Name
5.4
?
Number and
Operations—5.3
MATHEMATICAL PROCESSES
5.1.F
Common Denominators and
Equivalent Fractions
Essential Question
How can you rewrite a pair of fractions so that they
have a common denominator?
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the Problem
Problem
Sarah planted two 1-acre gardens. One had 3 sections of flowers and the
other had 4 sections of flowers. She plans to divide both gardens into more
sections so that they have the same number of equal-sized sections. How
many sections will each garden have?
You can use a common denominator or a common multiple of two or more
denominators to write fractions that name the same part of a whole.
Find the common denominator.
RECORD
THINK
• Multiply the denominators to find a
common denominator.
A common denominator of 1_3 and 1_4 is _.
Divide each 1_3 into fourths and divide each 1_4 into thirds,
each of the wholes will be divided into the same size
parts, twelfths.
• Write 1_3 and 1_4 as equivalent fractions using the
common denominator.
1=
__
3
1=
__
4
So, both gardens will have _ sections.
Find the least common denominator of 3_4 and 1_6 .
• List nonzero multiples of the denominators.
Find the least common multiple.
Multiples of 4: _____
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Multiples of 6: _____
So, the least common denominator
of 3_4 and 1_6 is _.
• Use the least common denominator to write
equivalent fractions.
3
× 3 = ____
? =3
__ = ___
_____
4 12 4 × 3
? =1
1
×
__ = ___
______
= ____
6 12 6 ×
3 can be rewritten as
__
4
_ and 1__6 can be
rewritten as _.
Module 5
213
Share
Share and
and Show
Show
Math Talk
1. Find a common denominator of 1_6 and 1_9 . Rewrite the pair of
Mathematical Processes
fractions using the common denominator.
Explain two methods for finding
a common denominator of
two fractions.
• Multiply the denominators.
A common denominator of 1_6 and 1_9 is _.
• Rewrite the pair of fractions using the common denominator.
1 = ____
__
6
1 = ____
__
9
Use a common denominator to write an equivalent fraction for
each fraction.
2. _1, 1_
3 5
common
denominator: _
____
3. _2, 5_
3 9
1
4. _2, __
9 15
common
denominator: _
____
common
denominator: _
____
Use the least common denominator to write an equivalent fraction
for each fraction.
5. _1, 3_
4 8
least common
denominator: _
____
11, 5_
6. __
12 8
7. _4, 1_
5 6
least common
denominator: _
____
least common
denominator: _
____
Problem
Problem Solving
Solving
Practice: Copy and Solve Use the least common denominator to
write an equivalent fraction for each fraction.
8
9. 7_, __
9 27
8. _1, 4_
6 9
7 , 3_
10. __
10 8
5
11. _1, __
3 11
Algebra Write the unknown number for each ■.
least common
denominator: ■
■ = __
1
13. _2, __
5 ■
least common
denominator: 15
3 , 5_
14. __
■6
■ = __
15. What does a common denominator of two fractions represent? Explain.
214
least common
denominator: 42
■ = __
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12. _1, 1_
5 8
Name
Unlock
Unlock the
the Problem
Problem
16. Katie made two pies for the bake sale. One was cut into three equal
slices and the other into 5 equal slices. She will continue to cut the pies
so each one has the same number of equal-sized slices. What is the least
number of equal-sized slices each pie could have?
a. What information are you given?
b. What problem are you being asked to solve?
c. When Katie cuts the pies more, can she cut each pie the same number
of times and have all the slices the same size? Explain.
d. Use the diagram to show the steps you use to
solve the problem.
e. Complete the sentences.
The least common denominator of
1_
3
and 1_5 is _.
Katie can cut each piece of the first pie
into _ and each piece of the
second pie into _.
That means that Katie can cut each pie into
pieces that are _ of the whole pie.
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17.
Multi-Step Arnold had three pieces of different color
string all the same length. Arnold cut the blue string into 2 equal lengths.
He cut the red string into 3 equal-size lengths, and the green string into
6 equal-size lengths. He needs to cut the string so each color has the
same number of equal-size lengths. What is the least number of
equal-sized lengths each color string could have?
Module 5 • Lesson 4
215
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
7 into a computer
18. Reasoning Magara entered the fractions 1_4 and __
■
program. The computer used the least common denominator to rename
5
14
__
the fractions as __
20 and 20 . What is the unknown denominator?
A
20
C
12
B
8
D
10
19. Alejandro wants to use the least common denominator to write
15
__ and 20
__ .
equivalent fractions for 3_7 and 4_5 . He rewrites the fractions as 35
35
How should he change his answer?
A
The numerators are correct, but the denominators should be 7.
B
20
__
35
__ should be 21
__ .
is correct, but 15
35
25
C
15
__
35
__ should be 28
__ .
is correct, but 20
35
35
D
The denominators are correct, but both numerators should be 12.
20. Multi-Step Aiesha and her mom are cutting two sandwiches into
smaller bite-size pieces. They cut the first sandwich in four equalsized pieces. They cut the second sandwich into six equal-sized pieces.
However, they want an equal number of pieces from each sandwich.
What is the least number of pieces they could cut from each sandwich?
A
4
C
10
B
6
D
12
TEXAS Test Prep
21. Which fractions use the least common denominator and are equivalent
216
A
10 and 14
__
__
40
40
B
25 and 21
__
__
80
80
C
25 and 28
__
__
40
40
D
50 and 56
__
__
80
80
© Houghton Mifflin Harcourt Publishing Company
7
to 5_8 and __
10 ?
Number and Operations—5.3
MATHEMATICAL PROCESSES 5.1.F
H o mewo rk
and Practice
5.4
Name
Common Denominators and
Equivalent Fractions
Use the least common denominator to write an equivalent fraction
for each fraction.
1 , __
1
1. ___
10 5
__, 3
__
5. 3
4 8
__
__
3
1, ___
9. __
4 16
__
__, 2
__
2. 1
3 9
__
___, 1
__
6. 11
12 6
__, 3
__
10. 2
5 4
__
__
2
1, __
3. __
6 4
2
__, __
7. 1
2 5
1
__, __
4. 2
__
3 2
3
__, __
8. 5
__
5
2 , __
11. ___
15 6
7 5
1
7, __
12. __
__
8 2
__
__
__
Write the unknown number for each ■.
__, 1
__ least common
13. 2
3 6
denominator: ■
■ = __
2 least common
1, ___
14. __
8
■
denominator: 24
■ = __
1 , __
2 least common
15. ___
■
7
denominator: 21
■ = __
Problem
Problem Solving
Solving
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16. Daria bought two same-sized posterboards. She
cut the posterboards into equal-sized pieces to
make placemats for her dinner guests. She cut
the first posterboard into 5 pieces and the second
posterboard into 2 pieces. She will continue to
cut the pieces of posterboard so that each one
is divided into the same number of equal-sized
pieces. What is the least number of equal-sized
pieces each posterboard could have?
17. A recipe for homemade goop calls for 1_4 cup
of cornstarch and 1_8 cup of glue. Find the least
common denominator of the fractions used in
the recipe.
Module 5 • Lesson 4
217
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
_1
8
denominator for and
_2 ?
9
A
Multiply 8 and 9.
B
Add 8 and 9.
C
Multiply each number by 2.
D
Add 2 to 8 and 1 to 9.
20. Which fractions use the least common
denominator and are equivalent
3 and 1_ ?
to __
10
6
A
B
C
D
18 and ___
10
___
60
60
30 and ___
10
___
60
60
10 and ___
18
___
30
30
5 and ___
9
___
30
30
22. Multi-Step An archeologist marks off two
equal-sized sites for excavation. She uses a
grid system to divide each square site into
sections. One square has 8 sections. The other
square has 6 sections. She plans to divide both
squares into more sections so that they have
the same number of equal-sized sections. How
many sections will each square have?
218
A
14
B
8
C
24
D
36
1 and __
5
19. If the least common denominator for __
12
■
is 12, which of the following could not be the
unknown denominator?
A
2
B
3
C
4
D
5
21. Lindsay writes two fractions with a least
common denominator of 36. Which fractions
does Lindsay write?
A
B
C
D
2, ___
5
__
3 12
2, ___
1
__
9 12
3, ___
7
__
8 72
1__, ___
5
8 36
23. Multi-Step Mr. Nickelson tells the class that
they double the least common denominator
9 to find the number of the day.
for 1_2 , 3_5 , and __
15
Which number is the number of the day?
A
30
B
15
C
60
D
32
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18. How can you find the least common