Simplify each expression. Justify each step.

49. 25 · 3.9 · 4 25 middle dot 3.9 middle dot 4
50. ( 4.4 ÷ 4.4 ) ( x + 7 ) open 4.4 divides 4.4 close open x plus 7 close
51. ( 7 6 − 6 5 ) ( 8 − 8 ) open , 7 to the sixth , minus , 6 to the fifth , close open 8 minus 8 close

Reasoning Answer each question. Use examples to justify your answers.

52. Is subtraction commutative?
53. Is subtraction associative?
54. Is division commutative?
55. Is division associative?

C Challenge

56. Patterns The Commutative Property of Addition lets you rewrite addition expressions. How many different ways can you write a + b + c? Show each way.
57. Reasoning Suppose you know that a(b + c) = ab + ac is true for all real numbers a, b, and c. Use the properties of real numbers to prove that (b + c)a = ba + ca is true for all real numbers a, b, and c.

Standardized Test Prep

SAT/ACT

58. What is the simplified form of (1.2 + 0) + 4.6 + 3.8?
    1. 1.2
    2. 8.0
    3. 8.4
    4. 9.6
59. Which expression is equal to 3 · 3 · 8 · 8 · 3 ? 3 middle dot 3 middle dot 8 middle dot 8 middle dot 3 question mark
    6. 3 · 8 3 middle dot 8
    7. 3 8 3 to the eighth
    8. 3 3 · 8 2 3 cubed , middle dot , 8 squared
    9. 3 · 3 + 2 · 8 3 middle dot 3 plus 2 middle dot 8
60. There are four points plotted on the number line below.

    

    Which expression represents the greatest amount?

    1. M ÷ L m divides l
    2. M − L m minus l
    3. J + K j plus k
    4. L − K l minus k
61. Lane 1 at your local track is 0.25 mi long. You live 0.5 mi away from the track. Which of the following results in the shortest jog?
    6. jogging 6 times around the track in Lane 1
    7. jogging to the track and then 5 times around the track in Lane 1
    8. jogging to the track, 3 times around the track in Lane 1, and then home
    9. jogging 8 times around the track in Lane 1

Mixed Review

See Lesson 1-3.

Order the numbers in each exercise from least to greatest.

62. − 6 , 6 3 , negative 6 comma , 6 cubed , comma  1.6, 6 square root of 6
63. 8 5 , 8 fifths , comma  1.4, − 17 , 10 2 negative 17 comma , 10 squared
64. 1.75, − 4.5 , 4 , 14 1 negative 4.5 comma , square root of 4 comma . 14 to the first

Get Ready! To prepare for Lesson 1-5, do Exercises 65–68.

See p. 791.

Find each sum or difference.

65. 3 + 11
66. 3 8 + 5 8 3 eighths , plus , 5 eighths
67. 9.7 − 8.6 9.7 minus 8.6
68. 5 9 − 5 10 5 ninths , minus , 5 tenths

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