38 Chapter 1 The Set of Real Numbers Applying the Order of Operations Example 4 Simplify the expressions. a. 25 12 3 4 b. 6.2 02.1 0 116 9 c. 28 23 16 322 44 Solution: a. Multiply or divide in order from left to right. 25 4 4 12 3 Notice that the operation is performed first (not ). Multiply before subtracting. Subtract. b. 25 16 4 4 Simplify within the square root. Simplify the absolute value and square root. Add or subtract from left to right. Add. c. Simplify within the inner parentheses first. Simplify exponents. Add within the square brackets. Multiply before subtracting. Subtract. 9 6.2 02.1 0 116 9 6.2 02.1 0 125 6.2 12.12 5 4.1 5 9.1 28 23 16 322 44 28 23 1322 44 28 23 192 44 28 23134 28 26 2 Skill Practice Simplify the expressions. 11. 12. 13. 1 2 32 6 020 0 2 20 4 60 53 17 42 22 4 Applying the Order of Operations Simplify the expression. Solution: In this expression, the fraction bar acts as a grouping symbol. First, simplify the expressions above and below the fraction bar using order of operations. The last step is to simplify the fraction. 32 8 2 2 32 32 4 2 9 36 18 2 32 8 2 2 32 Example 5 3 4 25 12 3 4 Avoiding Mistakes In Example 4(a), division is performed before multiplication because it occurs first as we read from left to right. Answers 11. 4 12. 16 13. 25
miller_beginning_intermediate_algebra_4e_ch1_3
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