LESSON
Page 1 of 5
5.2
Adding and Subtracting Like Fractions Now
Review Vocabulary
BEFORE
variable expression, p. 5
You added and subtracted decimals.
WHY?
You’ll add and subtract like fractions.
So you can analyze a lobster’s growth, as in Ex. 52.
Astronomy One night, 77 of the moon’s visible 100
surface is illuminated. The 9 100
next night, an additional is illuminated. What fraction of the moon’s visible surface is illuminated on the second night?
Adding and Subtracting Like Fractions Words To add or subtract fractions with the same denominator,
write the sum or difference of the numerators over the denominator.
Review Help For help with adding and subtracting fractions, see p. 779.
4 1 5 Numbers 9 9 9
9 2 7 11 11 11
a b ab Algebra , c 0 c c c
a b ab , c 0 c c c
Example 1
Adding Like Fractions
To find the fraction of the moon’s visible surface that is illuminated on 77 100
9 100
the second night, as described above, find the sum of and . 77 9 77 9 100 100 100 86 100
Write sum of numerators over denominator. 43 50
Add. Then simplify. 43 50
Answer On the second night, of the visible surface is illuminated.
Lesson 5.2
Adding and Subtracting Like Fractions
225
Page 2 of 5
Example 2 4
Study Strategy When you perform operations with negative fractions, be sure to assign a negative sign in front of a fraction to the numerator of the fraction. For instance, in part (a) of
Subtracting Like Fractions 4 2
2
Write difference of numerators over denominator.
a. 7 7 7 6 7
6 7
1
3
1
Subtract. 3
3 10
b. 10 10 10 10 13 10
Write sum of numerators over denominator.
4 Example 2, is written 7 4 as . 7
4 10
3 10
To subtract , add .
2 5
Add. Then simplify.
Checkpoint Find the sum or difference. 3 2 1. 8 8
2 7 3. 15 15
1 5 2. 6 6
1 7 4. 12 12
Mixed Numbers To add or subtract mixed numbers, you can first write the mixed numbers as improper fractions.
Example 3 5
7
Adding and Subtracting Mixed Numbers 50
25
a. 5 9 2 9 9 9 50 25 9
Write sum of numerators over denominator.
75 9
Add.
25 3
1 3
8
136
8 6
Write mixed numbers as improper fractions.
Simplify. Then write fraction as a mixed number. 86
Write mixed numbers as improper fractions.
b. 10 13 6 13 13 1 3 136 86 13
Write difference of numerators over denominator.
222 13
1 13
17
Subtract. Then write fraction as a mixed number.
Checkpoint Find the sum or difference. 3 3 5. 2 1 4 4
226
Chapter 5
Rational Numbers and Equations
2 1 6. 6 3 3 3
1 3 7. 4 2 5 5
2 3 8. 3 6 7 7
Page 3 of 5
Example 4 3a
Simplifying Variable Expressions 3a 5a
5a
a. 2 0 20 20
Review Help
Write sum of numerators over denominator.
2
8a 20
For help with simplifying fractions that include variables, see p. 184.
Add. Divide out common factor.
5
2a 5
8
Simplify.
2
8
2
2 3b
b. 3b 3b 3b 3b 8 2 3b
Write sum of numerators over denominator.
6 2 3b
Add. Divide out common factor.
1
2 b
2 b
5.2
2 3b
To subtract , add .
Simplify.
Exercises
INTERNET
More Practice, p. 807
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eWorkbook Plus
Guided Practice Vocabulary Check
1. Copy and complete: To find the sum of two fractions with the same
denominator, write the sum of the _?_ over the denominator.
5m 2m 2. Explain how to simplify the expression . 3 3
Skill Check
Guided Problem Solving
Find the sum or difference. 7 1 3. 9 9
2 5 4. 7 7
3 5 5. 8 8
9 8 6. 5 9 13 13
7 11 7. 3 8 16 16
3 5 8. 1 10 14 14
1 9. Crafts You have 5 feet of ribbon. You want to cut one piece that is 4 3 3 3 feet long and one that is 1 feet long. Do you have enough ribbon? 4 4 3 3 1 Write 3 and 1 as improper fractions. 4 4 2
Find the sum of the improper fractions.
3
Compare the sum in Step 2 with 5
1 4
to determine whether you have enough ribbon. Lesson 5.2
Adding and Subtracting Like Fractions
227
Page 4 of 5
Practice and Problem Solving Homework Help Example 1 2 3 4
Exercises 10–17, 27 10–17 18–25, 28, 37, 44 29–36
Online Resources
Find the sum or difference.
8 12 11. 19 19
17 13 12. 27 27
3 6 13. 7 7
8 13 14. 15 15
21 15 15. 26 26
9 19 16. 22 22
6 12 17. 17 17
1 3 18. 4 5 4 4
4 4 19. 3 8 5 5
3 9 20. 6 7 10 10
1 2 21. 2 3 3
9 6 22. 8 3 11 11
5 17 23. 5 18 18
7 11 24. 3 8 16 16
3 5 25. 1 10 14 14
3 4 10. 5 5
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• More Examples • eTutorial Plus
26. Error Analysis Describe 3 7
and correct the error in
2 7
3 2 77
3 2 adding and . 7 7
1 14
3 27. Homework One day, you studied math for hour and English 4 3 for hour. What was the total time that you studied both subjects? 4 2 28. Baking A blueberry muffin recipe calls for 1 cups of flour. A banana 3 2 muffin recipe calls for 2 cups of flour. How much flour do you need to 3
make both recipes? Simplify the expression. x 5x 29. 8 8
t 12t 30. 13 13
11 17 31. 6p 6p
29 19 32. 12s 12s
2n 7n 33. 15 15
m 5m 34. 21 21
5 23 35. 18a 18a
15 21 36. 4d 4d
3 37. Carpentry You are making a shelf from a board that is 12 inches long. 4 1 You want to cut the board so that it is 10 inches long. What length 4
should you cut from the board? Evaluate the expression. 3 7 4 38. 9 9 9
1 3 2 41. 5 5 5
3 5 7 39. 10 10 10
7 2 4 40. 9 9 9
17 21 27 42. 31 31 31
9 13 11 43. 14 14 14
3 44. Shot Put The school record for the shot put is 45 feet, 3 inches. Your 8 7 personal record is 42 feet, 6 inches. How much farther must you 8
throw the shot put to match the school record? 228
Chapter 5
Rational Numbers and Equations
Page 5 of 5
45. Critical Thinking Find two fractions, one positive and one negative, 1 having the same denominator and a sum of . 2
Solve the equation. Check your solution. 3 5 46. x 7 7
8 2 47. y 11 11
7 5 48. z 12 12
4 2 49. m 2 5 9 9
3 5 50. 7 n 6 8 8
5 10 51. 1 t 4 13 13
52. Lobsters A lobster periodically sheds its shell
and grows a new shell. During this process, which is called molting, the weight of the lobster increases, as shown in the table. In the
Real World
Lobsters Suppose a lobster
molts 25 times during the first 7 years of its life. After that, it molts once per year. After 12 years, how many times will it have molted?
a. How many pounds did the lobster gain after each molting? b. How many pounds in all did the lobster gain after four moltings? 1
c. Suppose the lobster gains 2 4 pounds
Lobster Weights (lb) 1 4
Before molting
1
After 1 molting
1 3
4 After 2 moltings 2 2 4 After 3 moltings 3 3 4 After 4 moltings 5 1 4
after molting one more time. How much does it weigh then? 5 7x 8x 53. Challenge Solve the equation . Explain how you found 8 3 3
the solution.
Mixed Review
54. Watch You buy a watch and a battery for $57.99. The battery costs $2.99.
Write and solve an equation to find the cost of the watch. (Lesson 2.5) Write the fraction in simplest form. (Lesson 4.3) 15s 3 55. 5s 2
120t 2 56. 5 140t
65m4 57. 2 80m
54a 5 58. 2 78a
Find the least common multiple of the monomials. (Lesson 4.4) 59. 18m, 3mn
Standardized Test Practice
60. 5t, 20s 2t
61. 12a 3b, 6a
62. 9vw, 36v 2w 2
7 13 63. Multiple Choice Find the difference . 16 16 1 3 3 A. 1 B. C. 4 8 8
D. 1
16 28 64. Multiple Choice Simplify the expression . 3y 3y 12 4 G. H. 0 F. 3y y
I.
1 4
44 3y
65. Short Response A rectangular picture frame is made of wooden strips 3 1 that are inch wide. The outside edge of the frame is 8 inches long 4 4 3 and 6 inches wide. Can a rectangular picture that is 7 inches long and 4 1 5 inches wide fit inside the frame? Explain your answer. 2 Lesson 5.2
Adding and Subtracting Like Fractions
229
