Simplify each expression using the order of operations. a) 9 10 3 10 5 2 b) 7 20 a 1 8 4 5 b c) 4 3 a 5 6 b 2 7 12 Solution a) Be careful! Do not subtract fi rst. Remember that we multiply before we subtract. 9 10 3 10 5 2 9 10 3 10 2 5 1 2 Divide 10 and 5 by 5. Multiply. Write each fraction with the LCD, 20. Subtract. 9 10 3 4 18 20 15 20 3 20 b) When an expression contains parentheses or other grouping symbols, simplify what is inside them fi rst. 7 20 a 1 8 4 5 b 7 20 a 5 40 32 40 b Write the fractions in parentheses with the LCD, 40. Add the fractions in parentheses. Change division to multiplication by the reciprocal. Divide 20 and 40 by 20. Multiply. 7 20 37 40 7 20 40 37 7 20 1 2 40 37 14 37 c) Look at the expression 4 3a 5 6 b 2 7 12 . Notice that there is no operation symbol between the 3 and the expression in parentheses. Remember, this means the operation is multiplication. What do we do fi rst? Find a 5 6 b 2 . 4 3 a 5 6 b 2 7 12 4 3 a 25 36 b 7 12 First, fi nd a 5 6 b 2 . Next, multiply. Divide 3 and 36 by 3. Multiply. 4 3 1 1 25 36 12 7 12 4 25 12 7 12 EXAMPLE 4 Is this any different from using the order of operations in Section 2.6? www.mhhe.com/messersmith SECTION 4.6 Order Relations and Order of Operations 275
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