10
(C) 28 = b – 10
(D) 10 = b + 28

The equation is 10 + b = 28
The equation b = 28 – 10 is used to find the number of bracelets.
Morgan has 18 bracelets. So, option B is correct.
Explanation:
Morgan has 28 pieces of jewelry, 10 of which are necklaces. The rest of the jewelry pieces are bracelets. The equation b = 28 – 10 is used to find the number of bracelets. Morgan has 18 bracelets. So, option B is correct.

Multi-Step Joseph bought 5 folders for school that cost $3 each. He also bought a new backpack. If the total cost was$35, how much did the backpack cost?
(A) $5 (B)$15
(C) $20 (D)$50

5 x $3 =$15
The folders cost is $15.$15 + b = $35 b =$35 – $15 b =$20
The backpack cost is $20. So, option C is correct. Explanation: Joseph bought 5 folders for school that cost$3 each. He also bought a new backpack. The total cost was $35. First we have to calculate the folders cost. Multiply 5 folders with$3 the product is $15. The equation to calculate the new backpack cost is$15 + b = $35. Subtract$15 from $35 the difference is$20. The backpack cost is $20. So, option C is correct. Texas Test Prep Question 11. A football team scored 16 points, which was 12 fewer points than their opponents scored. How many points, y, did their opponents score? (A) y = 24 (B) y = 28 (C) y = 4 (D) y = 18 Answer: y – 16 = 12 y = 12 + 16 y = 28 Their opponents scored 28 points. SO, option B is correct. Explanation: A football team scored 16 points, which was 12 fewer points than their opponents scored. The equation y – 16 = 12 is used to calculate the opponents score. Perform addition operation. Add 12 with 16 the sum is 28. Their opponents scored 28 points. SO, option B is correct. ### Texas Go Math Grade 5 Lesson 8.2 Homework and Practice Answer Key Use the strip diagram to write an equation. Then solve. Question 1. Kiki had 17 mystery books. She got some more mystery books as a gift. Now she has a total of 21 mystery books. How many books did Kiki receive as a gift? Equation: _____________ _______ = p Answer: Equation: 17 + p = 21 p = 21 – 17 p = 4 Kiki receive 4 books as a gift. Explanation: Kiki had 17 mystery books. She got some more mystery books as a gift. Now she has a total of 21 mystery books. The equation is 17 + p = 21. Perform subtraction operation to calculate the p value. Subtract 17 books from 21 books the difference is 4 books. Kiki receive 4 books as a gift. Go Math 5th Grade Lesson 8.2 Write Equations Answer Key Question 2. Joe scored 45 points. He scored 12 fewer points than Randy. How points did Randy score? Equation: _____________ s = _____________ Answer: Equation: s – 12 = 45 s = 45 + 12 s = 57 Randy scored 57 points. Explanation: Joe scored 45 points. He scored 12 fewer points than Randy. The equation is s – 12 = 45. To calculate the s value we need to perform addition operation. Add 45with 12 the sum is 57. So, Randy scored 57 points. Question 3. The pet store had some goldfish. Eight goldfish were sold. There are 28 goldfish left. How many goldfish did the pet store have before some were sold? Equation: ______________ f = ___________ Answer: 8 + 28 = f 36 = f The pet store have 36 goldfish before some were sold. Explanation: The pet store had some goldfish. Eight goldfish were sold. There are 28 goldfish left. The equation is 8 + 28 = f. To calculate the f value we need to perform addition operation. Add 8 gold fish with 28 goldfish the sum is 36 goldfish. The pet store have 36 goldfish before some were sold. Question 4. Joaquin and Erik worked together on a project. Erik worked 13 hours. Together, they worked 22 hours. How many hours did Joaquin work? Equation: ____________ _______ = h Answer: Equation: 13 + h = 22 h = 22 – 13 h = 9 Joaquin worked 9 hours. Explanation: Joaquin and Erik worked together on a project. Erik worked 13 hours. Together, they worked 22 hours. The equation is 13 + h = 22. Perform subtraction operation to calculate the h value. Subtract 13 hours from 22 hours the difference is 9 hours. Joaquin worked 9 hours. Problem Solving Question 5. Nina arranges a bouquet of flowers for herself and for her mother. She uses 9 more daisies in her bouquet than in her mother’s bouquet. Her mother’s bouquet has 15 daisies. She represents the number of daisies in her bouquet by using the equation d – 9 = 15. How many daisies does Ninaâ€™s bouquet have? Answer: Equation: d – 9 = 15 d = 15 + 9 d = 24 Nina’s bouquet have 24 daisies. Explanation: Nina arranges a bouquet of flowers for herself and for her mother. She uses 9 more daisies in her bouquet than in her mother’s bouquet. Her mother’s bouquet has 15 daisies. She represents the number of daisies in her bouquet by using the equation d – 9 = 15. To calculate the d value we have to perform addition operation. Add 15 with 9 the sum is 24. Nina’s bouquet have 24 daisies. Question 6. Kierra has 49 pennies in a drawer and some pennies in a jar. She has 81 pennies in all. She represents the number of pennies by using the equation 49 + j = 81. How many pennies does Kierra have in the jar? Answer: Equation: 49 + j = 81 j = 81 – 49 j = 32 Kierra have 32 pennies in the jar. Explanation: Kierra has 49 pennies in a drawer and some pennies in a jar. She has 81 pennies in all. She represents the number of pennies by using the equation 49 + j = 81. Perform subtraction operation to calculate the j value. Subtract 49 from 81 the difference is 32. Kierra have 32 pennies in the jar. Lesson Check Fill in the bubble completely to show your answer. Question 7. Last weekend, Ryan earned$27 babysitting. He earned $19 on Friday and the rest of the money on Saturday. Which equation can you use to find the amount, m, Ryan earned on Saturday? (A) m =$27 + $19 (B)$19 = m + $27 (C)$27 = m – $19 (D) m =$27 – $19 Answer: Equation:$19 + m = $27 m =$27 – $19 m =$8
Ryan earned $8 on Saturday. So, option D is correct. Explanation: Last weekend, Ryan earned$27 babysitting. He earned $19 on Friday and the rest of the money on Saturday. The equation is m =$27 – $19. To calculate the m value we need to perform subtraction operation. Subtract$19 from $27 the difference is$8. Ryan earned $8 on Saturday. So, option D is correct. Question 8. Fatima used a coupon to pay for a pair of jeans. The original price of the jeans was$25. The coupon reduced the price to $16. Which equation can you use to help you find the value of the coupon? (A)$16 + c = $25 (B)$25 + $16 = c (C)$25 + c = $16 (D)$16 – c = $25 Answer: The equation$25 + $16 = c is used to find the value of the coupon. So, option B is correct. Explanation: Fatima used a coupon to pay for a pair of jeans. The original price of the jeans was$25. The coupon reduced the price to $16. The equation$25 + $16 = c is used to find the value of the coupon. So, option B is correct. Question 9. Hailey received 33 text messages on Saturday, which were 18 fewer messages than she received on Sunday. How many text messages, t, did Hailey receive on Sunday? (A) t = 15 (B) t = 25 (C) t = 51 (D) t = 41 Answer: t – 18 = 33 t = 33 + 18 t = 51 Hailey received 51 text messages on Sunday. So, option C is correct. Explanation: Hailey received 33 text messages on Saturday, which was 18 fewer messages than she received on Sunday. The equation is t – 18 = 23. To calculate the t value we have to perform an addition operation. Add 33 with 18 the sum is 51. Hailey received 51 text messages on Sunday. So, option C is correct. Go Math Lesson 8.2 5th Grade Answer Key Question 10. At the second bus stop, 26 people got off the bus, which was 9 more than the number of people that got off at the first bus stop. How many people, p, got off the bus at the first stop? (A) P = 17 (B) p = 35 (C) P = 23 (D) p = 15 Answer: p + 9 = 26 p = 26 – 9 p = 17 At the first bus stop 17 people got off the bus. So, option A is correct. Explanation: At the second bus stop, 26 people got off the bus, which was 9 more than the number of people that got off at the first bus stop. The equation is p + 9 = 26. To calculate the p value we have to perform a subtraction operation. Subtract 9 people from 26 people the difference is 17 people. At the first bus stop, 17 people got off the bus. So, option A is correct. Question 11. Multi-Step There were 14 dogs adopted from the animal shelter last week. This week, 8 dogs were adopted. There are 5 dogs left. How many dogs, d, did the shelter have for adoption? (A) d = 27 (B) d = 22 (C) d = 13 (D) d = 17 Answer: 14 + 8 = 22 22 – 5 = 17 17 dogs have the shelter for adoption. So, option D is correct. Explanation: There were 14 dogs adopted from the animal shelter last week. This week, 8 dogs were adopted. Add 14 dogs with 8 dogs the sum is 22 dogs. There are 5 dogs left. Subtract 5 dogs from 22 dogs the difference is 17 dogs. 17 dogs have the shelter for adoption. So, option D is correct. Question 12. Multi-Step Lorenzo spent$47 at the shoe store. He bought 3 pairs of socks that cost $6 per pair. He also bought a pair of shoes. He paid$4 in sales tax. How much did Lorenzoâ€™s
shoes, s, cost?
(A) s = $25 (B) s =$22
(C) s = $34 (D) s =$29

He bought 3 pairs of socks that cost $6 per pair. 3 x$6 = $18 He paid$4 in sales tax.
$18 +$4 = $22 Lorenzo spent$47 at the shoe store.
$47 –$22 = $25 Lorenzo’s shoes cost is$25.
So, option A is correct.
Explanation:
Lorenzo spent $47 at the shoe store. He bought 3 pairs of socks that cost$6 per pair. Multiply 3 with $6the product is$18. The 3 pairs of socks cost is $18. He also bought a pair of shoes. He paid$4 in sales tax. Add $18 with$4 the sum is $22. Subtract$22 from $47 the difference is$25. Lorenzo’s shoes cost is \$25. So, option A is correct.

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Module 9 Assessment Answer Key.

Vocabulary

Choose the best term from the box.

Question 1.
When you multiply the tens and the ones separately and then add the products, you are finding ___. (p. 293)
Partial products
Explanation:
The partial product method involvesÂ multiplying each digit of a number in turn with each digit of another where each digit maintains its place.

Concepts and Skills

Use place value to find the product. TEKS 3.4.G

Question 2.
4 Ã— 80 = 4 Ã— __ tens
= __ tens = ____
8 tens = 32 tens = 320
Explanation:
4 Ã— 80 = 4 Ã— 8 tens
= 32 tens = 320

Question 3.
7 Ã— 70 = 7 Ã— __ tens
= ___ tens = ___
7 tens = 49 tens = 490
Explanation:
7 Ã— 70 = 7 Ã— 7 tens
= 49 tens = 490

Find the product. Use models or strategies to help. TEKS 3.4.F, 3.4.G

Fill in the bubble for the correct answer choice.

Question 4.
6 Ã— 40 = ___
Explanation:
6 x 4 tens = 24 tens = 240

Question 5.
7 Ã— 60 = ___
Explanation:
7 x 6 tens = 42 tens = 420

Question 6.
3 Ã— 54 = ___
Explanation:
The product of 3 x 54 = 162

Question 7.
__ = 8 Ã— 37
Explanation:
The product of
8 x 37 = 296

Question 8.

Explanation:
The product of
30 and 6Â  is 180

Question 9.
4 Ã— 20 Ã— 2
Explanation:
The product of
4 x 20 x 2 = 160

Question 10.

Explanation:
The product of
18 and 5 is 90

Explanation:
The product of
28 and 9 is 252

Question 12.

Explanation:
The product of
47 and 4 is188

Question 13.

Explanation:
The product of
79 andÂ  0 is 0

Question 14.

Explanation:
The product of
83 and 9 are 747

Question 15.

Explanation:
The product of
66 and 3 is 198

Texas Test Prep

Fill in the bubble for the correct answer choice.

Question 16.
In Blake’s school, there are 6 third-grade classrooms with 23 students and 1 teacher in each class. How many
third-grade students and teachers are there? TEKS 3.4.G
(A) 138
(B) 144
(C) 30
(D) 124
Explanation:
In Blake’s school, there are 6 third-grade classrooms with 23 students
6 x 23 = 138
and 1 teacher in each class.
138 + 6 = 144

Question 17.
Which equation is an example of the Distributive Property of Multiplication? TEKS 3.4.G
(A) 8 Ã— 20 = 8 Ã— (10 + 10)
(B) 8 Ã— 20 = 20 Ã— 8
(C) 20 Ã— 0 = 0
(D) (8 Ã— 3) Ã— 2 = 8 Ã— (3 Ã— 2)
Explanation:
8 Ã— 20 = 8 Ã— (10 + 10)Â  is an example of the Distributive Property of Multiplication

Question 18.
Alli put 10 pages of 2 CDs in each of 4 albums. How many CDs did she put in the albums? TEKS 3.4.G
(A) 16
(B) 80
(C) 40
(D) 20
Explanation:
Alli put 10 pages of 2 CDs
2 x 10 = 20
in each of 4 albums.
20 x 4 = 80 CD’sÂ  she put in the albums.

Question 19.
Use the number line to find 4 Ã— 20. What is the product? TEKS 3.4.G
Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.