#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
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