Page 111 - Basic College Mathematics with Early Integers

88 C HAPTE R 1 I THE WHOLE NUMBERS

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PRACTICE 13 Example 13 Simplify: 4 , 2 4
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Simplify: 48 , 3 2 2
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Solution: We start by evaluating 4 .
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4 , 2 4 = 16 , 2 4 Write 4 2 as 16.
Next we multiply or divide in order from left to right. Since division appears
before multiplication from left to right, we divide first, then multiply.
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16 , 2 4 = 8 4 Divide.
= 32 Multiply.
Work Practice 13
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PRACTICE 14 Example 14 Simplify: (8 - 6) + 2 3 # 3
4
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Simplify: (10 - 7) + 2 3 2
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Solution: (8 - 6) + 2 3 # 3 = 2 + 2 3 # 3 Simplify inside parentheses.
b b
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= 4 + 8 3 Write 2 2 as 4 and 2 3 as 8.
= 4 + 24 Multiply.
= 28 Add.
Work Practice 14

PRACTICE 15 3 2
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Example 15 Simplify: 4 + [3 - (10 , 2)] - 7 3
Simplify:
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3
36 , [20 - (4 2)] + 4 - 6 Solution: Here we begin with the innermost set of parentheses.
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3
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4 +[3 -(10÷2)]-7 3=4 +[3 -5]-7 3 Simplify inside parentheses.
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=4 +[9-5]-7 3 Write 3 2 as 9.
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=4 +4-7 3 Simplify inside brackets.
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=64+4-7 3 Write 4 3 as 64.
=64+4-21 Multiply.
=47 Add and subtract from
left to right.
Work Practice 15
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PRACTICE 16 Example 16 Simplify: 7 - 2 3 + 3 2
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25 + 8 2 - 3 3 5(2 - 1)
Simplify:
2(3 - 2) Solution: Here, the fraction bar is like a grouping symbol.We simplify above
and below the fraction bar separately.
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7 - 2 3 + 3 2 7 - 2 3 + 9
= Evaluate 3 2 and (2 - 1).
5(2 - 1) 5(1)
7 - 6 + 9
= Multiply 2 # 3 in the numerator and multiply 5
5 and 1 in the denominator.
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= Add and subtract from left to right.
5
Answers = 2 Divide.
13. 64 14. 99 15. 61 16. 7
Work Practice 16