Lesson 8.1
Reteach
Name Multiples of Unit Fractions
A unit fraction is a fraction with a numerator of 1. You can write
a fraction as the product of a whole number and a unit fraction.
7
Write ​ __
10  ​as the product of a whole number and a
unit fraction.
7
Write ​ __
10  ​as the sum of unit fractions.
1   __
1
1
1
1
1
1
__
__
__
__
__
7 ​ 5 __
​ __
1 10   1 10   1 10   1 10   1 10   1 10  
10
10
Use multiplication to show repeated addition.
​  ​ ​  ​ ​  ​ ​  ​
__
​ 7 ​ 5
10
​  ​ ​  ​ ​  ​
​ 1 ​ 
7 3 __
10
__
​ 1 ​
7 ​ 5 7 3
  
So, ​ __
10 .
10
The product of a number and a counting number is a multiple of the
number. You can find multiples of unit fractions.
List the next 4 multiples of _
​1​. 
8
Make a table and use repeated addition.
1
13_
​ ​ 
8
1
23_
​ ​ 
8
331
​_ ​
8
431
​_ ​
8
1
_
​ ​ 
1
1
_
​ ​ 
​ ​ 1 _
1
1
_
_
​ ​ 1 1
​  ​1 _
​  ​
1
_
​ ​ 1 _
​1​ 1 _
​1 ​1 _
​1 ​
1
_
​ ​ 
​2_8​  
​​
4
_  
8
8
8
8
8
The next 4 multiples of ​ _18 ​are
8
8 8
3
_  
8
8
8
​​
8
531
​_ ​
8
8
1
​_ ​1 _
​1​ 1 _
​1​ 1 _
​1​ 1 _
​1​ 
8 8 8 8 8
5
_  
8
​​
2
5
_   3_   4_  
_  
and
8 , 8 , 8 ,
8 .
​​ ​​ ​​
​​
Write the fraction as the product of a whole number
and a unit fraction.
__
1. 2
​ ​ 5
5
1
23_
​ ​ 
5
2. ___
​ 5 ​ 5
12
5 3 __
​ 1 ​ 
12
List the next four multiples of the unit fraction.
__
4. 1
​ ​, 
4
4
2
_
​_ ​
​  ​ 5
​_ ​ _
​ ​  3
4,4,4,4
Reteach
© Houghton Mifflin Harcourt Publishing Company
1
5. __
​  ​,
6
R64
7
3. __
​  ​5
2
1
73_
​ ​ 
2
4
5
2
3
​ ​  _
​ ​ 
​_ ​ _
​  ​ _
6
6, 6, , 6
Grade 4
Lesson 8.2
Reteach
Name Multiples of Fractions
You have learned to write multiples of unit fractions. You can also
write multiples of other fractions.
2
Write the next 4 multiples of _
​ ​. 
5
Make a table.
13_
​2​ 
5
2
23_
​ ​ 
5
332
​_ ​
5
432
​_ ​
5
2
_
​ ​ 
2
2
_
​ ​ 1 _
​ ​ 
2
_
_
​ ​ 1 2
​  ​1 _
​2 ​
2
_
​ ​ 1 _
​2​ 1 _
​2 ​1 _
​2 ​
2
_
​ ​ 
5
4
_​ ​  
5
​​
_8​ ​  
5
5
5
5
5 5
6
_  
5
5
5
532
​_ ​
5
5
2
2
​_ ​1 _
​2​ 1 _
​2​ 1 _
​2​ 1 _
​  ​
5 5 5 5 5
10   
__
5
5
​​
5
_4​ ​ ​6_​ ​8_​
10
__
​ ​   
  ,    ,    , and
So, the next 4 multiples of ​ _25 ​are 5 
5
5
5 .
Write 3 3 ​ _25 ​as the product of a whole number and
a unit fraction.
2
Use a number line. Make three jumps of _
​ ​. 
5
6
25_
33_
5 5
0
1
5
2
5
1
23_
5
_1 .
6
2
​ ​,  or 6 3 5 
So, 3 3 _
​ ​ 5 _
5 5
​​
3
5
4
5
5
5
1
43_
5
6
5
7
5
1
63_
5
6
_
​ ​ 
4,
4
9
​_ ​
4,
12
15
​__ ​  __
​  ​  
4, 4
9
5
1
83_
5
List the next four multiples of the fraction.
__
1. 3
​  ​,
8
5
5
2. __
​ ​, 
6
10
20
​__ ​  15
​__ ​  __
​  ​  25
​__ ​  
6 , 6, 6, 6
Write as the product of a whole number and a unit fraction.
3.
4.
0
3 3 __
​3 ​5
8
Reteach
0
1 2 3 4 5 6 7 8 9 10
8 8 8 8 8 8 8 8 8 8
1
93_
​ ​ 
8
© Houghton Mifflin Harcourt Publishing Company
1
3
2
4 3 __
​ ​ 5
R65
3
2
3
3
3
4
3
5
3
6 7 8 9 10
3 3 3 3 3
831
​_ ​
3
Grade 4
Lesson 8.3
Reteach
Name Multiply a Fraction by a
Whole Number Using Models
You can use a model to multiply a fraction by a whole number.
3
Find the product of 4 3 _
​ ​. 
5
3
Use fraction strips. Show 4 groups of _
​ ​ each.
5
1
5
1
5
1
5
1
5
1
5
3
​ ​ 
1 group of 3
​_ ​5 _
5 5
1
5
1
5
1
5
1
5
1
5
6
​ ​ 
2 groups of 3
​_ ​5 _
5 5
1
5
1
5
1
5
1
5
1
5
9
3 groups of 3
​_ ​5 _
​ ​ 
5 5
1
5
1
5
1
5
1
5
1
5
4 groups of 3
​_ ​5 12
​__ ​  
5
5
So, 4 3 _
​3​ 5 __
​12 ​.  
5
5
Multiply.
1.
2.
2 3 __
​5 ​5
6
3. 6 3 __
​2​ 5
3
6. 4
3 __
​5​ 5
8
10
__
​  ​  
6
12
__
​  ​  
3
20
__
​  ​  
8
Reteach
© Houghton Mifflin Harcourt Publishing Company
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
7
3 3 __
​  ​5
8
4. 2 3 ___
​ 9 ​ 5
10
7. 7
2
3 __
​ ​ 5
5
18
​__ ​ 
10
14
__
​  ​  
5
R66
21
​__ ​  
8
3
5. 5 3 __
​ ​ 5
4
8. 8
4
3 __
​ ​ 5
6
15
​__ ​  
4
32
​__ ​  
6
Grade 4
Lesson 8.4
Reteach
Name Multiply a Fraction or Mixed
Number by a Whole Number
To multiply a fraction by a whole number, multiply the numerators.
Then multiply the denominators.
A recipe for one loaf of bread calls for 2​ _14 ​cups of flour. How many
cups of flour will you need for 2 loaves of bread?
Step 1 Write and solve an equation.
2
9
2
1​ as a fraction.
_ ​5 _
2 3 2​1
​ ​ 3 _
​ ​ 
Write 2 as _
​ ​.  Write 2​_
4 1 4
1
4
3 9 
52
​_____
​Multiply the numerators.
134
Then multiply the denominators.
Simplify.
5 18
​__ ​  
4
Step 2 Write the product as a mixed number.
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
__
​  ​  5 _
​1​ 1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​ ​ 1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​1 _
​  ​
4
4
4
4
4
4
4
1
1 1
4
4
4
4 4 4 4
1 1
4
5
5
4
5
5
4
1 1
4
4
1 _
1_
​ ​ 1 1
​ ​ 
4 4
1
_   _1  
4
5
+ 4 + 4 Combine the wholes. Then combine the remaining parts.
1  
_  
42
4_
4
2 Add. Write the sum as a mixed number.
5
, or
1  
4_
2 cups of flour.
So, you will need
​​
​​
​​
​​
​​
Multiply. Write the product as a mixed number.
1. 3
3 __
​2​ 5
5
1​ 
1​_
5
6 ​ 
__
2​ 
3 ​5
4. 2 3 1​ ___  
10
10
Reteach
© Houghton Mifflin Harcourt Publishing Company
2. 4
3
3 __
​ ​ 5
8
4​ 
1​_
8
2
_ ​
6​
2
__
5. 4 3 1​ ​ 5
3
3
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3. 5
6. 7
1
3 __
​ ​ 5
3
1​ 5
3 1​__
6
2​ 
1​_
3
1​ 
8​_
6
Grade 4
Lesson 8.5
Reteach
Name Problem Solving • Comparison
Problems with Fractions
The Great Salt Lake in Utah is about ​ _45 ​mile above sea level. Lake
Titicaca in South America is about 3 times as high above sea level as
the Great Salt Lake. About how high above sea level is Lake Titicaca?
Read the Problem
Solve the Problem
What do I need to find?
I need to find about how high above
sea level Lake Titicaca is.
Draw a comparison model. Compare the
heights above sea level of the Great Salt Lake
and Lake Titicaca, in miles.
Great Salt Lake 4
​_ ​
5
Lake Titicaca
​_45​   4_​5  ​
4
_​ ​  
5
mile
The Great Salt Lake is about
above sea level. Lake Titicaca is about
3 times as high above sea level.
How will I use the information?
I can draw a diagram to compare the
heights.
_4​ ​  
5
5
What information do I need to use?
Write an equation and solve.
t
t is the height above sea level of
Lake Titicaca, in miles.
t5
t5
t5
3
3
12
__
​5 ​  
2
​ ​  
2_
5
2  
2_
So, Lake Titicaca is about 5 miles above sea level.
4
_​ ​  
5
Write an equation.
Multiply.
Write the fraction as a
mixed number.
​​
1. Amelia
is training for a triathlon. She
3
_
swims ​ 5 ​mile. Then she runs about 6
times farther than she swims. About
how far does Amelia run?
week, Meg bought 1​ _34 ​pounds of
fruit at the market. This week, she buys
4 times as many pounds of fruit as last
week. In pounds, how much fruit does
Meg buy this week?
2. Last
_ ​miles
3​3
5
Reteach
© Houghton Mifflin Harcourt Publishing Company
7 pounds
R68
Grade 4