Page 1 of 5
Adding and Subtracting
Fractions
BEFORE
Now
WHY?
You added and subtracted
whole numbers and decimals.
You’ll add and subtract
fractions.
So you can find the length of
an alligator, as in Ex. 22.
You can use models to add and subtract fractions.
Word Watch
Review Words
least common denominator
(LCD), p. 181
1
3
1
3
2
3
3
5
1
5
2
5
Use a model to find the sum or difference.
2
1
1. 3
3
1
1
2. 5
5
7
3
3. 9
9
3
1
4. 4
4
The activity suggests the following rules about adding and subtracting
fractions with common denominators.
Fractions with Common Denominators
Words To add or subtract two fractions with a common
denominator, write the sum or difference of the numerators
over the denominator.
1
2
3
Numbers 5
5
5
a
b
ab
Algebra c
c
c
(c 0)
4
1
3
7
7
7
a
b
ab
c
c
c
(c 0)
EXAMPLE
1
2
5
25
9
9
9
7
9
Adding Fractions
Add numerators.
Simplify numerator.
Lesson 5.1
Adding and Subtracting Fractions
205
Page 2 of 5
2
EXAMPLE
with
Review
Need help with simplifying
fractions? See p. 169.
Subtracting Fractions
7
3
73
8
8
8
Subtract numerators.
4
8
Simplify numerator.
1
2
Simplify fraction.
Your turn now
Add or subtract. Simplify if possible.
3
1
1. 8
8
3
4
2. 5
5
4
2
3. 5
5
5
11
4. 12
12
Different Denominators When adding or subtracting fractions with
different denominators, rewrite the fractions so they have the same
denominator. Then add or subtract the numerators as before.
Fractions with Different Denominators
1. Rewrite the fractions using the LCD.
2. Add or subtract the numerators.
3. Write the result over the LCD.
4. Simplify if possible.
with
Solving
Need help with writing
improper fractions as
mixed numbers? See
p. 185.
EXAMPLE
3
Adding Fractions
9
8
3
2
12
12
4
3
3
4
98
12
Add numerators.
5
12
17
12
, or 1 ✓Check
2
3
Rewrite fractions using the LCD of and .
Simplify.
You can use estimation to check that your answer
3
4
1
2
2
3
1
2
is reasonable. Because is greater than and is greater than ,
3
4
2
3
the sum of and should be greater than 1.
206
Chapter 5
Fraction Operations
Page 3 of 5
EXAMPLE
4
Subtracting Fractions
Construction Before a rough piece of wood can be used in building a
house, it needs to be squared off and sanded. During this process, the
Housing
5
8
thickness of a rough piece of wood inch thick is always reduced to
7
inch. How much thinner is the wood now?
16
Solution
7
16
5
8
To find how much thinner the wood is, subtract from .
7
7
5
10
16
16
8
16
10 7
16
Subtract numerators.
3
16
Simplify numerator.
■
Construction
From 1976 to 2001, the
volunteers of Habitat for
Humanity have built more
than 100,000 houses in
more than 80 countries,
including about 30,000
houses across the United
States. How many houses do
you think they build in a
year?
5
8
Rewrite using the LCD of the fractions.
3
16
ANSWER The wood is now inch thinner.
Your turn now
1
3
5. 12
4
Add or subtract. Simplify if possible.
3
1
6. 5
2
7
2
7. 8
3
1
5
8. 10
6
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 709
Getting Ready to Practice
1. Vocabulary Copy and complete: To add fractions with different
denominators, first rewrite the fractions using the _?_.
Find the sum or difference. Simplify if possible.
5
1
2. 7
7
7
4
3. 9
9
11
3
4. 12
4
7
3
5. 10
5
1
1
6. Swimming In a mile relay swimming event, Brad swims mile.
2
8
What is the total distance that his teammates have left to swim?
Lesson 5.1
Adding and Subtracting Fractions
207
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
8–19, 28–33
8–19, 28–33
8–19, 28–34
8–19, 22, 28–33
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
3
4
1
1
7. Writing Describe how is related to .
12
12
4
3
Find the sum or difference.
1
8
8. 10
10
4
5
9. 7
7
9
7
10. 20
20
3
1
11. 5
5
7
5
12. 12
12
8
2
13. 9
9
11
3
14. 12
4
3
4
15. 10
5
7
5
16. 12
18
1
3
17. 6
4
1
5
18. 9
6
2
1
19. 3
4
1
1
20. Algebra Evaluate x when x .
2
7
21. School Day From the time you wake up, you need 43 minutes to get
ready for school and 24 minutes to travel from home to school. Using
fractions of an hour, approximate the time it takes for you to get to
school from the time you wake up.
5
3
22. Alligators A recently hatched alligator is foot long and grows foot
12
4
over the next 5 months. How long is the alligator at 5 months old?
1 1 3 1
23. Look for a Pattern Describe the following pattern: , , , , . . . .
16 8 16 4
Then write the next three fractions.
Algebra Use mental math to solve the equation.
5
3
24. x
7
7
4
5
25. x 8
8
3
1
26. x 11
11
27. Critical Thinking Can the sum of three fractions greater than zero and
less than 1 be greater than 1? Explain your reasoning with an example.
Find the sum or difference.
5
1
11
28. 12
12
12
4
5
2
29. 9
9
9
5
3
7
30. 16
4
8
2
6
13
31. 15
15
15
7
5
2
32. 30
6
5
2
3
2
33. 3
4
5
3
1
34. Trail Mix A recipe for trail mix calls for cup dried mixed fruit, cup
4
2
1
mixed nuts, and cup granola. How many cups of trail mix does this
3
recipe make? Estimate to check your answer.
208
Chapter 5
Fraction Operations
Page 5 of 5
Music In music, a 4
time signature means that there are 4 beats
4
per measure. The beats for seven musical notes with this time
signature are in the table below. In Exercises 35 and 36, tell
whether the measure contains 4 beats. Explain your reasoning.
Note
Beats
4
2
1
3
4
1
2
3
8
1
4
35.
William Eddins, conductor
of the Chicago Symphony
Orchestra
36.
5
3
37. Challenge When you find , what advantage does using the LCD
6
8
of the two fractions have over any other common denominator?
Mixed Review
Find the sum or difference. (Lesson 2.2)
38. 32.8 4.25
39. 13.6 7.07
40. 400 29.1
41. 240.24 0.533
Write the decimal as a fraction or mixed number. (Lesson 4.7)
42. 0.6
43. 0.17
44. 5.375
45. 10.34
Basic Skills Use long division to find the quotient.
46. 547 8
47. 6552 5
48. 387 12
49. 8284 16
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
50. Multiple Choice Which of the following numbers, when added
1
1
to , results in a number greater than ?
4
2
1
8
A. 1
6
1
4
B. C. 1
3
D. 5
2
1
51. Multiple Choice What is the value of the expression ?
6
3
8
6
11
F. 31
30
G. Lesson 5.1
11
8
H. I. 6
Adding and Subtracting Fractions
209