Develop Skills and Strategies
Lesson 9
Part 1: Introduction
CCSS
5.NBT.B.7
Divide Decimals
Now that you know how to multiply with decimals, you’ll learn how to divide with
decimals. Take a look at this problem.
Mr. Kovich is preparing materials for a craft project. He has 2 meters of string and
needs to cut it into pieces that are 0.2 meter long. How many 0.2-meter pieces can
he cut from 2 meters of string?
Explore It
Use the math you already know to solve the problem.
You need to find how many groups of 0.2 meter are in 2 meters. Look at the
drawing below.
2 meters
0
1
2
How many tenths of a meter are in 1 meter? In 2 meters? Circle groups of 2 tenths. How many groups of 2 tenths are in 1 meter? In 2 meters? Explain how you could find how many 0.2-meter pieces can be cut from 2 meters
of string.
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L9: Divide Decimals
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Part 1: Introduction
Lesson 9
Find Out More
On the previous page, you saw that 2 4 0.2 5 10. Notice that the digits are the same as
in 2 4 2 5 1.0, but the quotients differ by a factor of 10.
Look at the table below to see some patterns.
Expression
242
2 4 0.2
2 4 0.02
Expression in words
How many groups of 2 are in 2?
How many groups of 0.2 are in 2?
How many groups of 0.02 are in 2?
Quotient
1
10
100
When the divisor is greater than 1, the quotient is less than the dividend. When the
divisor is less than 1, the quotient is greater than the dividend.
Reflect
1 Look at the table above. What do you think 2 4 0.002 equals? Explain your reasoning.
L9: Divide Decimals
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Part 2: Modeled Instruction
Lesson 9
Read the problem below. Then explore different ways to understand dividing a
decimal by a whole number.
Coach Ann is setting up a 2.7-kilometer race. She uses flags to mark off 9 equal
sections of the race. How far apart should she space the flags to mark off the
sections?
Picture It
You can draw a bar model to represent the problem.
You know the number of kilometers to be divided into equal groups and the number of
groups.
2.7 kilometers
?
Model It
You can use the relationship between multiplication and division to understand
the problem.
To find 2.7 4 9, think 9 3 ? 5 2.7.
2.7 5 27 tenths
9 3 ? = 27 tenths
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L9: Divide Decimals
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Part 2: Guided Instruction
Lesson 9
Connect It
Now use your understanding of division and place value to solve the problem.
2 Look at Picture It. Why is the bar divided into 9 equal parts?
What do you need to find? 3 Look at Model It. How does the division expression 2.7 4 9 relate to the bar model?
4 Explain how you know that 2.7 5 27 tenths.
5 How far apart should Coach Ann space the flags? tenths of a kilometer.
Write that answer as a decimal: of a kilometer
6 Explain how you could divide a decimal by a whole number.
Try It
Use what you have learned about dividing a decimal by a whole number to solve
these problems. Show your work on a separate sheet of paper.
7 How much will each person receive if $20.35 is split equally among 5 people? 8 What is 0.99 4 11? L9: Divide Decimals
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Part 3: Modeled Instruction
Lesson 9
Read the problem below. Then explore different ways to divide by tenths.
Grant has 3.6 pounds of pretzels. He puts the pretzels into bags that can each hold
0.3 pound. How many bags does Grant use to hold the pretzels?
Picture It
You can picture dividing by tenths with decimal grids.
Each large square represents 1 pound of pretzels.
You know the amount to be shared equally and the size of each group.
Model It
You can use the relationship between multiplication and division to understand
the problem.
To find 3.6 4 0.3, think 0.3 3 ? 5 3.6.
3.6 5 36 tenths
Use words to describe the problem situation:
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3 tenths 3 ? 5 36 tenths
L9: Divide Decimals
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Part 3: Guided Instruction
Lesson 9
Connect It
Now use your understanding of division and place value to solve the problem.
9 Look at Picture It. How do you decide what to shade?
10 Why are the columns in the grids separated into groups of 3?
11 Look at Model It. How do you know this is a division problem?
12 Explain why 3.6 5 36 tenths. 13 Both Picture It and Model It tell me that Grant uses bags of pretzels.
14 Explain how to divide tenths by tenths. Try It
Use what you have learned about dividing by tenths to solve these problems.
Show your work on a separate sheet of paper.
15 How many dimes are there in a jar of dimes worth $2.70? 16 What is 42 4 0.7? L9: Divide Decimals
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Part 4: Modeled Instruction
Lesson 9
Read the problem below. Then explore different ways to divide by hundredths.
Fiona has $1.20 with which to buy some elastic tape. The elastic tape is on sale for
$0.08 per foot. How many feet of elastic tape can Fiona buy?
Picture It
You can picture the division problem using a bar model.
You know the total amount of money and the size of one group.
$1.20
?
$0.08
Model It
You can use the relationship between multiplication and division to understand
the problem.
To find 1.20 4 0.08, think 0.08 3 ? 5 1.20.
1.20 5 120 hundredths
Use words:
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8 hundredths 3 ? 5 120 hundredths
L9: Divide Decimals
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Part 4: Guided Instruction
Lesson 9
Connect It
Use your understanding of division and place value to solve the problem.
17 Look at Picture It. What are you trying to find in this problem?
18 What operation will solve this problem? How do you know?
19 Explain why 1.20 5 120 hundredths. 20 Write a division expression for the situation. 21 How many feet of elastic tape can Fiona buy? Show your work.
22 Check your answer using the decimals in a multiplication equation:
feet of elastic tape 3 $ 5 $ Fiona can buy feet of elastic tape.
23 Explain how to divide by a decimal in the hundredths. Try It
Use what you have learned about dividing by hundredths to solve these problems.
Show your work on a separate sheet of paper.
24 How many quarters are in a jar of quarters worth $9.75? 25 What is 16 4 0.16? L9: Divide Decimals
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Part 5: Guided Practice
Lesson 9
Study the model below. Then solve problems 26–28.
Student Model
The student wrote a
related multiplication
equation to solve the
problem.
Nancy used 2.5 gallons of gas to drive 35 miles. How many miles
per gallon did Nancy’s car get?
Look at how you could show your work using equations.
2.5 3
h 5 35
2.5 5 25 tenths, 35 5 350 tenths
25 3
h 5 350
350 4 25 5 14
Pair/Share
Can you solve the
problem in another way?
What is a good estimate
for your answer?
Nancy’s car got 14 miles per gallon.
Solution: 14 miles per gallon
26 What number multiplied by 8 will give a product of 9.6? Write an
equation and solve.
Show your work.
Pair/Share
How could you model
this problem with a
number line?
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Solution: L9: Divide Decimals
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Part 5: Guided Practice
27 The width of a math textbook is 0.75 inches. How many math
textbooks can be placed standing up on a shelf that is 18 inches
wide?
Lesson 9
Will the answer be greater
or less than 18?
Show your work.
Pair/Share
Solution: 28 What is 6.5 4 0.5? Circle the letter of the correct answer.
A3.25
Explain how you
decided what operation
to use to solve the
problem.
I could draw a model to
represent this problem.
B6
C7
D13
Gwen chose A as the correct answer. How did she get that answer?
L9: Divide Decimals
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Pair/Share
Does Gwen’s answer
make sense?
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Part 6: Common Core Practice
Lesson 9
Solve the problems.
1
Jordan has $20 to spend at the used book store. Each book costs $2.85. How many books can
Jordan buy?
A4
B5
C6
D7
2
3
Keith bought 3.4 pounds of peanuts on Monday, 2.5 pounds on Tuesday, and 4 pounds on
Wednesday. He is going to divide them equally among himself and two friends. How many
pounds of peanuts will each friend get?
A
99 pounds
B
33 pounds
C
9.9 pounds
D
3.3 pounds
A sticker is 1.2 centimeters wide. How many stickers will fit edge to edge on a strip of paper
that is 108 centimeters long?
stickers
4
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If you put 0.7 on the blank for each equation below, will it make the equation true? Select Yes
or No for each equation.
A______ 3 5.2 5 36.4 Yes
No
B49 4 ______ 5 70
Yes
No
C______ 4 3.5 5 0.02 Yes
No
D9.1 3 ______ 5 13
Yes
No
L9: Divide Decimals
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Part 6: Common Core Practice
5
Lesson 9
Jamie has 5 jars to fill with beads for a carnival game. She has 7.5 cups of multi-colored beads.
How many cups of beads can she place into each jar?
Part A
Use pictures to solve the problem.
Answer cups
Part B
Justify your answer.
Self Check Go back and see what you can check off on the Self Check on page 1.
L9: Divide Decimals
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