Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 29 ���������������������� Order of Operations When simplifying a numerical expression, perform the operations in the following order: Step 1: Simplify expressions inside grouping symbols first, starting with the innermost set. If there is a fraction bar, simplify the numerator and denominator separately. Step 2: Simplify any exponential expressions. Step 3: Perform multiplication or division in order from left to right. Step 4: Perform addition or subtraction in order from left to right. �� ������������������������ ������������������ Use the order of operations to simplify each expression. 2a. 9 + 5(6) 2b. 4 · 5 ÷ 2 + 3 · 8 2c. 2 3 (6 - 2)2 - 1 3 2d. 6 -162 - 4(5)(1) 2(1) 2e. 47 - u9 - 4(5 - 3)u Solutions 2a. 9 + 5(6) 9 + 30 Multiply 5 and 6. 39 Add. 2b. 4 · 5 ÷ 2 + 3 · 8 20 ÷ 2 + 3 · 8 Multiply 4 and 5. 10 + 3 · 8 Divide 20 by 2. 10 + 24 Multiply 3 and 8. 34 Add the numbers. 2c. 2 3 (6 - 2)2 - 1 3 2 3 (4)2 - 1 3 Simplify inside parentheses. 2 3 (16) - 1 3 Simplify 42. 32 3 - 1 3 Multiply: 2 3 a 16 1 b = 32 3 . 31 3 Subtract the resulting fractions. 2d. 6 - 162 - 4(5)(1) 2(1) 6 - 136 - 4(5)(1) 2 Simplify 62. Multiply the numbers in the denominator. 6 - 136 - 20 2 Multiply: 4(5)(1) = 20(1) = 20. 6 - 116 2 Subtract the numbers in the square root. 6 - 4 2 Simplify 116. 2 2 Subtract the numbers in the numerator. 1 Divide the numbers.
hendricks_beginning_algebra_1e_ch1_3
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