60 Chapter 1 Whole Numbers 3. Order of Operations A numerical expression may contain more than one operation. For example, the following expression contains both multiplication and subtraction. The order in which the multiplication and subtraction are performed will affect the overall outcome. Multiplying first yields Subtracting first yields 18 5122 18 10 18 5122 13122 8 26 (correct) (incorrect) To avoid confusion, mathematicians have outlined the proper order of operations. In particular, multiplication is performed before addition or subtraction.The guidelines for the order of operations are given next. These rules must be followed in Using the Order of Operations all cases. Example 3 Simplify. a. b. c. Solution: a. 15 10 2 3 12 2 15 32 164 36 23 15 10 2 3 f 15 5 3 10 2 Perform the division first. Perform addition and subtraction from left to right. Add. b. Perform the operation inside parentheses first. Perform multiplication before subtraction. f 10 3 13 12 2 15 32 f 12 2 122 f 12 4 8 Subtract. 18 5122 18 6 2 4 Answers 8. 17 9. 9 10. 3 Order of Operations Step 1 First perform all operations inside parentheses or other grouping symbols. Step 2 Simplify any expressions containing exponents or square roots. Step 3 Perform multiplication or division in the order that they appear from left to right. Step 4 Perform addition or subtraction in the order that they appear from left to right. Skill Practice Simplify. 8. 9. 10. 23 116 9 120 42 2 1
miller_prealgebra_2e_ch1_3
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