Simplify. See Examples 1 through 9.EXAMPLE 1 Multiply.a. (−8) (4)b. 14(− 1)c. −9(−10)Solut...

Simplify. See Examples 1 through 9.

EXAMPLE 1 Multiply.

a. (−8) (4)

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b. 14(− 1)

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c. −9(−10)

Solution

a. −8(4) = −32

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b. 14(−1) = −14

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c. −9(−10) = 90

EXAMPLE 2 Perform the indicated operations.

a. (7) (0) (−6)

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b. (−2) (−3) (−4)

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c. (−l) (5) (−9)

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d. (−4) (−11) − (5) (−2)

Solution

a. By the order of operations, we multiply from left to right. Notice that, because one of the factors is 0, the product is 0.

(7) (0) (−6) = 0(−6) = 0

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b. Multiply two factors at a time, from left to right.

(−2) (−3) (−4)	=	(6) (−4)
	=	−24

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c. Multiply from left to right.

(−1) (5) (−9)	=	(−5) (−9)
	=	45

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d. Follow the rules for order of operations.

(−4) (−11) – (5) (−2)	=	44 – (−10)
	=	44 + 10
	=	54

EXAMPLE 3 Multiply

a. (−1.2) (0.05)

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b.

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c.

Solution

a. The product of two numbers with different signs is negative.

(−1.2) (0.05)	=	−[(1.2) (0.05)]
	=	−0.06

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b.

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c.

EXAMPLE 4 Evaluate.

a. (−2)3

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b. −23

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c. (−3)2

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d. −32

Solution

a. d. (−2)3 = (−2) (−2) (−2) = −8

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b. −23 = −(2·2·2) = −8

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c. (−3)2 = (−3) (−3) =9

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d. −32 = −(3·3) = −9

EXAMPLE 5 Find the reciprocal of each number.

a. 22

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b.

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c. −10

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d.

Solution

a. The reciprocal of 22 is since

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b. The reciprocal of is since

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c. The reciprocal of -10 is

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d. The reciprocal of is

EXAMPLE 6 Use the definition of the quotient of two numbers to divide.

a. −18 , ÷ 3

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b.

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c.

Solution

a.

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b.

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c.

EXAMPLE 7 Divide.

a.

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b.

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c.

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d.

Solution

a.

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b.

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c.

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d.

EXAMPLE 8 Perform the indicated operations.

a.

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b.

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c.

Solution

a.

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b.

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c.

EXAMPLE 9 Simplify each expression

a.

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b.

Solution

a. First, simplify the numerator and denominator separately, then divide.

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b. Simplify the numerator and denominator separately, then divide.