Order of Operations

If multiplication, division, powers, addition, parentheses, and so on, are all contained in one problem, the order of operations is as follows.

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An easy way to remember the order of operations is Please Excuse MDear Aunt Sally ( Parentheses, Exponents, Multiplication/ Division, Addition/ Subtraction).

Example 1

Simplify each of the following.

1. 16 + 4 × 3

2. 10 – 3 × 6 + 10 2 + (6 + 1) × 4

1. First, the multiplication,

16 + 4 × 3 = 16 + 12

Then, the addition,

16 + 12 = 28

2. First, the parentheses,

10 – 3 × 6 + 10 2 + (6 + 1) × 4 = 10 – 3 × 6 + 10 2 + (7) × 4

Then, the exponents,

10 2 = 10 × 10 = 100,

so 10 – 3 × 6 + 10 2 + (7) × 4 = 10 – 3 × 6 + 100 + (7) × 4

Then, multiplication,

10 – 3 × 6 + 100 + (7) × 4 = 10 – 18 + 100 + 28

Then, addition and subtraction left to right,

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