Name
Multiplying a Fraction
and a Whole Number
Find 12 12 1
.
4
3
3
of 15, or
15.
5
5
1
15 5 3, so
15 3.
5
1
3
Since
is 3 times ,
5
5
3
1
15 3 15 3 3 9.
5
5
3
15 9
5
Find
1
is the same as dividing
4
12 by 4.
(
12 4 3
12 R 5-1
1
3
4
)
Find each product.
1.
4
5
20 2.
6
7
4.
2
5
of 15 5. 400 38 of 14 3. 24 34 6.
7
1
0
of 80 7. Reasoning Can you use division and mental math to find 32 of 24?
Why or why not?
The chart shows the average high temperatures for different months
in Phoenix, Arizona.
Phoenix Weather
Average High
February
May
July
70°F
93°F
105°F
8. What is 45 the average temperature in July?
9. What is 12 the average temperature in February?
10. What is 23 the average temperature in May?
54
Use with Lesson 5-1.
© Pearson Education, Inc. 6
Month
Name
Multiplying Fractions
R 5-2
Find 34 27.
One Way
Draw a picture. Simplify if
possible.
2
7
Another Way
Simplify First
Multiply the numerators
and denominators.
Simplify if possible.
Find the GCF of any
numerator and any
denominator.
3 2
4 7
6
32
4 7 28
3
14
The GCF of 2 and 4 is 2.
Divide 2 and 4 by the GCF.
1
2
3
3
7
4
14
2
3
4
6 of the 28 squares have
overlapping shading.
2
3
6
So, .
7 28
4
3
6
Simplify
to .
14
28
Write an equation for each picture.
1.
2.
© Pearson Education, Inc. 6
Find each product. Simplify if possible.
3.
6
8
13 4.
5
6
17
0 5.
4
5
38 6.
1
2
49 7. Number Sense Can you simplify before multiplying 14 2257? Explain.
Use with Lesson 5-2.
55
Name
Estimating with Fractions and
Mixed Numbers
Estimate 5 1 23 5 using
8
6
rounding and compatible numbers.
5
1
5
23
8
6
5 24
Round each mixed
number to the nearest
whole number.
4 25 is easier to
multiply than 5 24.
4 25 100
5
1
5 23 100
6
8
R 5-3
8
1
3 using
9
7
rounding and compatible numbers.
Estimate 17
17
1
8
3
7
9
17 4
Round each mixed
number to the nearest
whole number.
Use compatible
numbers to divide.
16 4 4
17
8
1
3 4
9
8
Estimate each product or quotient.
1.
6
7
12
2. 25 4 23
3. 3 89 7 34
1
4. 19 112
5 5 4
5. 2 15 36
6. 39 7 23
7. 12 18 2 19
0
8. 35 45 5 78
9.
15
16
62
10. 48 79 923
© Pearson Education, Inc. 6
11. Writing in Math Explain how you would estimate 3 65 29 54 using
compatible numbers.
56
Use with Lesson 5-3.
Name
Multiplying Mixed Numbers
R 5-4
How to find the product of two mixed numbers:
Find 323 412.
Step 1
Estimate by rounding.
3
2
1
4
3
2
4 5 20
Step 2
Look for common
factors and simplify.
3
3
11
11
9
2
3
1
2
1
Multiply. Write the product
as a mixed number.
11
33
3
1
16
1
2
2
2
1
16 2 is close to 20, so the
Then write each mixed
number as an improper
fraction.
3
Step 3
answer is reasonable.
1
2
4
2
3
9
11
2
3
Find each product. Simplify if possible.
1. 2 34 3 12 2. 2 15 2 23 3. 6 3 14 4. 1 25 3 14 5. 4 12 16 6. 1 38 2 12 © Pearson Education, Inc. 6
7. Number Sense Is 2 17 65 greater than or less than 36? Explain.
Use with Lesson 5-4.
57
Name
PROBLEM-SOLVING STRATEGY
R 5-5
Make an Organized List
Standing in Line How many different ways can Jose, Sumi, and Tina
be arranged in a straight line?
Read and Understand
Step 1: What do you know?
Step 2: What are you trying to find?
There are 3 different people who must be
arranged in a straight line: Jose, Sumi, and Tina.
How many different ways they can be arranged?
Plan and Solve
Step 3: What strategy will you
use?
Strategy: Make an organized list
Jose first
Jose, Sumi, Tina
Jose, Tina, Sumi
Sumi first
Sumi, Jose, Tina
Sumi, Tina, Jose
Tina first
Tina, Jose, Sumi
Tina, Sumi, Jose
Answer: The students can be arranged 6 different ways.
Look Back and Check
Is your answer reasonable? Yes, no combinations are repeated.
2
2369
2396
2_93
263_
58
Use with Lesson 5-5.
3
6
9
3269
6239
9236
© Pearson Education, Inc. 6
1. How many different four-digit combinations can be made using the
digits 2, 3, 6, and 9? No digit combinations can be repeated.
Complete the chart.
Name
Dividing Fractions
R 5-6
Dividing by a fraction is the same as multiplying by its reciprocal.
The product of a number and its reciprocal is 1. For example:
Number
Reciprocal
Product
3
1
1
8
2
3
1
3
8
1
3
2
1
1
Find 45 13
0.
Step 1
Step 2
Rewrite the problem as
a multiplication problem.
Rewrite the divisor as
its reciprocal.
Simplify if possible.
Multiply. If your answer
is an improper fraction,
change it to a mixed
number.
2
The reciprocal
of 3 is 10.
3
10
8
10
4
3
3
5
4
10
5
3
8
2
2
3
3
1
Write the reciprocal of each fraction or number.
1.
2
5
2.
3. 9
1
7
4. 15
Find each quotient. Simplify if possible.
© Pearson Education, Inc. 6
5. 6 14 6.
2
3
12 10 8.
1
3
89 9. 12 38 10.
7
1
0
12.
5
8
7.
11.
4
5
11
12
13 34 6
13. Marcus is making tea for his friends. He has 6 tbsp of honey. If he puts
1
2 tbsp of honey in each cup of tea, how many cups can he make?
Use with Lesson 5-6.
59
Name
Dividing Mixed Numbers
R 5-7
You can follow these steps to find 513 113 and 21 213.
Step 1
Step 2
Step 3
First estimate.
Then write each number
as an improper fraction.
Find the reciprocal of
the divisor. Rewrite
as a multiplication
problem.
Look for common
factors. Simplify,
then multiply.
1
1
1 .
3
3
Estimate 5 1 5.
4
16
3
3
16
3
3
4
16
3
3
4
Find 5
5
1
1
1 3
3
21 2
1
3
1
1
1
4 is close to 5,
so the answer is
reasonable.
16
4
3
3
Find 21 2 1 .
3
1
Estimate 21 2 10 .
2
4
16
3
4
4
3
4
1
21
7
1
3
21
3
1
7
21
7
1
3
21
3
1
7
3
9
21
3
9
1
1
7
1
1
9 is close to 10 ,
2
so the answer is
reasonable.
1. 2 23 3 14 2. 1 34 4 18 3. 2 15 2 13 4. 5 14 3 5. 10 3 14 6. 7 14 2 18 7. Writing in Math Paper needs to be cut for voting ballots. Each
piece of paper is 1012 in. long. Each ballot should be 134 in. long.
How many ballots can be cut from one piece of paper?.
60
Use with Lesson 5-7.
© Pearson Education, Inc. 6
Find each quotient. Simplify if possible.
Name
Expressions with Fractions
R 5-8
Writing an Algebraic Expression
Evaluating an Algebraic Expression
Yesterday the temperature in Portland,
Oregon, was 10° more than half
the temperature in Phoenix, Arizona.
Write an algebraic expression for the
temperature in Portland.
If the temperature in Phoenix was 80°
yesterday, what was the temperature in
Portland?
Let m the temperature in Phoenix.
Use order of operations to simplify.
Substitute 80 for m.
1
2(80)
The temperature in Portland
was 12m 10.
10
40 10 50
It was 50° in Portland.
Write each word phrase as an algebraic expression.
1. 1 more than 35f
2.
2
3
Tom’s weight
3. 5 fewer than 56 the amount
4. Number Sense Write a word phrase that represents 12n 4.
Evaluate each expression for n 13 and n 114.
© Pearson Education, Inc. 6
5.
7
8 n
6. 2 13n
7. 3 21n
8. 10n 3
Use with Lesson 5-8.
61
Name
Solving Equations with Fractions
R 5-9
Here is how to solve addition, subtraction, multiplication, and division
equations with fractions.
Addition
3
9.
5
3
n
9
5
3
3
3
n
9
5
5
5
2
n8
5
Solve n Multiplication
Solve
( 85 )
5
2
y1 .
8
3
5
2
y1
8
3
5 8
5
y
3 5
8
1
1
6 .
3
9
1
1
x2 6
3
9
1
1
1
1
x2 2 6 2
3
3
9
3
1
3
x6 2
9
9
4
x8
9
Solve x 2
Division
1
4
1
a
4
4
a
1
4
1
a
1 4
Solve a ( )
1
y
Subtraction
5
8
3
5
1
8
2
y
2
3
3
1
3 .
2
1
3
2
1
3
2
7
1
2 4
7
a
8
( )
( )
1. z 2 13 3 16
2. 6n 34
3. x 1 4 23
4. y 12 2 18
5.
3
8
n 10
6. 229 5 x
7. Algebra The rainfall total for June is 4 19
0 in. Yesterday it
1
1
9
rained 2 1
0 in. Use the equation n 2 1
0 4
1
0 to calculate
how much rainfall was received before yesterday.
62
Use with Lesson 5-9.
© Pearson Education, Inc. 6
Solve each equation and check your answer.