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#3 ORDER OF OPERATIONS The order of operations establishes the necessary rules so that expressions are evaluated in a consistent way by everyone. The rules, in order, are: • When grouping symbols such as parentheses are present, do the operations within them first. • Next, perform all operations with exponents. • Then do multiplication and division in order from left to right. • Finally, do addition and subtraction in order from left to right. Also see the textbook, page 49. Example 12 ÷ 22 ! 4 + 3(1 + 2)3 Simplify the numerical expression at right: Start by simplifying the parentheses: 3(1 + 2)3 = 3(3)3 so 12 ÷ 22 ! 4 + 3(3)3 Then perform the exponent operation: 2 2 = 4 and 33 = 27 so 12 ÷ 4 ! 4 + 3(27) Next, multiply and divide left to right: 12 ÷ 4 = 3 and 3(27) = 81 so 3 – 4 + 81 Finally, add and subtract left to right: 3 – 4 = -1 so -1 + 81 = 80 Simplify the following numerical expressions. 1. 29 + 16 ÷ 8! 25 4. 1 2 3. 2 (3 ! 1) ÷ 8 2. 36 + 16 ! 50 ÷ 25 ( 6 ! 2) 2 ! 4 " 3 7. !62 + 4 " 8 [ 5. 3 2 (1 + 5 ) + 8 ! 32 ] 6. (8 + 12 ) ÷ 4 ! 6 8. 18 ! 3 ÷ 33 9. 10 + 52 ! 25 10. 20 ! (33 ÷ 9) " 2 11. 100 ! (2 3 ! 6) ÷ 2 12. 22 + (3 ! 2)2 ÷ 2 13. 85 ! (4 " 2)2 ! 3 14. 12 + 3 12 !9 ! 2 19!15 ( 8!2 ) ( 9!1 ) ( 11!2 ) ( 12! 4 ) 15. 15 + 4 9 !6 ! 2 18!10 Answers 1. 79 2. 50 3. 1 2 4. -4 5. 33 6. -1 7. -4 8. 2 9. 10 10. 14 11. 99 12. 40 13. 18 14. 14 15. 25 © 2006 CPM Educational Program. All rights reserved.