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Order of Operations
Introduction
When several math operations are combined in a single calculation, it can be tricky
to decide which calculations to perform first. Sometimes parentheses are used to partially
specify the order of operations. Nonetheless, even when parentheses are used, it is
important to follow a standard order in performing math operations—otherwise
different people might obtain different results.
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The Professor Says: When you are performing a mathematical
calculation containing a number of different operations, follow this order:
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1. Simplify inside parentheses (following the order of operations
in the remaining steps if necessary).2. Raise numbers to
powers.
3. Multiply.
4. Divide.
5. Add.
6. Subtract. |
Examples
| 1. Simplify: 3 + 6
(22 + 5) – 8 2 3
+ 6 (4 + 5) – 8 2
Simplify inside parentheses
3 + 6 • 9 – 8 2
3 + 54 – 8 2
Multiply 6 • 9
3 + 54 – 4
Divide 8 2
57 – 4
Add 3 + 54
53
Subtract 57 – 4
2. Simplify: 48 3 (7 – 9)2
+ 6 2
48 3 (–2)2 + 6 2
Simplify inside parentheses
48 3 • 4 + 6 2
Raise numbers to powers
48 12 + 6 2
Multiply 3 • 4
4 + 3
Divide 48 12 and 6 2
7
Add 4 + 3 |
Practice
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