4-3 Add and Subtract Like Fractions
Add or subtract. Write in simplest form.
1. SOLUTION: ANSWER: 2. SOLUTION: ANSWER: 3. SOLUTION: ANSWER: 4. eSolutions Manual - Powered by Cognero
SOLUTION: Page 1
ANSWER: 4-3 Add and Subtract Like Fractions
4. SOLUTION: ANSWER: 5. SOLUTION: ANSWER: 6. SOLUTION: ANSWER: 7. In Mr. Navarro’s first period class,
of the students got an A on their math test. In his second period class, of
the students got an A. What fraction more of the students got an A in Mr. Navarro’s first period class than in his
second period class? Write in simplest form.
SOLUTION: Subtract
the
fractionbyofCognero
students who got an A in second period from the fraction of students who got an A in first
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period.
ANSWER: 4-3 Add and Subtract Like Fractions
7. In Mr. Navarro’s first period class,
of the students got an A on their math test. In his second period class, of
the students got an A. What fraction more of the students got an A in Mr. Navarro’s first period class than in his
second period class? Write in simplest form.
SOLUTION: Subtract the fraction of students who got an A in second period from the fraction of students who got an A in first
period.
So,
more of the students got an A in Mr. Navarro’s first period class than in his second period class.
ANSWER: 8. To make a greeting card, Bryce used sheet of red paper,
How many sheets of paper did Bryce use?
sheet of green paper, and
sheet of white paper.
SOLUTION: So, Bryce used
sheets of paper.
ANSWER: 9. The table shows the Instant Messenger abbreviations students at Hillside Middle School use the most.
a. What fraction of these students uses LOL or CUL8R when using Instant Messenger?
b. What fraction of these students uses L8R or BRB when using Instant Messenger?
c. What fraction more of these students write L8R than CUL8R when using Instant Messenger?
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SOLUTION: a. Add the fraction of students using LOL to the fraction of students using CUL8R.
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So, Bryce used
sheets of paper.
ANSWER: 4-3 Add and Subtract Like Fractions
9. The table shows the Instant Messenger abbreviations students at Hillside Middle School use the most.
a. What fraction of these students uses LOL or CUL8R when using Instant Messenger?
b. What fraction of these students uses L8R or BRB when using Instant Messenger?
c. What fraction more of these students write L8R than CUL8R when using Instant Messenger?
SOLUTION: a. Add the fraction of students using LOL to the fraction of students using CUL8R.
So,
of these students uses LOL or CUL8R when using Instant Messenger.
b. Add the fraction of students using L8R to the fraction of students BRB.
So,
of these students uses L8R or BRB when using Instant Messenger.
c. Subtract the fraction of students who write CUL8R from the fraction of students who write L8R.
So,
more students write L8R than CUL8R.
ANSWER: a.
b.
c.
10. Model with Mathematics Cross out the expression that does not belong. Explain your reasoning.
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b.
4-3 Add
c. and Subtract Like Fractions
10. Model with Mathematics Cross out the expression that does not belong. Explain your reasoning.
SOLUTION: or 1
since it equals or 1. Three of the expressions equal . So, cross out the expression
ANSWER: Sample answer: Three of the expressions equal . The crossed out expression equals
11. Justify Conclusions Select two like fractions with a difference of
or 1.
and with denominators that are not 3. Justify
your selection.
SOLUTION: Students should select two like fractions with denominators that are multiples of 3 so that the difference is a fraction
that simplifies to
Sample answer:
–
= .
and , which simplifies to
ANSWER: Sample answer:
and ;
–
= , which simplifies to
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12. Persevere with Problems Simplify the following expression.
.
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ANSWER: 4-3 Add and Subtract Like Fractions
Sample answer: Three of the expressions equal . The crossed out expression equals
11. Justify Conclusions Select two like fractions with a difference of
or 1.
and with denominators that are not 3. Justify
your selection.
SOLUTION: Students should select two like fractions with denominators that are multiples of 3 so that the difference is a fraction
that simplifies to
Sample answer:
–
= .
and , which simplifies to
ANSWER: Sample answer:
and ;
–
= , which simplifies to
.
12. Persevere with Problems Simplify the following expression.
SOLUTION: First, identify the pattern of the terms in the expression. Starting with
, add a like fraction with a numerator that is
decreased by 1, then subtract a like fraction with a numerator that is decreased by 1, then add a like fraction with a
numerator that is decreased by 1, and so on.
Use the pattern to write the entire expression. Then simplify from left to right.
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First, identify the pattern of the terms in the expression. Starting with
, add a like fraction with a numerator that is
decreased
by 1, thenLike
subtract
a like fraction with a numerator that is decreased by 1, then add a like fraction with a
4-3 Add
and Subtract
Fractions
numerator that is decreased by 1, and so on.
Use the pattern to write the entire expression. Then simplify from left to right.
ANSWER: 13. Justify Conclusions Is the difference between a positive like fraction and a negative like fraction always,
sometimes, or never positive? Justify your answer with an example.
SOLUTION: eSolutions
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by Cognero
always;
Sample
answer:
ANSWER: Page 7
ANSWER: 4-3 Add and Subtract Like Fractions
13. Justify Conclusions Is the difference between a positive like fraction and a negative like fraction always,
sometimes, or never positive? Justify your answer with an example.
SOLUTION: always; Sample answer:
ANSWER: always; Sample answer:
14. Use Math Tools Explain how you could use mental math to find the following sum. Then find the sum. Support your answer with a model.
SOLUTION: Sample answer: First, find the sum of the whole numbers, 21. Then group the fractions that have the same
denominator together. Each group has a sum of 1:
21 + 1 + 1 + 1 = 24; See students' work for model.
ANSWER: Sample answer: First, find the sum of the whole numbers, 21. Then group the fractions that have the same
denominator together. Each group has a sum of 1. 21 + 1 + 1 + 1 = 24; See students' work for model.
15. Persevere with Problems A construction company is replacing a window in a house. The window is currently 3
feet wide by 4 feet tall. The homeowner wants to add 9 inches to each side of the window. What is the new
perimeter of the window in feet? Justify your reasoning.
SOLUTION: 17 ft; Sample answer: Since there is 12 inches in a foot, adding 9 inches to each side is adding
ft to each side. So,
or 17 ft
ANSWER: 17 ft; Sample answer:
or 17 ft
Add or subtract. Write in simplest form.
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ANSWER: Page 8
or 17 ft
ANSWER: 4-3 Add and Subtract Like Fractions
17 ft; Sample answer:
or 17 ft
Add or subtract. Write in simplest form.
16. SOLUTION: ANSWER: 17. SOLUTION: ANSWER: 18. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero
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ANSWER: 4-3 Add and Subtract Like Fractions
18. SOLUTION: ANSWER: 19. SOLUTION: ANSWER: 20. SOLUTION: ANSWER: 21. SOLUTION: eSolutions Manual - Powered by Cognero
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ANSWER: 4-3 Add and Subtract Like Fractions
21. SOLUTION: ANSWER: 22. Two nails are
inch and
inch long. How much shorter is the
-inch nail?
SOLUTION: Subtract.
So, it is
inch shorter.
ANSWER: inch
Identify Structure Add. Write in simplest form.
23. SOLUTION: ANSWER: 24. SOLUTION: Add numerators.
or 1 by Cognero
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ANSWER: 4-3 Add and Subtract Like Fractions
24. SOLUTION: Add numerators.
or 1
So, ANSWER: 25. A recipe for Michigan blueberry pancakes calls for
cup flour, cup milk, and cup blueberries. How much more flour is needed than milk? Write in simplest form.
SOLUTION: Subtract the amount of milk from the amount of flour.
So,
cup more flour is needed than milk.
ANSWER: 26. The graph shows the location of volcanic eruptions.
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ANSWER: 4-3 Add and Subtract Like Fractions
26. The graph shows the location of volcanic eruptions.
a. What fraction represents the volcanic eruptions for both North and South America? b. How much larger is the section for Asia and South Pacific than for Europe? Write in simplest form.
SOLUTION: a. Add the fractions for North and South America.
So,
represents the volcanic eruptions for both North and South America.
b. Subtract the fraction for Europe from the fraction for Asia and South Pacific.
So, the section for Asia and South Pacific is larger than the section for Europe by
.
ANSWER: a.
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27. A group of friends bought two large pizzas and ate only part of each pizza. The picture shows how much was left.
b. 4-3 Add and Subtract Like Fractions
27. A group of friends bought two large pizzas and ate only part of each pizza. The picture shows how much was left.
How many pizzas did they eat?
SOLUTION: Add the amount eaten from each pizza.
So, the friends ate
pizzas.
ANSWER: or 1.375 pizzas
28. The table shows the results af a survey on students' favorite kind of movie. Select the appropriate values to
complete the model to find the fraction of students that prefer comedy or action movies.
What fraction of the students who were surveyed prefers comedy or action movies?
SOLUTION: First add up the number of students surveyed. 29 + 42 + 14 + 15 = 100
Set up the fraction of students who like comedy and the fraction of students who like action. Then, add the two eSolutions
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fractions together.
ANSWER: 4-3 Addorand
Subtract
1.375
pizzas Like Fractions
28. The table shows the results af a survey on students' favorite kind of movie. Select the appropriate values to
complete the model to find the fraction of students that prefer comedy or action movies.
What fraction of the students who were surveyed prefers comedy or action movies?
SOLUTION: First add up the number of students surveyed. 29 + 42 + 14 + 15 = 100
Set up the fraction of students who like comedy and the fraction of students who like action. Then, add the two fractions together.
So,
of the students prefer comedy or action movies. ANSWER: ;
Fill in the
29. with <, >, or = to make a true sentence.
SOLUTION: Find equivalent fractions. The LCD is 8.
Since
,
.
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ANSWER: >
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ANSWER: 4-3 Add and Subtract Like Fractions
;
Fill in the
29. with <, >, or = to make a true sentence.
SOLUTION: Find equivalent fractions. The LCD is 8.
Since
,
.
ANSWER: >
30. SOLUTION: Find equivalent fractions. The LCD is 9.
Since
,
.
ANSWER: <
31. SOLUTION: Find equivalent fractions. The LCD is 35.
Since
,
.
ANSWER: < 32. SOLUTION: eSolutions
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Find equivalent fractions. The LCD is 154.
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Since
,
.
ANSWER: 4-3 Add
and Subtract Like Fractions
< 32. SOLUTION: Find equivalent fractions. The LCD is 154.
Since
,
.
ANSWER: < Find the least common denominator for the pair of fractions.
33. SOLUTION: List the multiples of each denominator.
2: 2, 4, 6, 8, 10,...
3: 3, 6, 9, 12, 15,...
Since the least common multiple is 6, the least common denominator is 6.
ANSWER: 6
34. SOLUTION: List the multiples of each denominator.
7: 7, 14, 21, 28, 35,...
28: 28, 56, 84,...
Since the least common multiple is 28, the least common denominator is 28.
ANSWER: 28
35. SOLUTION: List the multiples of each denominator.
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eSolutions
5: 5, 10, 15, 20, 25, 30,...
6: 6, 12, 18, 24, 30, 36,... Page 17
Since the least common multiple is 28, the least common denominator is 28.
ANSWER: 4-3 Add
and Subtract Like Fractions
28
35. SOLUTION: List the multiples of each denominator.
5: 5, 10, 15, 20, 25, 30,...
6: 6, 12, 18, 24, 30, 36,... Since the least common multiple is 30, the least common denominator is 30.
ANSWER: 30
36. SOLUTION: List the multiples of each denominator.
15: 15, 30, 45, 60, 75,...
12: 12, 24, 48, 60, 72,...
Since the least common multiple is 60, the least common denominator is 60.
ANSWER: 60
37. The results of a survey about favorite lunch choices are shown. Which lunch was chosen most often?
SOLUTION: The LCD is 50.
Since
ANSWER: pizza
, pizza was the lunch chosen most often.
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Since the least common multiple is 60, the least common denominator is 60.
ANSWER: 4-3 Add
and Subtract Like Fractions
60
37. The results of a survey about favorite lunch choices are shown. Which lunch was chosen most often?
SOLUTION: The LCD is 50.
Since
, pizza was the lunch chosen most often.
ANSWER: pizza
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