64. Error Analysis Describe and correct the error in dividing the fractions below.

    

65. Reasoning You can derive the rule for division involving 0 shown on page 40.
    1. Suppose 0 ÷ x = y , 0 divides x equals y comma  where x ≠ 0 . x not equal to 0 .  Show that y = 0. (Hint: If 0 ÷ x = y , 0 divides x equals y comma  then x · y = 0 x middle dot y equals 0  by the definition of division.)
    2. If x ≠ 0 , x not equal to 0 comma  show that there is no value of y such that x ÷ 0 = y . x divides 0 equals y .  (Hint: Suppose there is a value of y such that x ÷ 0 = y . x divides 0 equals y .  What would this imply about x?)

C Challenge

Determine whether each statement is always, sometimes, or never true. Explain your reasoning.

66. The product of a number and its reciprocal is − 1 . negative 1 .
67. The quotient of a nonzero number and its opposite is − 1 . negative 1 .
68. If the product of two fractions is negative, then their quotient is positive.
69. Reasoning What is the greatest integer n for which ( − n ) 3 open negative n close cubed  is positive and the value of the expression has a 2 in the ones place?

Standardized Test Prep

SAT/ACT

70. Which expression does NOT have the same value as − 11 + ( − 11 ) + ( − 11 ) ? negative 11 plus open negative 11 close plus open negative 11 close question mark
    1. − 33 negative 33
    2. 3 ( − 11 ) 3 open negative 11 close
    3. ( − 11 ) 3 open negative 11 close cubed
    4. 33 − 66 33 minus 66
71. Miguel measured the area of a piece of carpet and figured out that the approximate error was 3 | − 0.2 | . 3 vertical line negative 0.2 vertical line .  What is the decimal form of 3 | − 0.2 | ? 3 vertical line negative 0.2 vertical line question mark
    6. − 0.6 negative 0.6
    7. − 0.06 negative , 0.06
    8. 0.06
    9. 0.6
72. What is the perimeter of the triangle shown?

    

    1. 6y + 24
    2. 21y + 9
    3. 15y + 15
    4. 30Y

Mixed Review

See Lesson 1-5.

Find each difference.

73. 46 − 16 46 minus 16
74. 34 − 44 34 minus 44
75. − 37 − ( − 27 ) negative 37 minus open negative 27 close

Get Ready! To prepare for Lesson 1-7, do Exercises 76–78.

See Lesson 1-4.

Name the property that each statement illustrates.

76. − x + 0 = − x negative x plus 0 equals negative x
77. 13 ( − 11 ) = − 11 ( 13 ) 13 open negative 11 close equals negative 11 open 13 close
78. − 5 · ( m · 8 ) = ( − 5 · m ) · 8 negative 5 middle dot open m middle dot 8 close equals open negative 5 middle dot m close middle dot 8

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