Go through the enVision Math Common Core Grade 5 Answer Key Topic 3 Fluently Multiply Multi-Digit Whole Numbers regularly and improve your accuracy in solving questions.

## enVision Math Common Core 5th Grade Answers Key Topic 3 Fluently Multiply Multi-Digit Whole Numbers

Essential Question: What are the standard procedures for estimating and finding products of multi-digit numbers?

enVision STEM Project: Water Usage
Do Research Use the Internet or other sources to find how much water is used for household activities like taking a shower or bath, using a dishwasher, hand washing dishes, and using a washing machine.
Journal: Write a Report Include what you found. Also in your report:

• Choose 3 of the activities. Estimate how many times each activity is done each week in your household.
• Estimate the weekly water usage for each activity. Organize your results in a table.
• Make up and solve multiplication problems based on your data.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.
• multiple
• equation
• exponent
• power
• factor
• product

Question 1.
The answer to a multiplication problem is the ____.

The answer to a multiplication problem is the product.

Explanation:
In the above-given question,
given that,
the answer to a multiplication problem is called the product.
for example:
15 x 2 = 30.
15 is called multiplicand.
2 is the multiplier.
30 is the product.
So the answer to a multiplication problem is called the product.

Question 2.
A number sentence that shows two expressions with the same value is a(n) _____

A number sentence that shows two expressions with the same value is an equation.

Explanation:
In the above-given question,
given that,
A number sentence that shows two expressions with the same value is an equation.
for example:
4 + 8 = 12.
5 + 6 = 12.
so the number sentence that shows two expressions with the same value is an equation.

Queen 3.
A(n) ___ tells the number of times the base is used as a(n) ___.

A(n) tells the number of times the base is used as an exponent.

Explanation:
In the above-given question,
given that,
A(n) ___ tells the number of times the base is used as a(n).
for example:
5².
where 2 is the exponent.
5 is base.

Question 4.
50 is a(n) ____ of 10 because 5 × 10 = 50.

50 is a(n) base of 10 because 5 x 10 = 50.

Explanation:
In the above-given question,
given that,
50 is a(n) base of 10 because 5 x 10 = 50.
for example:
5 x a (n) = 10.
a(n) = 10 x 5.
a(n) = 50.

Operations

Find each sum or difference.

Question 5.
9,007 + 3,128

9007 + 3128 = 12,135.

Explanation:
In the above-given question,
given that,
the two numbers are 9007 and 3128.
add the two numbers.
9007 + 3128 = 12,135.

Question 6.
7,904 – 3,199

7904 – 3199 = 4705.

Explanation:
In the above-given question,
given that,
the two numbers are 7904 and 3199.
subtract the two numbers.
7904 – 3199 = 4705.

Question 7.
27,924 – 13,868

27924 – 13,868 = 14,056.

Explanation:
In the above-given question,
given that,
the two numbers are 27924 and 13868.
subtract the two numbers.
27924 – 13868 =14,056.

Question 8.
9.27 + 3.128

9.27 + 3.128 = 12.398.

Explanation:
In the above-given question,
given that,
the two numbers are 9.27 and 3.128.
add the two numbers.
9.27 + 3.128 = 12.398.

Question 9.
119.04 – 86.5

119.04 – 86.5 = 32.54.

Explanation:
In the above-given question,
given that,
the two numbers are 119.04 and 86.5.
subtract the two numbers.
119.04 – 86.5 = 32.54.

Question 10.
165.2 – 133.18

165.2 – 133.18 = 32.02.

Explanation:
In the above-given question,
given that,
the two numbers are 165.2 and 133.18.
subtract the two numbers.
165.2 – 133.18 = 32.02.

Round Whole Numbers and Decimals

Round each number to the place of the underlined digit.

Question 11.
14.3

14.3.

Explanation:
In the above-given question,
given that,
the number is 14.3.
the underlined digit is 4.
if the tenths place is greater than 5.
then add by 1.
if tenths place is less than 5.
then write the same number as zeros.
so the answer is 14.3.

Question 12.
385.7

395.7.

Explanation:
In the above-given question,
given that,
the number is 385.7.
the underlined digit is 8.
if the tenths place is greater than 5.
then add by 1.
if tenths place is less than 5.
then write the same number as zeros.
so the answer is 395.7.

Question 13.
0.545

0.500.

Explanation:
In the above-given question,
given that,
the number is 0.545.
the underlined digit is 5.
if the tenths place is greater than 5.
then add by 1.
if tenths place is less than 5.
then write the same number as zeros.
so the answer is 0.500.

Question 14.
496.533

497.533.

Explanation:
In the above-given question,
given that,
the number is 496.533.
the underlined digit is 6.
if the tenths place is greater than 5.
then add by 1.
if tenths place is less than 5.
then write the same number as zeros.
so the answer is 496.533.

Question 15.
496.353

496.000.

Explanation:
In the above-given question,
given that,
the number is 496.353.
the underlined digit is 6.
if the tenths place is greater than 5.
then add by 1.
if tenths place is less than 5.
then write the same number as zeros.
so the answer is 496.000.

Question 16.
1,857.205

1857.215.

Explanation:
In the above-given question,
given that,
the number is 1857.205.
the underlined digit is 0.
if the tenths place is greater than 5.
then add by 1.
if tenths place is less than 5.
then write the same number as zeros.
so the answer is 1857.205.

Compare Decimals

Question 17.
Write the numbers in order from least to greatest. 8.062 8.26 8.026 8.6

The numbers in order from least to greatest is 8.026, 8.062, 8.26, and 8.6.

Explanation:
In the above-given question,
given that,
the numbers are 8.062, 8.26, 8.026, and 8.6.
the numbers in order from least to greatest is
8.026, 8.062, 8.26, and 8.6.

Question 18.
Write the numbers in order from greatest to least. 0.115 0.15 0.005 0.5

The numbers in order from greatest to least are 0.005, 0.115, 0.15, and 0.5.

Explanation:
In the above-given question,
given that,
the numbers are 0.115, 0.15, 0.005, and 0.5.
the numbers in order from greatest to least are
0.115, 0.15, 0.005, and 0.5.

pick a Project

PROJECT ЗА
What puts the bounce in a bouncy ball?
Project: Make a Business Plan

PROJECT 3B
How can you build a fort?
Project: Build a Model Fort

PROJECT 3C
How many people can a ferry carry?
Project: Design a Prototype Ferry

3-ACT MATH PREVIEW

Math Modeling

Morning Commute

Before watching the video, think:
Train conductors don’t wear this kind of hat anymore. Even paper tickets are less common now that some train lines use an app to purchase tickets. What are some other ways we have updated transportation as part of our modern society? All aboard!

### Lesson 3.1 Multiply Greater Numbers by Powers of 10

Activity

At Izzy’s Party Store, party invitations come in packages of 8. How many invitations are in 10 packages? 100 packages? 1,000 packages? Solve this problem any way you choose.

The number of invitations is in 10 packages = 80.
the number of invitations is in 100 packages = 800.
the number of invitations is in 1000 packages = 8000.

Explanation:
In the above-given question,
given that,
At Izzy’s Party Store, party invitations come in packages of 8.
8 x 10 = 80.
8 x 100 = 800.
8 x 1000 = 8000.
so the number of invitations is in 10 packages = 80.
the number of invitations is in 100 packages = 800.
the number of invitations is in 1000 packages = 8000.

You can use appropriate tools. Place-value blocks are useful for picturing problems that involve powers of 10.

Look Back! What patterns do you notice in your work above?

Visual Learning Bridge

Essential Question
How Can You Use Patterns and Mental Math to Question Multiply a Whole Number by a Power of 10?

A.
The value of each place in a number is 10 times the value of the place to the right. The place-value chart shows this relationship for the number 4. Look for patterns.

10 times greater than 4
10 times greater than 40
10 times greater than 400
10 times greater than 4,000
10 times greater than 40,000

B.
Find 32 × 10,000 by using place-value relationships.
Multiply 32 by 1; 10; 100; 1,000; and 10,000.
32 × 1 = 32 ones = 32
32 × 10 = 32 tens = 320
32 × 100 = 32 hundreds = 3,200
32 × 1,000 = 32 thousands = 32,000
32 × 10,000 = 32 ten thousands = 320,000
Pattern
Pattern The product ends with the same number of zeros as the power of 10.

C.
Instead of using the standard form, write each power of 10 using exponents.
32 × 1 = 32 × 100 = 32
32 × 10 = 32 × 101 = 320
32 × 100 = 32 × 102 = 3,200
32 × 1,000 = 32 × 103 = 32,000
32 × 10,000 = 32 × 104 = 320,000

Pattern
The exponent tells how many additional zeros the product will end with.

Convince Me! Critique Reasoning Nellie says that 60 × 1,000 is 6,000 because there are three zeros in 1,000. Kara says that 60 × 1,000 = 60,000. Whose thinking is correct? Explain.

Kara says is correct.

Explanation:
In the above-given question,
given that,
Nellie says that 60 × 1,000 is 6,000.
Kara says that 60 × 1,000 = 60,000.
so kara says is correct.

Guided Practice

Do You Understand?

Question 1.
How many zeros will there be in the product of 39 × 1,000? How many zeros will there be in the product of 50 × 1,000?

There are 3 zeros in the 39000.
there are 4 zeros in the 50000.

Explanation:
In the above-given question,
given that,
39 x 1000 = 39000.
50 x 1000 = 50000.
so there are 3 zeros in the 39000.
there are 4 zeros in the 50000.

Question 2.
Explain how to find the product of 90 × 104.

The product of 90 x 104

Explanation:
In the above-given question,
given that,
90 x 104
90 x 10 x 10 x 10 x 10.
90 x 100 x 100.
90 x 10000.
900000.

Do You Know How?

In 3-5, use reasoning to fill in the missing numbers.

Question 3.
60 × 1 = ____
60 × 100 = ____
60 × 10,000 = ____

60 x 1 = 60.
60 x 100 = 6000.
60 x 1000 = 60000.

Explanation:
In the above-given question,
given that,
60 x 1 = 60.
60 x 100 = 6000.
60 x 1000 = 60000.

Question 4.
13 × ___ = 13,000

13 x 1000 = 13000.

Explanation:
In the above-given question,
given that,
13 x 10 x 10 x 10.
13 x 1000 = 13000.

Question 5.
___ × 104 = 100,000

10 × 104 = 100,000.

Explanation:
In the above-given question,
given that,
10 x 1 =10.
104 = 10 x 10 x 10 x 10 =10000.
10 x 10000 = 100,000.

Independent Practice

Leveled Practice In 6-13, find each product.

Question 6.
89 × 1
89 × 10
89 × 100
89 × 1,000
89 × 10,000

89 x 1 = 89.
89 x 10 = 890.
89 x 100 = 8900.
89 x 1000 = 89000.
89 x 10,000 = 890,000.

Explanation:
In the above-given question,
given that,
89 x 1 = 89.
89 x 10 = 890.
89 x 100 = 8900.
89 x 1000 = 89000.
89 x 10,000 = 890,000.

Question 7.
30 × 1
30 × 10
30 × 100
30 × 1,000
30 × 10,000

30 × 1 = 30.
30 × 10 = 300.
30 × 100 = 3000.
30 × 1,000 = 30,000.
30 × 10,000 = 300,000.

Explanation:
In the above-given question,
given that,
30 × 1 = 30.
30 × 10 = 300.
30 × 100 = 3000.
30 × 1,000 = 30,000.
30 × 10,000 = 300,000.

Question 8.
41 × 1
41 × 101
41 × 102
41 × 103
41 × 104

41 × 1 = 41.
41 × 101
41 × 102
41 × 103
41 × 104

Explanation:
In the above-given question,
given that,
41 × 1 = 41.
41 × 101= 4100.
41 × 102 = 42000.
41 × 103= 43000.
41 × 104= 430000.

Question 9.
90 × 1
90 × 101
90 × 102
90 × 103
90 × 104

90 x 1 = 90.
90 × 101
90 × 102
90 × 103
90 × 104

Explanation:
In the above-given question,
given that,
90 x 1 = 90.
90 × 101
90 × 102
90 × 103
90 × 104

Question 10.
4 × 103

4 x 103 = 4000.

Explanation:
In the above-given question,
given that,
4 x 103.
4 x 10 x 10 x 10.
4 x 1000.
4000.

Question 11.
85 × 100

85 x 100 = 8500.

Explanation:
In the above-given question,
given that,
85 x 100.
8500.

Question 12.
16 × 102

16 x 10 x 10 = 1600.

Explanation:
In the above-given question,
given that,
16 x 102.
16 x 10 x 10.
1600.

Question 13.
103 × 38

10 x 10 x 10 x 38 = 38000.

Explanation:
In the above-given question,
given that,
103 × 38.
10 x 10 x 10 x 38.
100 x 10 x 38.
38 x 1000.
38000.

In 14-19, use reasoning to fill in the missing numbers.

Question 14.
52 × 10- = 520,000

52 x 10 4 = 520,000.

Explanation:
In the above-given question,
given that,
52 x 10 x 10 x 10 x 10.
52 x 100 x 100.
52 x 10000.
520,000.

Question 15.
68,637 = 101 × ___

10 x 68637 = 686370.

Explanation:
In the above-given question,
given that,
68637 x 10.
686370.

Question 16.
___ = 382 × 104

382 x 10000 = 3820000.

Explanation:
In the above-given question,
given that,
382 x 10 x 10 x 10 x 10.
382 x 104.
382 x 100 x 100.
3820000.

Question 17.
___ = 103 × 80

80 x 103 = 80000.

Explanation:
In the above-given question,
given that,
80 x 103.
80 x 10 x 10 x 10.
80 x 1000.
80000.

Question 18.
10 × 374 = 37,400

10 x 374 x 10 = 37400.

Explanation:
In the above-given question,
given that,
10 x 374 x 10.
100 x 374.
37400.

Question 19.
500,000 = 50 × 10-

50 x 10000 = 50,000.

Explanation:
In the above-given question,
given that,
50 x 10 x 10 x 10 x 10.
50 x 100 x 100.
50 x 10000.
50,000.

Problem Solving

Question 20.
At a football championship game, the home team gave a football to each of the first 100 fans who arrived at the stadium. Each football cost the team $28. How much did the team pay for the footballs it gave away? Answer: The team pay for the footballs it gave away =$2800.

Explanation:
In the above-given question,
given that,
At a football championship game,
the home team gave a football to each of the first 100 fans who arrived at the stadium.
Each football cost the team $28. 28 x 100 = 2800. so the team pay for the football it gave away =$2800.

Question 21.
Construct Arguments Without multiplying, tell which expression is greater, 93 × 103 or 11 × 104? How do you know?

The expression 93 x 103 is greater.

Explanation:
In the above-given question,
given that,
the two expressions are 93 × 103 or 11 × 104.
93 x 10 x 10 x 10.
93 x 1000.
93000.
11 x 10 x 10 x 10 x 10.
11 x 10000.
110000.

Question 22.
A truck is carrying 102 bushels of onions, 101 bushels of peaches, and 103 bushels of corn. What is the total weight of the crops?

The total weight of the crops = 76,200.

Explanation:
In the above-given question,
given that,
A truck is carrying 102 bushels of onions.
101 bushels of peaches, and 103 bushels of corn.
57 x 100 = 5700.
50 x 10 = 500.
70 x 10 x 10 x 10 = 70000.
5700 + 500 + 70000 = 76,200.
so the total weight of the crops = 76200.

Question 23.
Norman bought a 16-pound bag of charcoal for $7.89 and a 10.4-pound bag of charcoal for$5.69. What was the total weight of the two bags of charcoal?

The total weight of the two bags of charcoal = $185.416. Explanation: In the above-given question, given that, Norman bought a 16-pound bag of charcoal for$7.89.
10.4-pound bag of charcoal for $5.69. 16 x 7.89 = 126.24. 10.4 x 5.69 = 59.176. 126.24 + 59.176 = 185.416. so the total weight of the two bags of charcoal =$185.416.

Question 24.
Higher Order Thinking There are 2,000 pounds in 1 ton. In the United States, the weight limit for a truck and its cargo is 40 tons. How many pounds is that? How did you find the answer?

The number of pounds = 80,000.

Explanation:
In the above-given question,
given that,
There are 2,000 pounds in 1 ton.
In the United States, the weight limit for a truck and its cargo is 40 tons.
2000 x 40 = 80000.
so the number of pounds = 80,000.

Assessment Practice

Question 25.
Which is equivalent to multiplying a number by 104?
A. multiplying by 40
B. multiplying by 100
C. multiplying by 1,000
D. multiplying by 10,000

The number is equivalent to multiplying a number by 10000.

Explanation:
In the above-given question,
given that,
multiplying by 10,000.
10 x 10 x 10 x 10 = 10,000.
so the number equivalent to multiplying a number by 10000.

Question 26.
Select the statements that are equivalent to multiplying 20 × 104.
Add 10 to 20 four times.
Multiply 20 by 10 four times.
Multiply 10 by 20 four times.
Multiply 20 by 10,000.
Multiply 20 by 100,000.

Option B is correct.

Explanation:
In the above-given question,
given that,
20 x 104.
20 x 10 x 10 x 10 x 10.
20 x 100 x 100.
200000.
so option B is correct.

### Lesson 3.2 Estimate Products

Activity

Solve & Share

A school club wants to buy shirts for each of its 38 members. Each shirt costs $23. About how much money will all the shirts cost? Solve this problem any way you choose. Answer: The much money will all the shirts cost =$874.

Explanation:
In the above-given question,
given that,
A school club wants to buy shirts for each of its 38 members.
Each shirt costs $23. 38 x 23 = 874. so the much money will all the shirts cost =$874.

Are you asked for an exact answer or an estimate?

Look Back! Construct Arguments How can you use number sense to tell that the exact answer has to be greater than $600? Explain how you know. Visual Learning Bridge Essential Question How Can You Estimate Products? You can use rounding to estimate. A. A store needs at least$75,000 in sales per month to make a profit. If the store is open every day in March and sales average $525 per day, will the store make a profit in March? B. Use Rounding to Estimate$525 rounds to $500. 31 rounds to 30. Find 30 × 500. 30 × 500 = 15,000 You know that 3 × 5 = 15. C. Both numbers used to estimate were less than the actual numbers, so 15,000 is an underestimate. The store will actually have more than$15,000 worth of sales.
So, the store will make a profit in March.

Convince Me! Critique Reasoning A different store needs to make at least $20,000 to make a profit in March. They average$685 a day for the month. James used rounding and estimation to say, “$685 is almost$700. $700 × 30 days is$21,000. I think it is going to be a close call!” What do you think?

$685 x 30 = 20,550. Explanation: In the above-given question, given that, A different store needs to make at least$20,000 to make a profit in March.
They average $685 a day for the month. James used rounding and estimation to say, “$685 is almost $700.$700 x 30 = $21000.$685 x 30 = 20,550.
so they can make the profit.

Another example
Estimate 24 × 398.
25 and 4 are compatible numbers because their product is easy to compute mentally.
25 × 4 = 100
25 × 40 = 1,000
25 × 400 = 10,000
So, 10,000 is a good estimate for 24 × 398.
You can also use compatible numbers to estimate.

Both numbers used to estimate were greater than the actual numbers.
So, 10,000 is an overestimate.

Guided Practice

Do You Understand?

Question 1.
Number Sense Each egg carton holds one dozen eggs. Michael’s chicken farm fills 121 egg cartons. He thinks that there were over 1,500 eggs. Is he correct? Use an estimate to find out.

Yes, the estimation was correct.

Explanation:
In the above-given question,
given that,
Each egg carton holds one dozen eggs.
1 dozen = 12.
Michael’s chicken farm fills 121 egg cartons.
121 is near to 125.
125 x 12 = 1500.
so the estimation was correct.

Do You Know How?

In 2-5, estimate. Then, tell if your estimate is an overestimate or underestimate.

Question 2.
29 × 688

29 x 688 = 19,952.

Explanation:
In the above-given question,
given that,
the two numbers are 29 and 688.
multiply the numbers.
29 x 688 = 19,952.

Question 3.
210 × 733

210 x 733 = 153930.

Explanation:
In the above-given question,
given that,
the two numbers are 210 and 733.
multiply the numbers.
210 x 733 = 153930.

Question 4.
43 × 108

43 x 108 = 4644.

Explanation:
In the above-given question,
given that,
the two numbers are 43 and 108.
multiply the numbers.
43 x 108 = 4644.

Question 5.
380 × 690

380 x 690 = 262200.

Explanation:
In the above-given question,
given that,
the two numbers are 380 and 690.
multiply the numbers.
380 x 690 = 262200.

Independent Practice

Leveled Practice In 6-17, estimate each product.

Question 6.
180 × 586

180 x 586 = 1,05,480.

Explanation:
In the above-given question,
given that,
the two numbers are 180 and 586.
multiply the numbers.
180 x 586 = 1,05,480.

Question 7.
300 × 118

300 x 118 = 35400.

Explanation:
In the above-given question,
given that,
the two numbers are 300 and 118.
multiply the numbers.
300 x 118 = 35400.

Question 8.
19 × 513

19 x 513 = 9,747.

Explanation:
In the above-given question,
given that,
the two numbers are 19 and 513.
multiply the numbers.
19 x 513 = 9,747.

Question 9.
38 × 249

38 x 249 = 9462.

Explanation:
In the above-given question,
given that,
the two numbers are 38 and 249.
multiply the numbers.
38 x 249 = 9462.

Question 10.
11 × 803

11 x 803 = 8833.

Explanation:
In the above-given question,
given that,
the two numbers are 11 and 803.
multiply the numbers.
11 x 803 = 8833.

Question 11.
44 × 212

44 x 212 = 9328.

Explanation:
In the above-given question,
given that,
the two numbers are 44 and 212.
multiply the numbers.
44 x 212 = 9328.

Question 2.
790 × 397

790 x 397 = 313630.

Explanation:
In the above-given question,
given that,
the two numbers are 790 and 397.
multiply the numbers.
790 x 397 = 313630.

Question 13.
42 × 598

42 x 598 = 25,116.

Explanation:
In the above-given question,
given that,
the two numbers are 42 and 598.
multiply the numbers.
42 x 598 = 25,116.

Question 14.
25 × 191

25 x 191 = 4775.

Explanation:
In the above-given question,
given that,
the two numbers are 25 and 191.
multiply the numbers.
25 x 191 = 4775.

Question 15.
408 × 676

408 x 676 = 275808.

Explanation:
In the above-given question,
given that,
the two numbers are 408 and 676.
multiply the numbers.
408 x 676 = 275808.

Question 16.
290 × 12

290 x 12 = 3,480.

Explanation:
In the above-given question,
given that,
the two numbers are 290 and 12.
multiply the numbers.
290 x 12 = 3,480.

Question 17.
854 × 733

854 x 733 = 6,25,982.

Explanation:
In the above-given question,
given that,
the two numbers are 854 and 733.
multiply the numbers.
854 x 733 = 6,25,982.

Problem Solving

Question 18.
Reasoning Estimate 530 × 375. Is the estimated product closer to 150,000 or 200,000? Explain.

The estimated product is closer to 200,000.

Explanation:
In the above-given question,
given that,
530 x 375 = 198,750.
198750 is equal to 200,000.

Question 19.
Vocabulary Is 500 an underestimate or overestimate for the product of 12 and 53?

500 is an underestimate for the product 12 and 53.

Explanation:
In the above-given question,
given that,
12 x 53 = 636.
10 x 50 = 500.
500 is an underestimate for the product 12 and 53.

Question 20.
Samuel needs to estimate the product of 23 × 495. Explain two different methods Samuel can use to estimate.

23 x 495 = 11,385.
25 x 500 = 12500.

Explanation:
In the above-given question,
given that,
the product of 23 and 495.
23 x 495 = 11,385.
25 x 500 = 12500.

Question 21.
Rebekah said that 103 is 30 because 10 + 10 + 10 = 30. Do you agree? Explain.

No, I do not agree with it.

Explanation:
In the above-given question,
given that,
Rebekah said that 103 is 30 because 10 + 10 + 10 = 30.
10 + 10 + 10 = 30.
30 is no equal to 103.
so I do not agree with it.

Question 22.
Higher Order Thinking Abby counts 12 large boxes and 18 small boxes of pencils in the supply cabinet. Each large box contains 144 pencils. Each small box contains 24 pencils. Estimate the total number of pencils. Is your estimate an overestimate or an underestimate? Explain why it might be better to have an underestimate rather than an overestimate.

The total number of pencils = 2160.

Explanation:
In the above-given question,
given that,
Abby counts 12 large boxes and 18 small boxes of pencils in the supply cabinet.
Each large box contains 144 pencils.
Each small box contains 24 pencils.
144 x 12 =1728.
24  x 18 = 432.
1728 + 432 = 2160.
so the total number of pencils = 2160.

Question 23.
Susan used rounding to estimate 24 × 413 and found 20 × 400. Jeremy used compatible numbers and found 25 × 400. Whose method gives an estimate closer to the actual product? Explain.

Jeremy used compatible numbers and found 25 x 400 = 10000.

Explanation:
In the above-given question,
given that,
Susan used rounding to estimate 24 × 413 and found 20 × 400.
Jeremy used compatible numbers and found 25 × 400.
24 x 413 = 9912.
20 x 400 = 8000.
25 x 400 = 10000.
so jeremy used compatible numbers and found 25 x 400 = 10000.

Assessment Practice

Question 24.
Lance has 102 packages of sports cards. Each package has 28 cards. Use rounding to estimate. About how many cards does Lance have?
A. 2,000
B. 2,500
C. 3,000
D. 3,500

The number of cards does Lance has = 3000.

Explanation:
In the above-given question,
given that,
Lance has 102 packages of sports cards.
Each package has 28 cards.
102 x 28 = 2856.
2856 is near to 3000.
so the number of cards does Lance has = 3000.

Question 25.
Which does NOT show a reasonable estimate of 24 338?
A. 6,000
B. 7,000
C. 7,500
D. 10,000

The reasonable estimate is 10,000.

Explanation:
In the above-given question,
given that,
the two numbers are 24 and 338.
338 x 24 = 8,112.
8112 is near to 10,000.
so the reasonable estimate is 10,000.

### Lesson 3.3 Multiply by 1-Digit Numbers

Activity

Solve & Share

Suppose a school ordered 7 boxes of books. There are 25 books in each box. How can you use paper and pencil to find how many books were ordered? How can you check if your answer is reasonable? Solve these problems using any strategy you choose.

The number of books that were ordered = 175.

Explanation:
In the above-given question,
given that,
Suppose a school ordered 7 boxes of books.
There are 25 books in each box.
7 x 25 = 175.
so the number of books that were ordered = 175.

You can make sense and persevere. Formulating a plan can help you solve problems. Show your work!

Look Back! Without finding the exact answer, how do you know that the answer to the problem above is less than 210?

Visual Learning Bridge

Glossary

Essential Question
What Is a Common Way to Essential Question Record Multiplication?

A.
Ms. Stockton ordered 6 boxes of T-shirts with the school name on them. Each 20 box contains 26 T-shirts. How many T-shirts did Ms. Stockton order?

You can multiply using partial products. You can write and add the partial products in any order.

B.
One Way to Record Multiplication

C.
Another Way to Record Multiplication
You can multiply each place value in order, beginning with the ones. Regroup if needed. Add any regrouped values to each place value.
Step 1: Multiply by the ones.

Step 2: Multiply by the tens.

Mrs. Stockton ordered 156 T-shirts.

Convince Me! Critique Reasoning A student did the calculation at the right. What did this student do wrong? What is the correct answer?

Another example!
Find 4 × 156.

Guided Practice

Do You Understand?

Question 1.
Use place value to explain each step in finding 3 × 2,746.

The product is 8238.

Explanation:
In the above-given question,
given that,
the numbers are 3 and 2746.
3 x 2746 = 8238.
6 x 3 ones = 18; 18 = 1 ten and 8 ones.
4 x 3 tens = 12 tens; 12 tens + 1 ten = 13 tens = 1 hundred 3 tens.
7 x 3 hundreds = 21 hundreds + 1 hundred = 22 hundreds; 2 thousands 2 hundreds.
2 x 3 thousands = 6 thousands + 2 thousands; 8 thousands.
so the product is 8238.

Do You Know How?

For 2-5, find each product. Estimate to check if your answer is reasonable.

Question 2.

23 x 4 = 92.

Explanation:
In the above-given question,
given that,
the two numbers are 23 and 4.
multiply the numbers.
23 x 4 = 92.

Question 3.

378 x 2 = 756.

Explanation:
In the above-given question,
given that,
the two numbers are 378 and 2.
multiply the numbers.
378 x 2 = 756.

Question 4.

157 x 5 = 785.

Explanation:
In the above-given question,
given that,
the two numbers are 157 and 5.
multiply the numbers.
157 x 5 = 785.

Question 5.

1746 x 3 = 5238.

Explanation:
In the above-given question,
given that,
the two numbers are 1746 and 3.
multiply the numbers.
1746 x 3 = 5238.

Independent Practice

For 6-13, find each product. Estimate to check if your answer is reasonable.

Question 6.

519 x 4 = 2076.

Explanation:
In the above-given question,
given that,
the two numbers are 519 and 4.
multiply the numbers.
519 x 4 = 2076.

Question 7.

28 x 3 = 84.

Explanation:
In the above-given question,
given that,
the two numbers are 28 and 3.
multiply the numbers.
28 x 3 = 84.

Question 8.

72 x 5 = 360.

Explanation:
In the above-given question,
given that,
the two numbers are 72 and 5.
multiply the numbers.
72 x 5 = 360.

Question 9.

138 x 5 = 690.

Explanation:
In the above-given question,
given that,
the two numbers are 138 and 5.
multiply the numbers.
138 x 5 = 690.

Question 10.

27 x 3 = 81.

Explanation:
In the above-given question,
given that,
the two numbers are 27 and 3.
multiply the numbers.
27 x 3 = 81.

Question 11.

123 x 9 = 1107.

Explanation:
In the above-given question,
given that,
the two numbers are 123 and 9.
multiply the numbers.
123 x 9 = 1107.

Question 12.

1445 x 5 = 7225.

Explanation:
In the above-given question,
given that,
the two numbers are 1445 and 5.
multiply the numbers.
1445 x 5 = 7225.

Question 13.

2204 x 6 = 13224.

Explanation:
In the above-given question,
given that,
the two numbers are 2204 and 6.
multiply the numbers.
2204 x 6 = 13224.

Problem Solving

For 14-16, use the information in the pictures below to find each mass.

Question 14.
Elephant Seal

The mass of Elephant Seal = 3480 kg.

Explanation:
In the above-given question,
given that,
the weight of elephants is 8 times as of zebra.
the weight of zebra is 435 kg.
435 x 8 = 3480 kg.

Question 15.
Sports Car

The weight of the sports car = 1740 kg.

Explanation:
In the above-given question,
given that,
the weight of the sports car is 4 times as of zebra.
the weight of zebra is 435 kg.
435 x 4 =1740.
so the weight of the sports car = 1740 kg.

Question 16.
Bison

The weight of the Bison = 870 kg.

Explanation:
In the above-given question,
given that,
the weight of the sports car is 2 times as of zebra.
the weight of zebra is 435 kg.
435 x 2 =870.
so the weight of the sports Bison = 870 kg.

Question 17.
Model with Math Last year, Anthony’s grandmother gave him 33 silver coins and 16 gold coins to start a coin collection. Now Anthony has six times as many coins in his collection. How many coins does Anthony have in his collection? Complete the bar diagram to show your work.

The number of coins does Anthony has in his collection = 294.

Explanation:
In the above-given question,
given that,
Last year, Anthony’s grandmother gave him 33 silver coins and 16 gold coins to start a coin collection.
Now Anthony has six times as many coins in his collection.
33 x 6 = 198.
16 x 6 = 96.
198 + 96 = 294.
so the number of coins does Anthony have in his collection = 294.

Question 18.
Vocabulary Use Distributive or Commutative to complete the definition.
According to the ____ Property of Multiplication, factors can be multiplied in any order and the product remains the same.

By using the commutative property, factors can be multiplied in any order.

Explanation:
In the above-given question,
given that,
By using the commutative property, factors can be multiplied in any order.
for example:
2 + 3 + 5.
5 + 5 = 10.
so the product remains the same.

Question 19.
Higher Order Thinking Do you think you could use a multiplication algorithm to multiply a 4-digit number by a 1-digit number? Explain.

Yes, we can use a 4-digit number by a 1-digit number.

Explanation:
In the above-given question,
given that,
we can use a 4-digit number by a 1-digit number.
for example:
1234 x 1 = 1234.
so we can multiply a 4-digit number by a 1-digit number.

Assessment Practice

Question 20.
Find the product.

768 x 8 = 6114.

Explanation:
In the above-given question,
given that,
the two numbers are 768 and 8.
multiply the numbers.
768 x 8 = 6114.

Question 21.
Find the product.

1945 x 3 = 5835.

Explanation:
In the above-given question,
given that,
the two numbers are 1945 and 3.
multiply the numbers.
1945 x 3 = 5835.

### Lesson 3.4 Multiply 2-Digit by 2-Digit Numbers

Solve & Share

Ms. Silva has 12 weeks to train for a race. Over the course of one week, she plans to run 15 miles. If she continues this training, how many miles will Ms. Silva run before the race? Solve this problem using any strategy you choose.

The number of miles will Ms. Silva run before the race = 180 miles.

Explanation:
In the above-given question,
given that,
Ms. Silva has 12 weeks to train for a race.
Over the course of one week, she plans to run 15 miles.
12 x 15 = 180.
so the number of miles will Ms. Silva run before the race = 180 miles.

You can use partial products to help make sense of and solve the problem. Show your work in the space below!

Look Back! Critique Reasoning Dwayne estimated 60 miles as an answer to the above problem. Is this estimate reasonable? If not, what mistake do you think Dwayne made?

Visual Learning Bridge

Essential Question What Is a Common Way to Record Multiplication?

A.
A ferry carried 37 cars per trip on the weekend. If the ferry made 11 trips on Saturday and 13 trips on Sunday, how many cars did it carry on the weekend?

You can add to find 24 trips were made on Saturday and Sunday. So the ferry carried 37 × 24 cars on the weekend.

B.
Use Partial Products
Use the area model to find the partial products for 24 × 37.

The ferry carried 888 cars on the weekend.

C.
Use the Standard Algorithm
Step 1: Multiply by the ones.

Step 2: Multiply by the tens.

The ferry carried 888 cars.

Convince Me! Make Sense and Persevere What are ways you can estimate to check the reasonableness of the answer?

Guided Practice

Do You Understand?

Question 1.
Janet said that the standard algorithm is just a shortcut for partial products. Do you agree? Explain.

Yes, I will agree.

Explanation:
In the above-given question,
given that,
Janet said that the standard algorithm is just a shortcut for partial products.
for example:
37 x 24 = 148 is the standard algorithm.
37 x 24 = 888 is the partial products.
so i will agree.

Do You Know How?

For 2, use an algorithm or partial products to find the product. Estimate to check if your answer is reasonable.

Question 2.

41 x 23 = 943.

Explanation:
In the above-given question,
given that,
the two numbers are 41 and 23.
40 + 1 = 43.
20 + 3 = 23.
20 x 40 = 800.
20 x 1 = 20.
800 + 20 = 820.
3 x 40 = 120.
3 x 1 = 3.
120 + 3 = 123.
820 + 123 = 943.

Independent Practice

Leveled Practice For 3-14, use an algorithm or partial products to find the product. Use and draw area models as needed.

Use estimation to check if your answers are reasonable.

Question 3.

16 x 22 = 352.

Explanation:
In the above-given question,
given that,
the two numbers are 16 and 22.
10 + 6 = 16.
20 + 2 = 22.
10 x 20 = 200.
20 x 6 = 120.
200 + 120 = 320.
2 x 10 = 20.
2 x 6 = 12.
20 + 12 = 32.
320 + 32 = 352.

Question 4.

15 x 16 = 240.

Explanation:
In the above-given question,
given that,
the two numbers are 16 and 15.
10 + 5 = 15.
10 + 6 = 16.
10 x 10 = 100.
10 x 5 = 50.
100 + 50 = 150.
6 x 10 = 60.
6 x 5 = 30.
60 + 30 = 90.
150 + 90 = 240.

Question 5.

27 x 12 = 324.

Explanation:
In the above-given question,
given that,
the two numbers are 27 and 12.
20 + 7 = 27.
10 + 2 = 12.
10 x 20 = 200.
10 x 7 = 70.
200 + 70 = 270.
2 x 20 = 40.
2 x 7 = 14.
40 + 14 = 54.
270 + 54 = 324.

Question 6.

18 x 15 = 270.

Explanation:
In the above-given question,
given that,
the two numbers are 18 and 15.
10 + 8 = 18.
10 + 5 = 15.
10 x 10 = 100.
10 x 8 = 80.
100 + 80 = 180.
5 x 10 = 50.
5 x 8 = 40.
50 + 40 = 90.
180 + 90 = 270.

Question 7.
53 × 17

53 x 17 = 901.

Explanation:
In the above-given question,
given that,
the two numbers are 53 and 17.
multiply the numbers.
53 x 17 = 901.

Question 8.
81 × 46

81 x 46 = 901.

Explanation:
In the above-given question,
given that,
the two numbers are 81 and 46.
81 x 46 = 901.

Question 9.
15 × 16

15 x 16 = 240.

Explanation:
In the above-given question,
given that,
the two numbers are 15 and 16.
15 x 16 = 240.

Question 10.
17 × 21

17 x 21 = 357.
Explanation:
In the above-given question,
given that,
the two numbers are 17 and 21.
17 x 21 = 357.

Question 11.
12 × 22

12 x 22 = 264.
Explanation:
In the above-given question,
given that,
the two numbers are 12 and 22.
12 x 22 = 264.

Question 12.
38 × 41

38 x 41 = 1558.

Explanation:
In the above-given question,
given that,
the two numbers are 38 and 41.
38 x 41 = 1558.

Question 13.
42 × 52

42 x 52 = 2184.
Explanation:
In the above-given question,
given that,
the two numbers are 42 and 52.
42 x 52 = 2184.

Question 14.
38 × 19

38 x 19 = 722.
Explanation:
In the above-given question,
given that,
the two numbers are 38 and 19.
38 x 19 = 722.

Problem Solving

Question 15.
Number Sense The Queen Mary 2’s height above water is about the same as a 14-story building. What is the Queen Mary 2’s height above water?

The Queen Mary 2’s height above water = 168 feet.

Explanation:
In the above-given question,
given that,
The Queen Mary 2’s height above water is about the same as a 14-story building.
14 x 12 = 168.
so the Queen Mary 2’s height above water = 168 feet.

Question 16.
Model with Math Write the multiplication equation illustrated by the array drawn on the grid. Find the partial products. Then calculate the final product.

The partial products are 18 and 15.
the final product is 270.

Explanation:
In the above-given question,
given that,
the two numbers are 18 and 15.
10 + 8 = 18.
10 + 5 = 15.
10 x 10 = 100.
10 x 8 = 80.
100 + 80 = 180.
5 x 10 = 50.
5 x 8 = 40.
50 + 40 = 90.
180 + 90 = 270.

Question 17.
Higher Order Thinking An elevator can carry 15 adults or 20 children at one time. During the course of a day, the elevator carries a full passenger load 52 times. If all the passengers were children, how many more people would the elevator carry than if all the passengers were adults?

The more people would the elevator carry than if all the passengers were adults = 1040.

Explanation:
In the above-given question,
given that,
An elevator can carry 15 adults or 20 children at one time.
During the course of a day, the elevator carries a full passenger load 52 times.
52 x 20 = 1040.
so the more people would the elevator carry than if all the passengers were adults = 1040.

Assessment Practice

Question 18.
Ten years ago, Melissa planted a tree in her backyard. She has taken a photo of the tree every week so she can see how it has grown as time passed. How many photos of the tree does Melissa now have?
A. 62 photos
B. 120 photos
C. 520 photos
D. 620 photos
There are 52 weeks in one year.

The number of photos of the tree does Melissa now has = 520 photos.

Explanation:
In the above-given question,
given that,
Ten years ago, Melissa planted a tree in her backyard.
She has taken a photo of the tree every week so she can see how it has grown as time passed.
there are 52 weeks in one year.
52 x 10 = 520.
so the number of photos of the tree does Melissa now have = 520 photos.

Question 19.
Mr. Morris bought sketchpads for 24 of his students. Each pad contained 50 sheets. How many sheets of paper were in all the pads?
A. 1,000 sheets
B. 1,200 sheets
C. 1,400 sheets
D. 1,600 sheets

The number of sheets of paper was in all the pads = 1200 sheets.

Explanation:
In the above-given question,
given that,
Mr. Morris bought sketchpads for 24 of his students.
Each pad contained 50 sheets.
24 x 50 = 1200.
so the number of sheets of paper were in all the pads = 1200 sheets.

### Lesson 3.5 Multiply 3-Digit by 2-Digit Numbers

Activity

Solve & Share

A local charity collected 163 cans of food each day for 14 days. How many cans did they collect in all? Explain how you found your answer.

You can use what you know about multiplying 2-digit numbers by 2-digit numbers to help solve the problem.

The number of cans did they collect in all = 2282 cans.

Explanation:
In the above-given question,
given that,
A local charity collected 163 cans of food each day for 14 days.
163 x 14 = 2282.
so the number of cans did they collect in all = 2282 cans.

Look Back! Make Sense and Persevere How can you check that your answer is reasonable?

Visual Learning Bridge

Essential Question How Do You Multiply 3-Digit Numbers by 2-Digit Numbers?

A.
Last month a bakery sold 389 boxes of bagels. How many bagels did the store sell last month? Find 12 × 389.

You can show all partial products or you can use the standard algorithm.

B.
Step 1
To use the Standard Algorithm, first multiply by the ones. Regroup as needed.

2 × 9 ones = 18 ones or 1 ten and 8 ones
2 × 8 tens =16 tens
16 tens + 1 ten = 17 tens
17 tens = 1 hundred 7 tens
2 × 3 hundreds = 6 hundreds
6 hundreds + 1 hundred = 7 hundreds

C.
Step 2
Multiply by the tens.
Regroup as needed.

10 × 9 ones = 90 ones
10 × 8 tens = 80 tens,
or 8 hundred 10 × 3 hundred = 30 hundred, or 3 thousand

D.
Step 3
Add to get the final product.

The store sold 4,668 bagels last month.

Convince Me! Construct Arguments Is 300 10 a good estimate for the number of bagels sold at the bakery? Explain.

Guided Practice

Do You Understand?

Question 1.
A theater can seat 540 people at one time. How many tickets are sold if the theater sells out every seat for one 30-day month?

The number of tickets is sold if the theater sells out every seat for one 30-day month = 16200.

Explanation:
In the above-given question,
given that,
A theater can seat 540 people at one time.
540 x 30 = 16200.
so the number of tickets are sold if the theater sells out every seat for one 30-day month = 16200.

Question 2.
Number Sense Is 500 30 a good estimate for the number of tickets sold at the theater in one month? Explain.

Yes, it is a good estimate for the number of tickets sold at the theater in one month.

Explanation:
In the above-given question,
given that,
A theater can seat 540 people at one time.
540 is equal to 500.
500 x 30 = 15000.
so it is a good estimate for the number of tickets sold at the theater in one month.

Do You Know How?

In 3-6, find each product. Estimate to check that your answer is reasonable.

Question 3.

236 x 46 = 10856.

Explanation:
In the above-given question,
given that,
the two numbers are 236 and 46.
multiply the numbers.
236 x 46 = 10856.

Question 4.

61 x 25 = 5185.

Explanation:
In the above-given question,
given that,
the two numbers are 61 and 25.
multiply the numbers.
61 x 25 = 5185.

Question 5.

951 x 62 = 58962.

Explanation:
In the above-given question,
given that,
the two numbers are 951 and 62.
multiply the numbers.
951 x 62 = 58962.

Question 6.

185 x 5 = 925.

Explanation:
In the above-given question,
given that,
the two numbers are 185 and 5.
multiply the numbers.
185 x 5 = 925.

Independent Practice

Leveled Practice In 7-18, find each product. Estimate to check that your answer is reasonable.

Question 7.

51 x 10 = 510.

Explanation:
In the above-given question,
given that,
the two numbers are 51 and 10.
multiply the numbers.
51 x 10 = 510.

Question 8.

892 x 18 = 16056.

Explanation:
In the above-given question,
given that,
the two numbers are 892 and 18.
multiply the numbers.
892 x 18 = 16056.

Question 9.

946 x 33 = 31218.

Explanation:
In the above-given question,
given that,
the two numbers are 946 and 33.
multiply the numbers.
946 x 33 = 31218.

Question 10.

735 x 41 = 30135.

Explanation:
In the above-given question,
given that,
the two numbers are 735 and 41.
multiply the numbers.
735 x 41 = 30135.

Question 11.

100 x 25 = 2500.

Explanation:
In the above-given question,
given that,
the two numbers are 100 and 25.
multiply the numbers.
100 x 25 = 2500.

Question 12.

81 x 11 = 891.

Explanation:
In the above-given question,
given that,
the two numbers are 81 and 11.
multiply the numbers.
81 x 11 = 891.

Question 13.

106 x 7 = 742.

Explanation:
In the above-given question,
given that,
the two numbers are 106 and 7.
multiply the numbers.
106 x 7 = 742.

Question 14.

90 x 59 = 5310.

Explanation:
In the above-given question,
given that,
the two numbers are 90 and 59.
multiply the numbers.
90 x 59 = 5310.

Question 15.

360 x 18 = 6480.

Explanation:
In the above-given question,
given that,
the two numbers are 360 and 18.
multiply the numbers.
360 x 18 = 6480.

Question 16.

222 x 75 = 16650.

Explanation:
In the above-given question,
given that,
the two numbers are 222 and 75.
multiply the numbers.
222 x 75 = 16650.

Question 17.

481 x 35 = 16835.

Explanation:
In the above-given question,
given that,
the two numbers are 481 and 35.
multiply the numbers.
481 x 35 = 16835.

Question 18.

659 x 17 = 11203.

Explanation:
In the above-given question,
given that,
the two numbers are 659 and 17.
multiply the numbers.
659 x 17 = 11203.

Problem Solving

Question 19.
enVision® STEM How many times does a rabbit’s heart beat in 1 hour?

Remember, there are 60 minutes in 1 hour.

The number of times does a rabbit’s heartbeat in 1 hour = 212 beats.

Explanation:
In the above-given question,
given that,
1 hour = 60 minutes.
212 beats per minute.
so the number of times does a rabbit’s heartbeat in 1 hour = 212 beats.

Question 20.
In 1 hour, how many more times does a rabbit’s heart beat than a dog’s heart? Write an equation to show your work.

The number of more times does a rabbit’s heartbeat than a dog’s heart = 112.

Explanation:
In the above-given question,
given that,
heart rate of the dog for a minute = 100.
heart rate of the rabbit for a minute = 212.
212 – 100 = 112.
so the number of more times does a rabbit’s heartbeat than a dog’s heart = 112.

Question 21.
Construct Arguments Is 3,198 a reasonable product for 727 × 44? Why or why not?

Yes, it is a reasonable product.

Explanation:
In the above-given question,
given that,
the two numbers are 727 and 44.
multiply the two numbers.
727 x 44 = 31,988.
yes, it is a reasonable product.

Question 22.
Higher Order Thinking A garden store sells plants in flats. There are 6 plants in each tray. Each flat has 6 trays. The garden store sold 18 flats on Saturday and 21 flats on Sunday. How many plants did the garden store sell in all?

The number of plants did the garden store sell in all = 234.

Explanation:
In the above-given question,
given that,
A garden store sells plants in flats.
There are 6 plants in each tray.
Each flat has 6 trays.
The garden store sold 18 flats on Saturday and 21 flats on Sunday.
18 x 6 = 108.
21 x 6 = 126.
108 + 126 = 234.
so the number of plants did the garden store sell in all = 234.

Assessment Practice

Question 23.
Tricia is building a rectangular patio. The patio will be 108 bricks wide and 19 bricks long. How many bricks does she need to build the patio?

The number of bricks does she need to build the patio = 2052.

Explanation:
In the above-given question,
given that,
Tricia is building a rectangular patio.
The patio will be 108 bricks wide and 19 bricks long.
area of the rectangle = l x b.
where l = length and b = breadth.
108 x 19 = 2052.
so the number of bricks does she need to build the patio = 2052.

Question 24.
What is the product?

A. 1,560
B. 1,568
C. 4,268
D. 4,368

312 x 14 = 4368.

Explanation:
In the above-given question,
given that,
the two numbers are 312 and 14.
multiply the two numbers.
312 x 14 = 4368.

### Lesson 3.6 Multiply Whole Numbers with Zeros

Activity

Solve & Share

A school district is replacing all of the desks in its classrooms. There are 103 classrooms and each classroom needs 24 new desks. How many desks will the school district need to buy? Solve this problem any way you choose!

Use what you know about multiplying 3-digit and 2-digit numbers. Show your work!

The number of desks will the school district need to buy = 2472.

Explanation:
In the above-given question,
given that,
A school district is replacing all of the desks in its classrooms.
There are 103 classrooms and each classroom needs 24 new desks.
103 x 24 = 2472.
so the number of desks will the school district need to buy = 2472.

Look Back! Make Sense and Persevere What is a good estimate for the problem above? Explain.

Visual Learning Bridge

Essential Question
How Can You Multiply with Zeros?

A.
An antique steam train makes one sight-seeing tour each day. If every seat is filled for each trip, how many passengers can it carry for 31 tours?

The standard algorithm does not change when there is a zero in a factor.

B.
Step 1
Find 31 × 208.
Estimate:
30 × 200 = 6,000

C.
Step 2
Multiply by the ones.
Regroup if necessary.
Remember that multiplying with a zero gives a product of zero.

D.
Step 3
Multiply by the tens.
Regroup if necessary.
Add to get the final product.

The train can carry 6,448 passengers.

Convince Me! Model with Math Suppose the train fills an average of 102 seats for each tour. What is a reasonable estimate for the number of passengers that the train can carry in 28 tours? Write an equation to show your work.

The number of passengers that the train can carry in 28 tours = 2856.

Explanation:
In the above-given question,
given that,
Suppose the train fills an average of 102 seats for each tour.
the two numbers are 102 and 28.
102 x 28 = 2856.
so the number of passengers that the train can carry in 28 tours = 2856.

Guided Practice

Do You Understand?

Question 1.
In an auditorium, there are 104 rows with 24 seats in each row. How many seats are available?

The number of seats is available = 2496 seats.

Explanation:
In the above-given question,
given that,
there are 104 rows with 24 seats in each row.
104 x 24 = 2496.
so the number of seats are available = 2496 seats.

Question 2.
Why is it important to “estimate to check for reasonableness”?

Do You Know How?

In 3-6, multiply to find the product. Estimate to check for reasonableness.

Question 3.

205  x 23 = 4715.

Explanation:
In the above-given question,
given that,
the two numbers are 205 and 23.
multiply the numbers.
205 x 23 = 4715.

Question 4.

108 x 34 = 3672.

Explanation:
In the above-given question,
given that,
the two numbers are 108 and 34.
multiply the numbers.
108 x 34 = 3672.

Question 5.

410 x 44 = 18040.

Explanation:
In the above-given question,
given that,
the two numbers are 410 and 44.
multiply the numbers.
410 x 44 = 18040.

Question 6.

302 x 30 = 9060.

Explanation:
In the above-given question,
given that,
the two numbers are 302 and 30.
multiply the numbers.
302 x 30 = 9060.

Independent Practice
Leveled Practice In 7-18, find each product. Estimate to check for reasonableness.

Question 7.

302 x 17 = 5134.

Explanation:
In the above-given question,
given that,
the two numbers are 302 and 17.
multiply the numbers.
236 x 46 = 5134.

Question 8.

608 x 23 = 13984.

Explanation:
In the above-given question,
given that,
the two numbers are 608 and 23.
multiply the numbers.
608 x 23 =13984.

Question 9.

109 x 47 = 5123.

Explanation:
In the above-given question,
given that,
the two numbers are 109 and 47.
multiply the numbers.
109 x 47 = 5123.

Question 10.

510 x 72 = 36864.

Explanation:
In the above-given question,
given that,
the two numbers are 510 and 72.
multiply the numbers.
510 x 72 = 36864.

Question 11.

902 x 35 = 31570.

Explanation:
In the above-given question,
given that,
the two numbers are 902 and 35.
multiply the numbers.
902 x 35 = 31570.

Question 12.

207 x 61 = 12627.

Explanation:
In the above-given question,
given that,
the two numbers are 207 and 61.
multiply the numbers.
207 x 61 = 12627.

Question 13.

108 x 58 = 6264.

Explanation:
In the above-given question,
given that,
the two numbers are 108 and 58.
multiply the numbers.
108 x 58 = 6264.

Question 13.

108 x 58 = 6264.

Explanation:
In the above-given question,
given that,
the two numbers are 108 and 58.
multiply the numbers.
108 x 58 = 6264.

Question 14.

505 x 77 = 38885.

Explanation:
In the above-given question,
given that,
the two numbers are 505 and 77.
multiply the numbers.
505 x 77 = 38885.

Question 15.

407 x 39 = 15873.

Explanation:
In the above-given question,
given that,
the two numbers are 407 and 39.
multiply the numbers.
407 x 39 = 15873.

Question 16.

280 x 66 =18480.

Explanation:
In the above-given question,
given that,
the two numbers are 280 and 66.
multiply the numbers.
280 x 66 = 18480.

Question 17.

105 x 24 =2520.

Explanation:
In the above-given question,
given that,
the two numbers are 105 and 24.
multiply the numbers.
105 x 24 =2520.

Question 18.

360 x 48 = 17280.

Explanation:
In the above-given question,
given that,
the two numbers are 360 and 48.
multiply the numbers.
360 x 48 = 17280.

Problem Solving

Question 19.
There are 27 students in Mr. Mello’s class. Find the total number of pages the students read by the end of November.

The total number of pages the students read by the end of November = 783 pages.

Explanation:
In the above-given question,
given that,
there are 27 students in Mr. Mello’s class.
in November there are 29 days.
29 x 27 = 783.
so the total number of pages the students read by the end of November = 783 pages.

Question 20.
Each student read 41 pages in December. How many total pages did the students read by the end of December?

The number of total pages did the students read by the end of December = 1271 pages.

Explanation:
In the above-given question,
given that,
Each student read 41 pages in December.
in December there are 31 pages.
41 x 31 = 1271.
so the number of total pages did the students read by the end of December = 1271 pages.

Question 21.
Meredith says that 15.17 is greater than 15.8 because 17 is greater than 8. Do you agree? Explain your reasoning.

No, I do not agree with it.

Explanation:
In the above-given question,
given that,
Meredith says that 15.17 is greater than 15.8 because
17 is greater than 8.
15.17 is less than 15.8.
so I do not agree with it.

Question 22.
Use Structure Trudy wants to multiply 66 × 606. She says that all she has to do is find 6 × 606 and then double that number. Explain why Trudy’s method will not give the correct answer. Then show how to find the correct product.

Yes, Trudy’s method will not give the correct answer.

Explanation:
In the above-given question,
given that,
Trudy wants to multiply 66 × 606.
She says that all she has to do is find 6 × 606.
66 x 606 =
6 x 606 =
the two values are not equal.
so Trudy’s method will not give the correct answer.

Question 23.
Higher Order Thinking Maria needs a trombone for only 12 months. Renting the trombone costs $34 per month. She can buy the trombone for$495. Should she buy or rent the trombone? Explain. How much does she pay?

Yes, she can rent the trombone.

Explanation:
In the above-given question,
given that,
Maria needs a trombone for only 12 months.
Renting the trombone costs $34 per month. She can buy the trombone for$495.
12 x $34 =$408.

Question 24.
Another music store rents trombones for $30 per month plus a yearly fee of$48. Which deal is better? Should Maria change her rental plan?

Yes, maria change her rental plan.

Explanation:
In the above-given question,
given that,
Another music store rents trombones for $30 per month plus a yearly fee of$48.
30 x 48 = $1440. Assessment Practice Question 25. What is the product? Answer: 659 x 17 = 11203. Explanation: In the above-given question, given that, the two numbers are 659 and 17. multiply the numbers. 659 x 17 = 11203. ### Lesson 3.7 Practice Multiplying Multi-Digit Numbers Activity Solve & Share Which of the two car payment options will cost less for 1 year? How much less? Solve this problem any way you choose! Show all of your work You can use reasoning to connect mathematics to everyday life. Think about the situations multiplication describes. Answer: The Look Back! How can you estimate the total for the year when paying monthly? When paying quarterly? Visual Learning Bridge Essential Question How Can You Use Multiplication to Solve Problems? A. What is the yearly total for water, gas, and electric? What is the yearly total for cell phones? The standard algorithm for multiplying whole numbers involves breaking numbers apart using place value. B. What is the yearly total for water, gas, and electric? Find 4 × (760 + 510). Estimate: 4 × (760 + 510) is about 4 × 1,200 = 4,800. 4 × (760+ 510) = 4 × 1,270 The yearly total for water, gas, and electric is$5,080.

C.
What is the yearly total for cell phones?
Find 12 × 271.
Estimate:
12 × 271 is about 10 × 270 = 2,700.

The process for multiplying is the same regardless of the number of digits in 3,252 the factors.

The yearly total for cell phones is $3,252. Convince Me! Be Precise How are the processes for multiplying alike for the two calculations above? How are they different? Guided Practice Do You Understand? Question 1. Carlos saves 18 cents every day of the year. If there are 365 days this year, how many cents will he have saved by the end of the year? Write an equation that represents the problem. Then, solve the equation. Answer: The number of cents will he have saved by the end of the year = 6570. Explanation: In the above-given question, given that, Carlos saves 18 cents every day of the year. If there are 365 days this year. 365 x 18 = 6570. so the number of cents will he have saved by the end of the year = 6570. Question 2. Lila drives 129 kilometers round trip to work. How many kilometers does she drive in 31 days? Write an equation that represents the problem. Then solve the equation. Answer: The number of kilometers does she drive in 31 days = 3999 km. Explanation: In the above-given question, given that, Lila drives 129 kilometers round trip to work. 129 x 31 = 3999. so the number of kilometers does she drive in 31 days = 3999 km. Do You Know How? In 3-6, estimate each product. Then complete each calculation. Check that your answer is reasonable. Question 3. Answer: 134 x 11 = 1474. Explanation: In the above-given question, given that, the two numbers are 134 and 11. multiply the numbers. 134 x 11 = 1474. Question 4. Answer: 208 x 26 = 5408. Explanation: In the above-given question, given that, the two numbers are 208 and 26. multiply the numbers. 208 x 26 = 5408. Question 5. Answer: 428 x 35 = 14980. Explanation: In the above-given question, given that, the two numbers are 428 and 35. multiply the numbers. 428 x 35 = 14980. Question 6. Answer: 275 x 56 = 15400. Explanation: In the above-given question, given that, the two numbers are 275 and 56. multiply the numbers. 275 x 56 = 15400. Independent Practice Leveled Practice In 7-22, estimate and then compute each product. Check that your answer is reasonable. Question 7. Answer: 531 x 47 = 24,957. Explanation: In the above-given question, given that, the two numbers are 531 and 47. multiply the numbers. 531 x 47 = 24,957. Question 8. Answer: 759 x 68 = 51,612. Explanation: In the above-given question, given that, the two numbers are 759 and 68. multiply the numbers. 759 x 68 = 51,612. Question 9. Answer: 367 x 92 = 33,764. Explanation: In the above-given question, given that, the two numbers are 367 and 92. multiply the numbers. 367 x 92 = 33,764. Question 10. Answer: 817 x 45 = 36,765. Explanation: In the above-given question, given that, the two numbers are 817 and 45. multiply the numbers. 817 x 45 = 36,765. Question 11. Answer: 1206 x 77 = 92862. Explanation: In the above-given question, given that, the two numbers are 1206 and 77. multiply the numbers. 1206 x 77 = 92862. Question 12 Answer: 543 x 18 = 9774. Explanation: In the above-given question, given that, the two numbers are 543 and 18. multiply the numbers. 543 x 18 = 9774. Question 13. Answer: 908 x 62 = 56,296. Explanation: In the above-given question, given that, the two numbers are 908 and 62. multiply the numbers. 908 x 62 = 56,296. Question 14. Answer: 750 x 81 = 60,750. Explanation: In the above-given question, given that, the two numbers are 750 and 81. multiply the numbers. 750 x 81 = 60,750. Question 15. 6,755 × 9 Answer: 6755 x 9 = 60,795. Explanation: In the above-given question, given that, the two numbers are 6755 and 9. multiply the numbers. 6755 x 9 = 60,795. Question 16. 869 × 46 Answer: 869 x 46 = 39,974. Explanation: In the above-given question, given that, the two numbers are 869 and 46. multiply the numbers. 869 x 46 = 39,974. Question 17. 922 × 81 Answer: 922 x 81 = 74,682. Explanation: In the above-given question, given that, the two numbers are 922 and 81. multiply the numbers. 922 x 81 = 74,682. Question 18. 783 × 14 Answer: 783 x 14 = 10,962. Explanation: In the above-given question, given that, the two numbers are 783 and 14. multiply the numbers. 783 x 14 = 10,962. Question 19. 684 × 15 Answer: 684 x 15 = 10,260. Explanation: In the above-given question, given that, the two numbers are 684 and 15. multiply the numbers. 684 x 15 = 10,260. Question 20. 650 × 22 Answer: 650 x 22 = 14,300. Explanation: In the above-given question, given that, the two numbers are 650 and 22. multiply the numbers. 650 x 22 = 14,300. Question 21. 2,525 × 37 Answer: 2,525 x 37 = 93,425. Explanation: In the above-given question, given that, the two numbers are 2525 and 37. multiply the numbers. 2525 x 37 = 93,425. Question 22. 615 × 41 Answer: 615 x 41 = 25,215. Explanation: In the above-given question, given that, the two numbers are 615 and 41. multiply the numbers. 615 x 41 = 25,215. Problem Solving For 23 and 24, use the table. Question 23. Model with Math Jason frequently travels for work. This year he plans to make 15 trips to Chicago. What is the total cost for the airfare? Write an equation that represents the problem. Then, solve the equation. Answer: The total cost for the airfare =$7335.

Explanation:
In the above-given question,
given that,
Jason frequently travels for work.
the cost of the chicago is $489. This year he plans to make 15 trips to Chicago.$489 x 15 = 7335.
so the total cost of the airfare = $7335. Question 24. Which would cost more: 15 trips to Boston or 11 trips to New York? Explain. Answer: The trip would cost more. Explanation: In the above-given question, given that, the ticket cost of Boston is$178.
the ticket cost of new york is $225. 15 x 178 = 2670. 225 x 11 = 1958. so the trip would cost more. Question 25. A cook at a restaurant is planning her food order. She expects to use 115 pounds of potatoes each day for 12 days. How many pounds of potatoes will she order? Answer: The number of pounds of potatoes will she order = 1380 pounds. Explanation: In the above-given question, given that, A cook at a restaurant is planning her food order. She expects to use 115 pounds of potatoes each day for 12 days. 115 x 12 = 1380. so the number of pounds of potatoes will she order = 1380. Question 26. Higher Order Thinking Carolyn bought a gallon of paint that covers 250 square feet. She wants to paint a wall that is 16 feet wide and 12 feet high. Explain whether or not she will need more than one gallon of paint. Answer: Yes, she needs only one gallon of paint. Explanation: In the above-given question, given that, Carolyn bought a gallon of paint that covers 250 square feet. She wants to paint a wall that is 16 feet wide and 12 feet high. 16 x 12 = 192. 192 is less than 250. so she needs less than one gallon of paint. Assessment Practice Question 27. The product of the following expression is 7,453. What is the missing digit? A. 1 B. 2 C. 4 D. 7 Answer: Option B is the correct. Explanation: In the above-given question, given that, 257 x 29 = 7453. so option B is correct. Question 28. When you multiply a 3-digit number by a 2-digit number, what is the greatest number of digits the product can have? Answer: The greatest number of digits the product can have 4. Explanation: In the above-given question, given that, the three-digit number is 123. the two-digit number is 10. 123 x 10 = 1230. ### Lesson 3.8 Solve Word Problems Using Multiplication Activity Solve&S are Kevin’s family took 239 photos on their summer vacation. Marco and his family took 12 times as many photos on their vacation. How many photos did Marco’s family take? Solve this problem any way you choose. How can you use an equation to model the situation with math? Answer: The number of photos did Marco’s family take = 2629 photos. Explanation: In the above-given question, given that, Kevin’s family took 239 photos on their summer vacation. Marco and his family took 12 times as many photos on their vacation. 239 x 12 = 2868. 2868 – 239 = 2629. so the number of photos did Marco’s family take = 2629 photos. Look Back! How can you use estimation to tell if your answer is reasonable? Explain. Visual Learning Bridge Essential Question How Can You Use a Bar Diagram to Solve a Multiplication Problem? A. In 1980, a painting sold for$1,575. In 2015, the same painting sold for 5 times as much. What was the price of the painting in 2015?

You can draw a bar diagram and use a variable to find the new price of the painting.

B.
What am I asked to find?
The price of the painting in 2015.
Let p = the price of the painting in 2015.
Draw a bar diagram to represent the problem.

C.
Write and solve an equation using the variable.
$1,575 × 5 =p$1,575 × 5 = $7,875. So, p=$7,875.
In 2015, the painting sold for $7,875. You can use repeated addition or division to check your answer! Convince Me! Construct Arguments How can you use estimation to justify that the answer$7,875 is reasonable?

Guided Practice

Do You Understand?

Question 1.
Write a real-world problem that uses multiplication. Then, draw a bar diagram and write an equation to solve your problem.

Do You Know How?

In 2, write and solve an equation.

Question 2.
Sharon’s Stationery Store has 1,219 boxes of cards. May’s Market has 3 times as many boxes of cards. How many boxes of cards does May’s Market have?

The number of cards does May’s market have = 2.

Explanation:
In the above-given question,
given that,
Sharon’s Stationery Store has 1,219 boxes of cards.
May’s Market has 3 times as many boxes of cards.
3 x 1219 = 3657.
3657 – 1219 = 2438.
1219 x 2 = 2438.
so the number of cards does May’s market have = 2.

Independent Practice

In 3-5, draw a bar diagram to model the situation. Then, write and solve an equation.

Question 3.
There are 14 theaters at the mall. Each theater has 175 seats. How many seats are there in all?

The number of seats is there in all = 2450.

Explanation:
In the above-given question,
given that,
There are 14 theaters at the mall.
Each theater has 175 seats.
14 x 175 = 2450.
so the number of seats are there in all = 2450.

Question 4.
Brad lives 12 times as far away from the ocean as Jennie. If Jennie lives 48 miles from the ocean, how many miles from the ocean does Brad live?

The number of miles from the ocean does Brad live = 576 miles.

Explanation:
In the above-given question,
given that,
Brad lives 12 times as far away from the ocean as Jennie.
If Jennie lives 48 miles from the ocean.
48 x 12 = 576.
so the number of miles from the ocean does Brad live = 576 miles.

Question 5.
A hardware store ordered 13 packs of nails from a supplier. Each pack contains 155 nails. How many nails did the store order?

The number of nails did the store order = 2015 nails.

Explanation:
In the above-given question,
given that,
A hardware store ordered 13 packs of nails from a supplier.
Each pack contains 155 nails.
13 x 155 = 2015 nails.
so the number of nails did the store order = 2015 nails.

Problem Solving

Question 6.
Algebra Sandi’s school has 1,030 students. Karla’s school has 3 times as many students as Sandi’s school. Write an equation to find s, the number of students in Karla’s school. Then, solve your equation.

The number of students in Karla’s school = 3090.

Explanation:
In the above-given question,
given that,
Sandi’s school has 1,030 students.
Karla’s school has 3 times as many students as Sandi’s school.
1030 x 3 = 3090.
so the number of students in Karla’s school = 3090.

Question 7.
enVision® STEM Jupiter is about 5 times the distance Earth is from the Sun. Earth is about 93,000,000 miles from the Sun. About how far is Jupiter from the Sun?
Look for a relationship to help you solve this problem.

The far is Jupiter from the sun = 46,50,00,000.

Explanation:
In the above-given question,
given that,
Jupiter is about 5 times the distance Earth is from the Sun.
Earth is about 93,000,000 miles from the sun.
93,000,000 x 5 = 46,50,00,000.
so the far is hupiter from the sun = 46,50,00,000.

Question 8.
Higher Order Thinking William travels only on Saturdays and Sundays and has flown 1,020 miles this month. Jason travels every weekday and has flown 1,200 miles this month. If each man travels about the same number of miles each day, who travels more miles per day for this month? Explain.

Jason travels more miles per day for this month.

Explanation:
In the above-given question,
given that,
William travels only on Saturdays and Sundays and has flown 1,020 miles this month.
Jason travels every weekday and has flown 1,200 miles this month.
1200 is greater than 1020.
so Jason travels more miles per day for this month.

Question 9.
Make Sense and Persevere Hwong can fit 12 packets of coffee in a small box and 50 packets of coffee in a large box. He has 10 small boxes of coffee and would like to reorganize the packets into large boxes. How many large boxes could he fill? Explain.

The number of large boxes could he fill = 6.

Explanation:
In the above-given question,
given that,
How can fit 12 packets of coffee in a small box and 50 packets of coffee in a large box.
He has 10 small boxes of coffee and would like to reorganize the packets into large boxes.
12 x 50 = 600.
10 x 6 = 600.
so the number of large boxes could he fill = 6.

Assessment Practice

Question 10.
Martin ran 108 miles last year. Katrina ran 13 times as many miles as Martin last year. How many miles did Katrina run last year?
A. 1,008 miles
B. 1,404 miles
C. 1,806 miles
D. 2,000 miles

The number of miles did Katrina run last year = 1404 miles.

Explanation:
In the above-given question,
given that,
Martin ran 108 miles last year. Katrina ran 13 times as many miles as Martin last year.
108 x 13 = 1404.
so option B is the correct.

Question 11.
The Erie shoe factory makes 245 pairs of shoes a day. The Columbus shoe factory makes 34 times as many pairs of shoes a day as the Erie shoe factory. How many pairs of shoes does the Columbus shoe factory make a day?
A. 7,545 pairs of shoes
B. 8,010 pairs of shoes
C. 8,330 pairs of shoes
D. 8,750 pairs of shoes

Option C is the correct answer.

Explanation:
In the above-given question,
given that,
The Erie shoe factory makes 245 pairs of shoes a day.
The Columbus shoe factory makes 34 times as many pairs of shoes a day as the Erie shoe factory.
245 x 34 = 8,330.
so the option C is the correct.

### Lesson 3.9 Critique Reasoning

Activity

Problem Solving

Solve & Share
A group of 44 students is planning a train trip to Washington, D.C. They held many fundraisers and raised $10,880. Nathan said, “We should have enough money to pay for the train tickets. There are about 50 students going on the trip and one round trip ticket costs about$200. That makes the total cost of the tickets less than $10,000.” Does Nathan’s reasoning make sense? Answer: The total cost of the tickets is less than$10,000.

Explanation:
In the above-given question,
given that,
A group of 44 students is planning a train trip to Washington, D.C.
They held many fundraisers and raised $10,880. Nathan said, “We should have enough money to pay for the train tickets. There are about 50 students going on the trip and one round trip ticket costs about$200.
50 x 200 = 10,000.
so the total cost of the ticket is less than $10000. Thinking Habits Be a good thinker! These questions can help you. • What questions can I ask to understand people’s thinking? • Are there mistakes in other people’s thinking? • Can I improve other people’s thinking? Look Back! Critique Reasoning What argument would you make to support Nathan’s estimate? Visual Learning Bridge Essential Question How Can You Critique Reasoning of Others? A. Ms. Lynch needs to ship 89 boxes. 47 boxes weigh 150 pounds each. Each of the other boxes weighs 210 pounds. Mia says that all 89 boxes can fit into one container. She reasons that 47 × 150 is less than 7,500 and 42 × 210 is a little more than 8,000, so the sum of their weights should be less than 15,400. What is Mia’s reasoning to support her estimate? Mia estimates the total weight of the lighter boxes and the total weight of the heavier boxes, then adds the two estimates. Here’s my thinking… B. How can I critique the reasoning of others? I can • ask questions for clarification. • decide if the strategy used makes sense. • look for flaws in estimates or calculations. C. Mia’s reasoning has flaws. She estimated that 42 × 210 is a little more than 8,000, but a better estimate is 9,000. She underestimated the products so her conclusion is not valid. The weight of the heavier boxes is 8,820 pounds. The weight of the lighter boxes is 7,050 pounds. The total weight is 15,870 pounds. The sum is greater than 15,400. Mia’s reasoning does not make sense. Convince Me! Critique Reasoning Raul states that one way to get the cargo under the weight limit is to remove two of the heavier boxes and one of the lighter boxes. How can you decide if Raul’s reasoning makes sense? Guided Practice Critique Reasoning A stadium has 58 sections of seats. There are 288 seats in each section. Mary estimated the total number of seats by multiplying 60 × 300. She concluded that the stadium has fewer than 18,000 seats. Question 1. What is Mary’s argument? How does she support it? Answer: Mary’s argument was correct. Explanation: In the above-given question, given that, A stadium has 58 sections of seats. There are 288 seats in each section. Mary estimated the total number of seats by multiplying 60 × 300. She concluded that the stadium has fewer than 18,000 seats. 58 x 288 = 16704. Question 2. Describe at least one thing you would do to critique Mary’s reasoning. Answer: Mary’s argument was correct. Explanation: In the above-given question, given that, A stadium has 58 sections of seats. There are 288 seats in each section. Mary estimated the total number of seats by multiplying 60 × 300. She concluded that the stadium has fewer than 18,000 seats. 58 x 288 = 16704. Question 3. Does Mary’s conclusion make sense? Explain. Answer: Mary’s argument was correct. Explanation: In the above-given question, given that, A stadium has 58 sections of seats. There are 288 seats in each section. Mary estimated the total number of seats by multiplying 60 × 300. She concluded that the stadium has fewer than 18,000 seats. 58 x 288 = 16704. Independent Practice Critique Reasoning An office manager has$10,000 to spend on new equipment. He planned to purchase 300 lamps for $72 each. He completed the calculations at the right and concluded that there would be plenty of money left to buy additional equipment. Question 4. What does the office manager do to support his thinking? Answer: Yes, he completed the calculations at the right and concluded that there would be plenty of money. Explanation: In the above-given question, given that, An office manager has$10,000 to spend on new equipment.
He planned to purchase 300 lamps for $72 each. 300 x 72 = 21,600. yes, he has enough money. Question 5. Describe how you could decide if the office manager’s calculation is reasonable. Answer: Yes, he completed the calculations at the right and concluded that there would be plenty of money. Explanation: In the above-given question, given that, An office manager has$10,000 to spend on new equipment.
He planned to purchase 300 lamps for $72 each. 300 x 72 = 21,600. yes, he has enough money. When you critique reasoning, you need to explain if the method used by another makes sense. Question 6. Does the office manager’s conclusion make sense? Explain. Answer: Yes, he completed the calculations at the right and concluded that there would be plenty of money. Explanation: In the above-given question, given that, An office manager has$10,000 to spend on new equipment.
He planned to purchase 300 lamps for $72 each. 300 x 72 = 21,600. yes, he has enough money. Problem Solving Performance Task Buying a Piano Over the summer Kathleen sold 1,092 jars of jam at outdoor markets. She made a$12 profit on each one. She wants to use the profits to buy the Ivory-5K piano. She said, “Since 1,000 × 12 = 12,000, and 1,092 is greater than 1,000, I know my profits add up to more than $12,000. So, I can buy the piano.” Question 7. Make Sense and Persevere Does it make sense for Kathleen to find an overestimate or an underestimate to decide if she has earned enough money? Why? Answer: Yes, she can make the Ivory panio. Explanation: In the above-given question, given that, Kathleen sold 1,092 jars of jam at outdoor markets. She made a$12 profit on each one.
1092 x 12 = 13,104.
She wants to use the profits to buy the Ivory-5K piano. She said, “Since 1,000 × 12 = 12,000, and 1,092 is greater than 1,000.
yes, she can make the Ivory patio.

Question 8.
Reasoning Should Kathleen use multiplication to estimate her total profits? Explain your reasoning.

Yes, she can make the total profits.

Explanation:
In the above-given question,
given that,
Kathleen sold 1,092 jars of jam at outdoor markets.
She made a $12 profit on each one. 1092 x 12 = 13,104. She wants to use the profits to buy the Ivory-5K piano. She said, “Since 1,000 × 12 = 12,000, and 1,092 is greater than 1,000. yes, she can make the total profits. When you critique reasoning, ask questions to help understand someone’s thinking. Question 9. Be Precise Is Kathleen’s estimate appropriate? Is her calculation correct? Explain. Answer: Question 10. Critique Reasoning Explain whether Kathleen’s conclusion is logical. How did you decide? If it is not logical, what can you do to improve her reasoning? Answer: ### Topic 3 Fluency Practice Activity Follow the path Solve each problem. Then follow multiples of 10 to shade a path from START to FINISH. You can only move up, down, right, or left. Answer: The multiples of 10 are 1, 10, 20, 5, 2, 30, 40, 50, 60, 70, 80, 90, and 100. Explanation: In the above-given question, given that, 53 x 20 = 1060. 70 x 89 = 6230. 84 x 40 = 3360. 60 x 90 = 5400. 10 x 570 = 5700. 80 x 14 = 1120. 50 x 30 = 1500. 70 x 12 = 840. 100 x 100 = 10000. Topic 3 Vocabulary Review Glossary Word List • expression • multiple • overestimate • partial products • power • underestimate • variable For each of these terms, give an example and a non-example. Answer: power of 10 = 200. multiple of 10 x 10 = 100. an expression with a variable an underestimate of 532 x 11 = 5852. Explanation: In the above-given question, given that, power of 10 = 200. multiple of 10 x 10 = 100. an expression with a variable an underestimate of 532 x 11 = 5852. Write always, sometimes, or never. Question 5. The sum of partial products is equal to the final product. Answer: Always the sum of partial products is equal to the final product. Explanation: In the above-given question, given that, the sum of partial products is equal to the final product. for example: 12 x 10 = 120. 10 + 2 = 12. so Always the sum of partial products is equal to the final product. Question 6. A multiple of a number is the power of the number. Answer: Sometimes a multiple of a number is a power of the number. Explanation: In the above-given question, given that, multiple of a number is a power of the number. for example: 2 x 2 = 4. Question 7. An underestimate results from rounding each factor to a greater number. Answer: Always an underestimate results from rounding each factor to a greater number. Explanation: In the above-given question, given that, An underestimate results from rounding each factor to a greater number. for example: 12.5 round the number to tenth. 12.6. Question 8. A power of a number is a multiple of the number. Answer: Yes, the power of a number is a multiple of the number. Explanation: In the above-given question, given that, power of a number is a multiple of the number. for example: 2 x 2 = 4. the square root of 2 is 4. Write T for true or F for false. Question 9. 642 × 12 = 642 tens + 1,284 ones Answer: The expression is false. Explanation: In the above-given question, given that, 642 x 12 = 7704. 642 + 1284 = 1926. so the expression is false. Question 10. 41 × 106 = 41,000,000 Answer: The expression is true. Explanation: In the above-given question, given that, 41 x 106. 41 x 10 x 10 x 10 x 10 x 10 x 10. 41000000. so the expression is true. Question 11. 80 × 103 = 8,000 Answer: The expression is false. Explanation: In the above-given question, given that, 80 × 103. 80 x 10 x 10 x 10. 80 x 1000. 80,000. so the expression is false. Question 12. Suppose both factors in a multiplication problem are multiples of 10. Explain why the number of zeros in the product may be different than the total number of zeros in the factors. Include an example. Answer: Topic 3 Reteaching Set A pages 81-84 Find 65 × 103. Look at the exponent for the power of 10. Annex that number of zeros to the other factor to find the product. Remember to look at the number of zeros or the exponent for the power of 10. Question 1. 12 × 104 Answer: The number of zeros is 4. Explanation: In the above-given question, given that, 12 × 104. 12 x 10000. 120000. Question 2. 100 × 815 Answer: The number of zeros is 2. Explanation: In the above-given question, given that, 100 x 815. 81500. so the number of zeros is 2. Question 3. 102 × 39 Answer: The number of zeros is 3900. Explanation: In the above-given question, given that, 102 × 39 100 x 39 = 3900. Question 4. 6,471 × 101 Answer: The number of zeros is 64710. Explanation: In the above-given question, given that, 6471 x 10. 64710. Set B pages 85-88 Estimate 37 × 88. Step 1 Round both factors. 37 is about 40 and 88 is about 90. Step 2 Multiply the rounded factors. 40 × 90 = 3,600 Remember to either round the factors or use compatible numbers. Estimate each product. Question 1. 7 × 396 Answer: 7 x 400 = 2800. Explanation: In the above-given question, given that, the two numbers are 7 and 396. 396 is equal to 400. 7 x 400 = 2800. Question 2. 17 × 63 Answer: 17 x 63 = 1071. Explanation: In the above-given question, given that, the two numbers are 17 and 63. 17 x 63 = 1071. Question 3. 91 × 51 Answer: 90 x 50 = 4500. Explanation: In the above-given question, given that, the two numbers are 91 and 51. 91 is equal to 90. 51 is equal to 50. 90 x 50 = 4500. Question 4. 45 × 806 Answer: 45 x 806 = 36000. Explanation: In the above-given question, given that, the two numbers are 45 and 806. 806 is equal to 800. 45 x 800 = 36000. Set C pages 89-92 Think: 4 × 9 ones = 36; 36 is 3 tens 6 ones. 4 × 4 tens = 16 tens; 16 tens + 3 tens = 19 tens; 19 tens is 1 hundred 9 tens. 4 × 2 hundreds = 8 hundreds; 8 hundreds + 1 hundred = 9 hundreds Remember to keep track of the place values. Find each product. Question 1. 133 × 3 Answer: 133 x 3 = 399. Explanation: In the above-given question, given that, the two numbers are 133 and 3. multiply two numbers. 133 x 3 = 399. Question 2. 343 × 5 Answer: 343 x 5 = 1715. Explanation: In the above-given question, given that, the two numbers are 343 and 5. multiply two numbers. 343 x 5 = 1715. Question 3. 893 × 7 Answer: 893 x 7 = 6251. Explanation: In the above-given question, given that, the two numbers are 893 and 7. multiply two numbers. 893 x 7 = 6151. Question 4. 1,278 × 4 Answer: 1278 x 4 = 5112. Explanation: In the above-given question, given that, the two numbers are 1278 and 4. multiply two numbers. 1278 x 4 = 5112. Set D pages 93-96 Find 17 × 35. Remember that you can draw arrays or area models to represent multiplication. Find each product. Question 1. 21 × 13 Answer: 21 x 13 = 273. Explanation: In the above-given question, given that, the two numbers are 21 and 13. multiply two numbers. 21 x 13 = 273. Question 2. 34 × 52 Answer: 34 x 52 = 1768. Explanation: In the above-given question, given that, the two numbers are 34 and 52. multiply two numbers. 34 x 52 = 1768. Question 3. 89 × 27 Answer: 89 x 27 = 2403. Explanation: In the above-given question, given that, the two numbers are 89 and 27. multiply two numbers. 89 x 27 = 2403. Question 4. 78 × 47 Answer: 78 x 47 = 3666. Explanation: In the above-given question, given that, the two numbers are 78 and 47. multiply two numbers. 78 x 47 = 3666. Set E pages 97-100, 101-104, 105-108 Find 53 × 406. Estimate: 50 × 400 = 20,000 Remember to regroup if necessary. Estimate to check that your answer is reasonable. Find each product. Question 1. 54 × 9 Answer: 54 x 9 = 486. Explanation: In the above-given question, given that, the two numbers are 54 and 9. multiply two numbers. 54 x 9 = 486. Question 2. 76 × 59 Answer: 76 x 59 = 4484. Explanation: In the above-given question, given that, the two numbers are 76 and 59. multiply two numbers. 76 x 59 = 4484. Question 3. 47 × 302 Answer: 47 x 302 = 14194. Explanation: In the above-given question, given that, the two numbers are 47 and 302. multiply two numbers. 47 x 302 = 14194. Question 4. 32 × 871 Answer: 32 x 871 = 27,872. Explanation: In the above-given question, given that, the two numbers are 32 and 871. multiply two numbers. 32 x 871 = 27872. Question 5. Answer: 604 x 55 = 33,220. Explanation: In the above-given question, given that, the two numbers are 604 and 55. multiply two numbers. 604 x 55 = 33220. Question 6. Answer: 7133 x 4 = 28532. Explanation: In the above-given question, given that, the two numbers are 7133 and 4. multiply two numbers. 7133 x 4 = 28532. Set F pages 109-112 Draw a picture and write an equation. Solve. The length of James’s pool is 16 feet. The length of the pool at Wing Park is 4 times as long. How long is the pool at Wing Park? 16 × 4 = l l = 64 feet The length of Wing Park pool is 64 feet. Remember that pictures and equations can help you model and solve problems. Draw a picture and write an equation. Solve. Question 1. Alexandria has a collection of 34 dolls. A toy store has 15 times as many dolls as Alexandria. How many dolls are in the store? Answer: The number of dolls is in the store = 510. Explanation: In the above-given question, given that, Alexandria has a collection of 34 dolls. A toy store has 15 times as many dolls as Alexandria. 34 x 15 = 510. so the number of dolls are in the store = 510. Question 2. A store received a shipment of 37 TVs valued at$625 each. What is the total value of the shipment?

The total value of the shipment = $23,125. Explanation: In the above-given question, given that, A store received a shipment of 37 TVS valued at$625 each.
37 x $625 = 23,125. so the total value of the shipment =$23,125.

Set G
pages 113-116
Think about these questions to help you critique the reasoning of others.

Thinking Habits
• What questions can I ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?

Remember you need to carefully consider all parts of an argument.

Sarah has 214 bags of beads. Each bag has enough beads for 22 bracelets. She estimates that since 200 × 20 = 4,000, there are enough beads for at least 4,000 bracelets.
Tell how you can critique Sarah’s reasoning.

### Topic 3 Assessment Practice

Question 1.
Dr. Peterson works 178 hours each month. How many hours does she work in a year?
A. 2,000
B. 2,136
C. 3,000
D. 2,200

The number of hours does she work in a year = 2136.

Explanation:
In the above-given question,
given that,
Dr. Peterson works 178 hours each month.
1 year = 365 days.
1 week = 7 days.
12 x 178 = 2136.
so option B is the correct.

Question 2.
A banana contains 105 calories. Last week, Brendan and Lea ate a total of 14 bananas. How many calories does this represent?

The number of calories does this represent = 1470 calories.

Explanation:
In the above-given question,
given that,
A banana contains 105 calories.
Last week, Brendan and Lea ate a total of 14 bananas.
105 x 14 = 1470 calories.
so the number of calories does this represent = 1470.

Question 3.
At a warehouse, 127 delivery trucks were loaded with 48 packages on each truck.
A. Estimate the total number of packages on the trucks. Write an equation to model your work.
B. Did you calculate an overestimate or an underestimate? Explain how you know.

The total number of packages on the trucks = 6096 trucks.

Explanation:
In the above-given question,
given that,
At a warehouse, 127 delivery trucks were loaded with 48 packages on each truck.
127 x 48 = 6096.
so the total number of packages on the trucks = 6096.

Question 4.
Is the equation below correct? Explain.
5.6 × 103 = 560
A. The equation is incorrect. The product should have 3 zeros.
B. The equation is correct. The product should have 1 zero.
C. The equation is incorrect. The product should have 0 zeros.
D. The equation is incorrect. The product should have 2 zeros.

Option A is correct.

Explanation:
In the above-given question,
given that,
5.6 × 103 = 560.
5.6 = 560.
560 x 1000 = 560000.
so option A is correct.

Question 5.
The latest mystery novel costs $24. The table shows the sales of this novel by a bookstore. A. What was the dollar amount of sales of the mystery novel on Saturday? Write an equation to model your work. B. What was the dollar amount of sales of the mystery novel on Friday? Write an equation to model your work. Answer: A. The dollar amount of sales of the mystery novel on Saturday = 2472. B. The dollar amount of sales of the mystery novel on Friday = 3768. Explanation: In the above-given question, given that, The latest mystery novel costs$24.
98 books were sold on Thursday.
103 books were sold on Friday.
157 books were sold on Saturday.
116 books were sold on Sunday.
103 x 24 = 2472.
157 x 24 = 3768.

Question 6.
There are 45 cans of mi×ed nuts. Each can has 338 nuts. Below is Mary’s work to find the total number of nuts. What is the missing number? Enter your answer in the box.

The missing number is 5.

Explanation:
In the above-given question,
given that,
There are 45 cans of mi×ed nuts.
Each can have 338 nuts.
338 x 45 = 15210.
so the missing number is 5.

Question 7.
There are 36 large fish tanks at the zoo. Each tank holds 205 gallons of water. How many gallons of water would it take to fill all of the tanks?

The number of gallons of water would it take to fill all of the tanks = 7380 gallons.

Explanation:
In the above-given question,
given that,
There are 36 large fish tanks at the zoo.
Each tank holds 205 gallons of water.
205 x 36 = 7380.
so the number of gallons of water would it take to fill all of the tanks = 7380 gallons.

Question 8.
Kai ordered 1,012 baseball cards. Sharon ordered 5 times as many cards as Kai. Write and solve an equation to find b, the number of baseball cards Sharon ordered.

The number of baseball cards Sharon ordered = 5060 cards.

Explanation:
In the above-given question,
given that,
Kai ordered 1,012 baseball cards.
Sharon ordered 5 times as many cards as Kai.
1012 x 5 = 5060.
so the number of baseball cards Sharon ordered = 5060 cards.

Question 9.
Multiply

289 x 16 = 4624.

Explanation:
In the above-given question,
given that,
the two numbers are 289 x 16.
multiply the two numbers.
289 x 16 = 4624.

Question 10.
Match each number on the left with an equivalent expression.

12 x 100 = 1200.
120 = 12 x 10.
12 = 12 x 10.
12000 = 12 x 1000.

Explanation:
In the above-given question,
given that,
12 x 100 = 1200.
120 = 12 x 10.
12 = 12 x 10.

Question 11.
Select all the expressions that are equal to 3 × 103.
3 × 1,000
3 × 100
30 × 100
300 × 100
300 × 10

3 x 1000, 30 x 100, 300 x 10.

Explanation:
In the above-given question,
given that,
3 x 1000 = 3000.
30 x 100 = 3000.
300 x 10 = 3000.

Question 12.
Rosanne has 142 songs on her MP3 player. Teresa has 11 times as many songs as Rosanne. How many songs does Teresa have?

The number of songs does Teresa has = 1562 songs.

Explanation:
In the above-given question,
given that,
Rosanne has 142 songs on her MP3 player.
Teresa has 11 times as many songs as Rosanne.
142 x 11 = 1562 songs.
so the number of songs does Teresa has = 1562 songs.

### Topic 3 Performance Task

Baseball Apparel
Coach Sandberg wants to buy items for the baseball league. The league already has caps with the league logo on them, but the coach would like to offer the option of purchasing a T-shirt, sweatshirt, sweatpants, or jacket with the logo. Use the information in the table to answer the questions.

Question 1.
The players asked their families and friends if they want to buy T-shirts with the league logo. If 254 people want T-shirts, what would be the total cost? Write an equation to model your work.

The total cost is $3556. Explanation: In the above-given question, given that, The players asked their families and friends if they want to buy T-shirts with the league logo. If 254 people want T-shirts, 254 x$14 = 3556.
so the total cost is $3556. Question 2. Coach Sandberg wants to order 127 sweatshirts. Part A Will the total cost of the sweatshirts be greater than or less than$3,000? Use estimation to decide. Explain your reasoning.
Part B
What is the total cost of 127 sweatshirts?

The total cost of 127 sweatshirts = $4064. Explanation: In the above-given question, given that, the cost of sweatshirts =$32.
127 x $32 =$4064.
so the total cost of 127 sweatshirts = $4064. Question 3. Which would cost more, 32 T-shirts or 14 sweatshirts? How can you tell without multiplying? Answer: The two items cost the same. Explanation: In the above-given question, given that, the cost of the T-shirts =$14.
cost of  sweatshirts = $32. 32 x 14 =$448.
14 x 32 = $448. so the two items cost the same. Question 4. There are 18 × 101 players in the league. Part A The league raised$1,560 through fundraisers. Trenton estimates the cost of buying jackets for each player in the league. He concludes that the league has raised enough money. Do you agree with Trenton? Explain.

Yes, I agree with it.

Explanation:
In the above-given question,
given that,
The league raised $1,560 through fundraisers. Trenton estimates the cost of buying jackets for each player in the league. 200 x 50 = 1000. so I agree with it. Part B How much would it cost to order sweatpants for each player? Write and solve an equation with a variable to show your work. Answer: The cost to order sweatpants for each player = Explanation: In the above-given question, given that,$24

Question 5.
Which costs more: 136 sweatpants or 103 sweatshirts? How much more?

The more is 32.

Explanation:
In the above-given question,
given that,
136 x $24 =$3264.
103 x $32 = 3296. 3296 – 3264 = 32. Question 6. Coach Sandberg wants to order 115 jackets and 27 caps for$12 each.
Part A
Estimate the total cost for his order. Show your work.
Part B
What is his total cost? Compare your answer to your estimate.

The total cost is $439. Explanation: In the above-given question, given that, Coach Sandberg wants to order 115 jackets and 27 caps for$12 each.
27 x 12 = $324.$324 + 115 = 439.