Lesson 2.

7
Name
Multiply Using Partial Products Number and Operations in Base
Essential Question How can you use place value and partial products to Ten—4.NBT.B.5
multiply by a 1-digit number? MATHEMATICAL PRACTICES
MP1, MP7

Unlock
Unlock the
the Problem
Problem
connect How can you use what you know about the • How can you write 182 as a sum
Distributive Property to break apart numbers to find of hundreds, tens, and ones?
products of 3-digit and 1-digit numbers?

Use place value and partial products.

Multiply. 6 × 182 Estimate. 6 × 200 = __

SHADE THE MODEL THINK AND RECORD

STEP 1
100 80 2 182
× 6
_
Multiply the hundreds.
6 ←
6 × 1 hundred = 6 hundreds

STEP 2 100 80 2 182

× 6
_
600
6 Multiply the tens.
←
6 × 8 tens = 48 tens

STEP 3 100 80 2 182

× 6
_
600
6 480
Multiply the ones.
←
6 × 2 ones = 12 ones

STEP 4 100 80 2 182

× 6
_
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600
6 480
+ 12
__
← Add the partial products.

So, 6 × 182 = 1,092. Since 1,092 is close to the Math MATHEMATICAL PRACTICES 2
estimate of 1,200, it is reasonable. Talk
Use Reasoning How can
you use the Distributive
Property to find 4 × 257?

Chapter 2 99
 Example
Use place value and partial products.

Multiply. 2 × 4,572 Estimate. 2 × 5,000 = __

4,572
×
__ 2
← 2 × 4 thousands = 8 thousands
← 2 × 5 hundreds = 1 thousand
← 2 × 7 tens = 1 hundred, 4 tens
← 2 × 2 ones = 4 ones
+
← Add the partial products.

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and Show
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Sh BOARD
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1. Use the model to find 2 × 137.

100 30 7 137
× 2
_
2

Estimate. Then record the product.

2. Estimate: __ 3. Estimate: __ 4. Estimate: __

190 471 $3,439

×
__ 3 ×
__ 4 ×
___ 7
© Houghton Mifflin Harcourt Publishing Company

+ +
+

Math MATHEMATICAL PRACTICES 6

Talk
Explain how using place
value and expanded form
makes it easier to find
products.
100
 Name

On
On Your
Your Own
Own
Estimate. Then record the product.

5. Estimate: __ 6. Estimate: __ 7. Estimate: __

$53 $473 608

×
__ 4 ×
__ 9 ×
__ 6

+
+ +

Practice: Copy and Solve Estimate. Then record the product.

8. 2 × 78 9. 2 × $210 10. 9 × $682 11. 8 × 8,145

MATHEMATICAL
PRACTICE 2 Use Reasoning Algebra Find the missing digit.

12. 5 13. 248 14. $395 15. 3,748

×
__ 7 × 3
__ ×
___ ×
___ 4
455 44 $2,370 1 ,992

16. DEEPER
A store bought 9 cases of light 17. DEEPER Mr. Wilson saved $2,500 to buy
bulbs in May and 8 cases in June. There are airline tickets for his family. He bought
48 light bulbs in a case. How many light 6 airline tickets for $372 each. How much
bulbs did the store buy in May and June? of his savings does Mr. Wilson have after he
buys the tickets?
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18. DEEPER
Coach Ramirez bought 8 cases of bottled water for a road
race. There are 24 bottles in each case. After the race, 34 bottles of
water were left. How many bottles were used at the race? Explain.

Chapter 2 • Lesson 7 101

 MATHEMATICAL PRACTICES
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19.
MATHEMATICAL
PRACTICE 4
Use Diagrams Look at the
picture. Kylie has 832 songs on her portable
media player. Lance has 3 times as many
songs. How many fewer songs can Lance
add to his player than Kylie can add to hers?

20. DEEPER James wants to buy the new

portable media player shown. He has
5 times as many songs as Susan. Susan has
1,146 songs. Will all of his songs fit on the
portable media player? How many songs
does James have?

WRITE Math
t Show Your Work

21. SMARTER
The sum of a WRITE Math
t Show Your Work
3-digit number and a 1-digit
number is 217. The product
of the numbers is 642. If one
number is between 200 and
225, what are the numbers?

22. SMARTER
Mrs. Jackson bought 6 gallons of juice for a
party. Each gallon has 16 cups. After the party, 3 cups of juice were
© Houghton Mifflin Harcourt Publishing Company

left over. At the party, how many cups did people drink? Show
your work and explain how you found your answer.

102
 Practice and Homework
Name
Lesson 2.7
Multiply Using Partial Products
COMMON CORE STANDARD—4.NBT.B.5
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Estimate. Then record the product.

1. Estimate: 1,200
_ 2. Estimate: _ 3. Estimate: _ 4. Estimate: _

243 640 $149 721

×
__ 6 ×
__ 3 ×
__ 5 ×
__ 8
1,200
240
+
__ 18
1,458

5. Estimate: _ 6. Estimate: _ 7. Estimate: _ 8. Estimate: _

293 $416 961 837

×
__ 4 ×
__ 6 ×
__ 2 × 9
__

Problem
Problem Solving
Solving

9. A maze at a county fair is made from 10. Pedro gets 8 hours of sleep each night. How
275 bales of hay. The maze at the state fair many hours does Pedro sleep in a year with
is made from 4 times as many bales of hay. 365 days?
How many bales of hay are used for the maze
at the state fair?
© Houghton Mifflin Harcourt Publishing Company

11. WRITE Math Explain how you can find 4 × 754 using two
different methods.

Chapter 2 103
Lesson Check (4.NBT.B.5)
1. A passenger jet flies at an average speed 2. Use the model to find 3 × 157.
of 548 miles per hour. At that speed, how 100 50 7
many miles does the plane travel in
4 hours?
3

Spiral Review (4.NBT.A.2, 4.NBT.B.4, 4.NBT.B.5)

3. The school fun fair made $1,768 on games 4. Use the table below.
and $978 on food sales. How much money
State Population
did the fun fair make on games and food
sales? North Dakota 646,844
Alaska 698,473
Vermont 621,760

List the states from least to greatest

population.

5. A National Park covers 218,375 acres. What 6. Last year a business had profits of $8,000.
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is this number written in expanded form? This year its profits are 5 times as great.
What are this year’s profits?

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