Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Use the Distributive Property to simplify each expression.

9. 6(a + 10)
10. 8(4 + x)
11. (5 + w)5
12. (2t + 3)11
13. 10 ( 9 − t ) 10 open 9 minus t close
14. 12 ( 2 j − 6 ) 12 open 2 j minus 6 close
15. 16(7b + 6)
16. (1 + 3d)9
17. ( 3 − 8 c ) 1.5 open 3 minus 8 c close 1.5
18. ( 5 w − 15 ) 2.1 open 5 w minus 15 close 2.1
19. 1 4 ( 4 f − 8 ) 1 fourth , open 4 f minus 8 close
20. 6 ( 1 3 h + 1 ) 6 open , 1 third , h plus 1 close
21. ( − 8 z − 10 ) ( − 1.5 ) open negative 8 z minus 10 close open negative 1.5 close
22. 0 ( 3.7 x − 4.21 ) 0 open 3.7 x minus , 4.21 , close
23. 1 ( 3 11 − 7 d 17 ) 1 . open . 3 elevenths , minus , fraction 7 d , over 17 end fraction . close
24. 1 2 ( 1 2 y − 1 2 ) 1 half . open . 1 half , y minus , 1 half . close

See Problem 2.

Write each fraction as a sum or difference.

25. 2 x + 7 5 fraction 2 x plus 7 , over 5 end fraction
26. 17 + 5 n 4 fraction 17 plus 5 n , over 4 end fraction
27. 8 − 9 x 3 fraction 8 minus 9 x , over 3 end fraction
28. 4 y − 12 2 fraction 4 y minus 12 , over 2 end fraction
29. 25 − 8 t 5 fraction 25 minus 8 t , over 5 end fraction
30. 18 x + 51 17 fraction 18 x plus 51 , over 17 end fraction
31. 22 − 2 n 2 fraction 22 minus 2 n , over 2 end fraction
32. 42 w + 14 7 fraction 42 w plus 14 , over 7 end fraction

See Problem 3.

Simplify each expression.

33. − ( 20 + d ) negative open 20 plus d close
34. − ( − 5 − 4 y ) negative open negative 5 minus 4 y close
35. − ( 9 − 7 c ) negative open 9 minus 7 c close
36. − ( − x + 15 ) negative open negative x plus 15 close
37. − ( 18 a − 17 b ) negative open 18 eh minus 17 b close
38. − ( 2.1 c − 4 d ) negative open 2.1 c minus 4 d close
39. − ( − m + n + 1 ) negative open negative m plus n plus 1 close
40. − ( x + 3 y − 3 ) negative open x plus 3 y minus 3 close

See Problem 4.

Use mental math to find each product.

41. 5.1 × 8 5.1 times 8
42. 3 × 7.25 3 times , 7.25
43. 299 × 3 299 times 3
44. 4 × 197 4 times 197
45. 3.9 × 6 3.9 times 6
46. 5 × 2.7 5 times 2.7
47. 6.15 × 4 6.15 , times 4
48. 6 × 9.1 6 times 9.1
49. You buy 50 of your favorite songs from a Web site that charges $.99 for each song. What is the cost of 50 songs? Use mental math.
50. The perimeter of a baseball diamond is about 360 ft. If you take 12 laps around the diamond, what is the total distance you run? Use mental math.
51. One hundred and five students see a play. Each ticket costs $45. What is the total amount the students spend for tickets? Use mental math.
52. Suppose the distance you travel to school is 5 mi. What is the total distance for 197 trips from home to school? Use mental math.

See Problem 5.

Simplify each expression by combining like terms.

53. 11x + 9x
54. 8 y − 7 y 8 y minus 7 y
55. 5 t − 7 t 5 t minus 7 t
56. − n + 4 n negative n plus 4 n
57. 5 w 2 + 12 w 2 5 , w squared , plus 12 , w squared
58. 2 x 2 − 9 x 2 2 , x squared , minus 9 , x squared
59. − 4 y 2 + 9 y 2 negative 4 , y squared , plus 9 , y squared
60. 6 c − 4 + 2 c − 7 6 c minus 4 plus 2 c minus 7
61. 5 − 3 x + y + 6 5 minus 3 x plus y plus 6
62. 2 n + 1 − 4 m − n 2 n plus 1 minus 4 m minus n
63. − 7 h + 3 h 2 − 4 h − 3 negative 7 h plus 3 , h squared , minus 4 h minus 3
64. 10 a b + 2 a b 2 − 9 a b 10 eh b plus 2 eh , b squared , minus 9 eh b

B Apply

Write a word phrase for each expression. Then simplify each expression.

65. 3 ( t − 1 ) 3 open t minus 1 close
66. 4(d + 7)
67. 1 3 ( 6 x − 1 ) 1 third , open 6 x minus 1 close

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