Lesson 1.8
Name
Relate Multiplication to Division
Essential Question How is multiplication used to solve a division problem?
You can use the relationship between multiplication and division to
solve a division problem. Using the same numbers, multiplication
and division are opposite, or inverse operations.
×
3
factor
8
factor
=
24
24
product
dividend
÷
3
=
divisor
Number and Operations in Base
Ten—5.NBT.B.6
MATHEMATICAL PRACTICES
MP2, MP6, MP7
8
quotient
Unlock
Unlock the
the Problem
Problem
Joel and 5 friends collected 126 marbles. They
shared the marbles equally. How many marbles
will each person get?
• Underline the dividend.
• What is the divisor? _
One Way Make an array.
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• Outline a rectangular array on the grid to model
126 squares arranged in 6 rows of the same length.
Shade each row a different color.
• How many squares are shaded in each row? _
• Use the array to complete the multiplication
sentence. Then, use the multiplication sentence
to complete the division sentence.
6 × _ = 126
126 ÷ 6 = _
So, each of the 6 friends will get _ marbles.
Chapter 1
49
Another Way Use the Distributive Property.
Divide. 52 ÷ 4
You can use the Distributive Property and an area model to solve
division problems. Remember that the Distributive Property states
that multiplying a sum by a number is the same as multiplying each
addend in the sum by the number and then adding the products.
STEP 1
?
Write a related multiplication sentence for
the division problem.
Think: Use the divisor as a factor and the dividend as
the product. The quotient will be the unknown factor.
4
52
52 ÷ 4 = ■
4 3 ? 5 52
4 × ■ = 52
STEP 2
Use the Distributive Property to break apart
the large area into smaller areas for partial
products that you know.
(
40
(4
×
+
_ ) + (4
12
) = 52
×
_ ) = 52
4
?
?
40
12
(4 3 ?) 1 (4 3 ?) 5 52
STEP 3
STEP 4
Find the sum of the unknown factors of the
smaller areas.
Write the multiplication sentence with the
unknown factor that you found. Then, use the
multiplication sentence to find the quotient.
_+_=_
4 × _ = 52
•
MATHEMATICAL
PRACTICE
6 Explain how you can use the Distributive Property to find
the quotient of 96 ÷ 8.
50
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52 ÷ 4 = _
Name
Share
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Share and
and Show
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MATH
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B
1. Brad has 72 toy cars that he puts into 4 equal groups. How many cars
does Brad have in each group? Use the array to show your answer.
4 × _ = 72
72 ÷ 4 = _
Use multiplication and the Distributive Property to find the quotient.
2. 108 ÷ 6 = _
3. 84 ÷ 6 = _
4. 184 ÷ 8 = _
____
____
____
____
____
____
Math
Talk
MATHEMATICAL PRACTICES 7
Look for Structure How
does using multiplication
help you solve a division
problem?
On
On Your
Your Own
Own
Use multiplication and the Distributive Property to find the quotient.
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5. 60 ÷ 4 = _
6. 144 ÷ 6 = _
7. 252 ÷ 9 = _
____
____
____
____
____
____
SMARTER
8. 51 ÷ 3
Find each quotient. Then compare. Write <, >, or =.
● 68 ÷ 4
_
_
9. 252 ÷ 6
_
● 135 ÷ 3
_
10. 110 ÷ 5
_
● 133 ÷ 7
_
Chapter 1 • Lesson 8 51
MATHEMATICAL PRACTICES
COMMUNICA5&t1&34E7&3&tCONSTRUCT ARGUMENTS
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Use the table to solve 11–12.
11.
SMARTER
Mr. Henderson has
2 bouncy-ball vending machines. He buys
one bag of the 27-millimeter balls and one
bag of the 40-millimeter balls. He puts an equal
number of each in the 2 machines. How many
bouncy balls does he put in each machine?
Bouncy Balls
Size
Number in Bag
27 mm
180
40 mm
80
45 mm
180
mm 5 millimeters
12.
13.
DEEPER
Lindsey buys a bag of each size of
bouncy ball. She wants to put the same number
of each size of bouncy ball into 5 party-favor
bags. How many of each size of bouncy ball will
she put in a bag?
MATHEMATICAL
PRACTICE
3 Verify the Reasoning of
WRITE
Math t Show Your Work
Others Sandra writes (4 × 30) + (4 × 2) and
says the quotient for 128 ÷ 4 is 8. Is she correct?
Explain.
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SMARTER
Joe collected
45 seashells. Joe wants to share his seashells
with 5 of his friends equally. How many
seashells will each friend get? Use the array to
show your answer.
Use the multiplication sentence to complete
the division sentence.
5×
52
= 45
45 ÷ 5 =
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14.
Practice and Homework
Name
Lesson 1.8
Relate Multiplication to Division
Common Core Standard—5.NBT.B.6
Perform operations with multi-digit whole
numbers and with decimals to hundredths.
Use multiplication and the Distributive Property to find the quotient.
14
1. 70 ÷ 5 = ___
2. 96 ÷ 6 = ___
3. 85 ÷ 5 = ___
(5 × 10) + (5 × 4) = 70
____
____
____
5 × 14 = 70
____
____
____
4. 171 ÷ 9 = ___
5. 102 ÷ 6 = ___
6. 210 ÷ 5 = ___
____
____
____
____
____
____
Problem
Problem Solving
Solving
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7. Ken is making gift bags for a party. He has 64
colored pens and wants to put the same number
in each bag. How many bags will Ken make if he
puts 4 pens in each bag?
9.
WRITE
8. Maritza is buying wheels for her skateboard
shop. She ordered a total of 92 wheels. If wheels
come in packages of 4, how many packages will
she receive?
Math For the problem 135 ÷ 5, draw
two different ways to break apart the array. Use
the Distributive Property to write products for
each different way.
Chapter 1
53
Lesson Check (5.NBT.B.6)
1. Write an expression using the Distributive
Property that can be used to find the
quotient of 36 ÷ 3.
2. Write an expression using the Distributive
Property that can be used to find the
quotient of 126 ÷ 7.
Spiral Review (4.OA.A.3, 5.NBT.A.1, 5.NBT.A.2)
4. A website had 2,135,789 hits. What is the value
of the digit 3?
5. The area of Arizona is 114,006 square miles.
What is the expanded form of this number?
6. What is the value of the fourth power of ten?
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3. Allison separates 23 stickers into 4 equal piles.
How many stickers does she have left over?
FOR MORE PRACTICE
GO TO THE
54
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