Preliminaries
Whole Numbers
If multiplication, division, powers, addition, parentheses, and so on, are all contained in one problem, the order of operations is as follows.
An easy way to remember the order of operations is Please Excuse My Dear Aunt Sally ( Parentheses, Exponents, Multiplication/ Division, Addition/ Subtraction).
Example 1
Simplify each of the following.
16 + 4 × 3
10 – 3 × 6 + 102 + (6 + 1) × 4
First, the multiplication,
16 + 4 × 3 = 16 + 12Then, the addition,
16 + 12 = 28First, the parentheses,
10 – 3 × 6 + 102 + (6 + 1) × 4 = 10 – 3 × 6 + 102 + (7) × 4Then, the exponents,
102 = 10 × 10 = 100,so 10 – 3 × 6 + 102 + (7) × 4 = 10 – 3 × 6 + 100 + (7) × 4
Then, multiplication,
10 – 3 × 6 + 100 + (7) × 4 = 10 – 18 + 100 + 28Then, addition and subtraction left to right,
