Download Divide Decimals by Whole Numbers

Name
4.2
?
Divide Decimals
by Whole Numbers
Essential Question
Number and
Operations—5.3.F
MATHEMATICAL PROCESSES
5.1.C, 5.1.G
How can you use a model to divide a decimal by a whole number?
Hands
On
Investigate
Investigate
Materials ■ decimal models ■ color pencils
Angela has enough wood to make a picture frame with a perimeter of 2.4 meters.
She wants the frame to be a square. What will be the length of each side of the frame?
A. Shade decimal models to show 2.4.
B. You need to share your model among _ equal groups.
C. Since 2 wholes cannot be shared among 4 groups without
regrouping, cut your model apart to show the tenths.
There are _ tenths in 2.4.
Share the tenths equally among the 4 groups.
There are _ ones and _ tenths in each group.
Write a decimal for the amount in each group. _
D. Use your model to complete the number sentence.
2.4 ÷ 4 = _
So, the length of each side of the frame will be _ meter.
Draw Conclusions
1. You can also use area models to represent division. Shade the area
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model below and circle groups to show 2.4 ÷ 4.
Math Talk
Mathematical Processes
What other manipulatives or
models could you use to
solve this problem?
Module 4
161
Make
Make Connections
Connections
You can also use base-ten blocks to model division of a decimal
by a whole number.
Hands
On
Materials ■ base-ten blocks
Kyle has a roll of ribbon 3.21 yards long. He cuts the ribbon
into 3 equal lengths. How long is each piece of ribbon?
Divide. 3.21 ÷ 3
STEP 1
Use base-ten blocks to show 3.21.
Remember that a flat represents one, a long represents
one tenth, and a small cube represents one hundredth.
There are _ one(s), _ tenth(s), and
_ hundredth(s).
STEP 2 Share the ones.
Share an equal number of ones among 3 groups.
There is _ one(s) shared in each group and _
one(s) left over.
STEP 3 Share the tenths.
Two tenths cannot be shared among 3 groups
without regrouping. Regroup the tenths by replacing
them with hundredths.
There are _ tenth(s) shared in each group and
_ tenth(s) left over.
There are now _ hundredth(s).
STEP 4 Share the hundredths.
There are _ hundredth(s) shared in each group
and _ hundredth(s) left over.
So, each piece of ribbon is __ yards long.
162
Math Talk
Mathematical Processes
Explain why your answer
makes sense.
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Share the 21 hundredths equally among the 3 groups.
Name
Share
Share and
and Show
Show
Use the model to complete the number sentence.
1. 1.6 ÷ 4 = __
2. 3.42 ÷ 3= __
Problem
Problem Solving
Solving
3.
What's the Error? Aida is
making banners from a roll of paper that
is 4.05 meters long. She will cut the paper
into 3 equal lengths. She uses base-ten
blocks to model how long each piece
will be. Describe Aida's error.
4. Multi-Step Sam can ride his bike 4.5 kilometers in 9 minutes, and
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Amanda can ride her bike 3.6 kilometers in 6 minutes. Which rider
might go farther in 1 minute?
5.
Explain how you can use inverse operations to find 1.8 ÷ 3.
Module 4 • Lesson 2 163
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
6. Multi-Step Yesterday, a bamboo plant was 12.62 yards tall. Today, the
bamboo had grown by 0.34 yard. Bryson chopped the bamboo into
6 equal pieces. How long was each piece?
A
21.6 yd
C
2.16 yd
B
0.216 yd
D
216 yd
7. Representations Terrance used base-ten blocks to help him divide a
decimal by 4. His model is shown. What division problem did he model?
A
1.26 ÷ 4
B
1.62 ÷ 4
C
6.48 ÷ 4
D
6.84 ÷ 4
8. Multi-Step Marvyn worked for 3 days. He earned $87.20 each day.
He uses his earnings to buy four chairs. If he has no money left over,
what is the cost of each chair?
A
$65.40
C
$116.27
B
$261.60
D
$21.80
TEXAS Test Prep
9. A bag of oranges costs $7.65. Five friends want to share the bag.
164
A
$38.25
C
$2.00
B
$1.53
D
$1.13
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How much will each friend pay?
H o mewo rk
and Practice
4.2
Number and Operations—5.3.F
MATHEMATICAL PROCESSES 5.1.C, 5.1.D
Name
Divide Decimals by Whole Numbers
Use the model to complete the number sentence.
1. 1.5 ÷ 3 = __
2. 2.48 ÷ 4 = __
3. 2.8 ÷ 4 = __
4. 3.54 ÷ 3 = __
5. Explain how you can use the whole number expression 248 ÷ 4 to check
that your answer to Exercise 2 is reasonable.
Problem
Problem Solving
Solving
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6. Mrs. Tillman builds furniture. She saws
a maple board that is 4.56 meters long into
4 equal lengths. She saws an oak board that is
3.69 meters long into 3 equal lengths. Which
is longer, a piece of oak or a piece of maple?
Explain.
7. Drew has a video game with five different
challenges. He sets the timer to play his game
for 10.75 minutes. He spends the same amount
of time playing each challenge. How long does
Drew play the fifth challenge?
Module 4 • Lesson 2 165
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
side of her garden. The length of the border is
3.6 meters. If she uses 9 concrete blocks, what
is the length of 1 block?
A
0.3 meter
B
0.9 meter
C
0.04 meter
D
0.4 meter
10. The base-ten blocks pictured below show
Carter’s solution to a division expression.
Which expression did Carter solve?
A
2.84 ÷ 4
B
0.71 ÷ 4
C
2.48 ÷ 4
D
7.1 ÷ 4
12. Multi-Step Mrs. Gonzales decorates the
perimeter of her rectangular bulletin board
with ribbon. She cuts a ribbon 3.72 yards long
in half to decorate the top and the bottom. She
cuts a ribbon 2.6 yards long in half to decorate
the two sides. How much shorter is one side
ribbon than the top ribbon?
166
A
0.56 yard
B
0.5 yard
C
0.66 yard
D
0.6 yard
9. Max used base-ten blocks to solve the division
problem 12.15 ÷ 3. Which set of blocks shows
the quotient for 12.15 ÷ 3?
A
4 ones, 5 tenths, 0 hundredths
B
4 ones, 0 tenths, 5 hundredths
C
0 ones, 4 tenths, 5 hundredths
D
5 ones, 0 tenths, 4 hundredths
11. Mr. Jefferson gives his two children $5.46
to spend at the garage sale. If they split the
money evenly, how much will each child have
to spend?
A
$1.82
B
$1.23
C
$2.23
D
$2.73
13. Multi-Step Tamika bought 6 fish at the pet
store for a total of $7.26. If two of the fish
together cost $4.10, and each of the other four
fish had the same cost, how much was each
remaining fish?
A
$1.21
B
$2.05
C
$0.79
D
$3.16
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8. Karina places concrete blocks along one