Download Multiples of Unit Fractions

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
7 5 __
__
10 1
1
__
1
1
1
1
1
__
__
__
__
__
10 1 10 1 10 1 10 1 10 1 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.
1.
List the next 4 multiples of _
8
Make a table and use repeated addition.
1
13_
8
1
23_
8
_
331
8
_
431
8
_
531
8
1
_
8
111
_
_
8 8
2
_
8
11_
11_
1
_
8 8 8
3
_
8
11_
111
_
_11
_
8 8 8 8
4
_
8
1
111
111
_1_
_1_
_
8 8 8 8 8
5
_
8
1
_
8
The next 4 multiples of 1_8 are
2
5
_ 3_ 4_
_
and
8 , 8 , 8 ,
8 .
Write the fraction as the product of a whole number
and a unit fraction.
2
1. __
5
5
2. ___
5
12
7
3. __
5
2
5
List the next four multiples of the unit fraction.
1,
4. __
4
,
,
1,
5. __
6
,
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8-5
,
,
,
Reteach
Lesson 8.1
Enrich
Name
Mixed Numbers and Unit Fractions
Write each mixed number as the product of a whole number
and a unit fraction.
1.
__
11
3
2.
__
31
2
3.
__
13
5
4.
__
23
8
5.
3
3 __
4
6.
__
52
3
7.
2
4 __
5
8.
__
51
5
9.
Explain how you found the answer in Exercise 1.
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8-6
Enrich
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.
2
13_
5
2
23_
5
_
332
5
_
432
5
_
532
5
2
_
5
212
_
_
5 5
_4
5
21_
21_
2
_
5 5 5
_6
5
21_
212
_
_12
_
5 5 5 5
_8
5
2
212
212
_1_
_1_
_
5 5 5 5 5
10
__
5
2
_
5
4
_
6
_
8
_
10
__
5 .
So, the next 4 multiples of 2_5 are 5 , 5 , 5 , and
Write 3 3 2_5 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
3
5
4
5
5
5
1
43_
5
6
5
7
5
1
63_
5
8
5
9
5
1
83_
5
1
256
_, or 6 3 _ .
So, 3 3 _
5
5 5
List the next four multiples of the fraction.
3,
1. __
,
4
,
,
5,
2. __
,
6
,
,
Write as the product of a whole number and a unit fraction.
3.
4.
0
0
1 2 3 4 5 6 7 8 9 10
8 8 8 8 8 8 8 8 8 8
35
3 3 __
8
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8-7
1
3
2
3
3
3
4
3
5
3
6 7 8 9 10
3 3 3 3 3
25
4 3 __
3
Reteach
Lesson 8.2
Enrich
Name
Multiples of Mixed Numbers
List the next three multiples of the mixed number. Write each
multiple as a mixed number or as a whole number.
1.
__
11
8
2.
__
21
2
3.
__
12
3
4.
__
21
3
5.
1
3 __
5
6.
1
1__
4
7.
__
13
5
8.
3
2 __
4
9.
Describe a method other than multiplication that
you can use to find the next three multiples of the mixed number in
Exercise 7.
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8-8
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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.
_.
Find the product of 4 3 3
5
3 each.
Use fraction strips. Show 4 groups of _
5
1
5
1
5
1
5
1
5
1
5
3
_5_
1 group of 3
5 5
1
5
1
5
1
5
1
5
1
5
6
_5_
2 groups of 3
5 5
1
5
1
5
1
5
1
5
1
5
9
_5_
3 groups of 3
5 5
1
5
1
5
1
5
1
5
1
5
_ 5 12
__
4 groups of 3
5
5
3 5 12
__.
So, 4 3 _
5
5
Multiply.
1.
2.
__ 5
235
6
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
__ 5
337
8
3.
25
6 3 __
3
4.
9 5
2 3 ___
10
5.
35
5 3 __
4
6.
55
4 3 __
8
7.
25
7 3 __
5
8.
45
8 3 __
6
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8-9
Reteach
Lesson 8.3
Enrich
Name
Fraction of a Whole Number
Find the product. Write the product as a whole number.
__
1. 1
3 24 5
__
2. 2
3 15 5
__
3. 3
3 10 5
__
4. 4
3 14 5
__
5. 5
3 18 5
__
6. 3
3 16 5
2
7. __
3 27 5
7
8. __
3 32 5
8
5
6
9
3
7
4
8
9
9. ___
3 50 5
4
10. __
3 45 5
5
11. ___
3 60 5
__
12. 8
3 54 5
10
12
13.
5
9
Explain how you can tell if the product of a fraction
and a whole number will be a whole number.
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8-10
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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 1_4 cups of flour. How many
cups of flour will you need for 2 loaves of bread?
Step 1 Write and solve an equation.
9
_52
_3_
2 3 21
4 1 4
39
_____
52
134
2. Write 21
_ as a fraction.
Write 2 as _
1
4
Multiply the numerators.
Then multiply the denominators.
__
Simplify.
5 18
4
Step 2 Write the product as a mixed number.
18 5 _
11_
11_
111
11_
11_
11_
11_
11_
11_
11_
11_
11_
11_
11_
11_
111
_
__
_1_
4
4
4
4
4
4
4
1
1
1
_1
_
4
4
5
+
+ 4
1
_
42
4_
4
2
5
, or
1
4_
2
So, you will need
4
4
1
1
4
4
4
4
4
4
5
5
4
5
5
4
1
1
1
4
4
1 _
1_11
4 4
Combine the wholes. Then combine the remaining parts.
Add. Write the sum as a mixed number.
cups of flour.
Multiply. Write the product as a mixed number.
1.
25
3 3 __
5
2.
__ 5
433
8
3.
__ 5
531
3
4.
3 5
2 3 1___
10
5.
25
4 3 1__
3
6.
__ 5
7 3 11
6
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8-11
Reteach
Lesson 8.4
Enrich
Name
Unknown Numbers
Find the unknown number that makes each equation true.
1.
3.
5.
1
3 5 2__
3 __
4
4
2.
3
4 3 __ 5 1__
5
5
5
5 1__
9
4.
23
73
1
55 9 __
3 1__
6
6
6.
2
1
__ 5 6 __
3
3
5
2 5 13 __
3 2__
7
7
Explain how you found the unknown number in
7.
Exercise 3.
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8-12
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Lesson 8.5
Reteach
Name
Problem Solving • Comparison
Problems with Fractions
The Great Salt Lake in Utah is about 4_5 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
_4
5
What information do I need to use?
_4
5
_4
5
_4
5
5
mile
The Great Salt Lake is about
above sea level. Lake Titicaca is about
3 times as high above sea level.
t
Write an equation and solve.
How will I use the information?
I can draw a diagram to compare the
heights.
t is the height above sea level of
Lake Titicaca, in miles.
t5
3
t5
t5
_4
3 5
12
__
5
_
22
5
Write an equation.
Multiply.
Write the fraction as a
mixed number.
_
22
So, Lake Titicaca is about 5 miles above sea level.
1.
2.
Amelia is training for a triathlon. She
swims 3_5 mile. Then she runs about 6
times farther than she swims. About
how far does Amelia run?
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8-13
Last week, Meg bought 1 3_4 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?
Reteach
Lesson 8.5
Enrich
Name
Heights and Depths
Solve each problem. You may find it helpful to draw a diagram.
1.
The depth of Lake Carl is about 1 1_8 miles. Lake Susan is 3 times as
deep as Lake Carl. Lake Wayne is 2 times as deep as Lake Susan.
How much deeper is Lake Wayne than Lake Susan?
2.
Mount Rogers rises 1_4 mile above sea level. Mount Taylor rises
6 times as high as Mount Rogers. Mount Sullivan rises 2 times as
high as Mount Rogers. What is the difference in the elevation of
Mount Taylor and the elevation of Mount Sullivan?
3.
A certain tree was 5 1_3 feet tall when it was first planted. A few
years later, the tree is 4 times as tall as it was when it was first
planted. How much has the tree grown since it was first planted?
4.
Explain how you solved Problem 3.
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8-14
Enrich