ORDER OF OPERATIONS
The Order of Operations is a set of rules that governs which operations take precedence. For example, in the expression below we might be tempted to add 3 and 4 first. But in reality, we multiply 4 x 2 first. Then, we do all operations inside the parentheses. Then we square. And finally, we divide by 2.
(3 + 4 x 2 – 1)2 ¸ 2 = ?
Here is the correct order of operations
(3 + 4 x 2 – 1)2 ¸ 2 =
(3 + 8 – 1)2 ¸ 2 =
(11 – 1)2 ¸ 2 =
(10)2 ¸ 2 =
100 ¸ 2 =
50
The Order of Operations is:
1. Do all operations inside parentheses first.
2. Do all exponent operations from left to right.
3. Do all dividing & multiplying from left to right.
4. Do all subtracting & adding from left to right.
Examples
Example: Evaluate 10 + 4 x 2 – (12 - 32)2 x 2
10 + 4 x 2 – (12 - 32)2 x 2 =
10 + 4 x 2 – (12 - 9)2 x 2 =
10 + 4 x 2 – (3)2 x 2 =
10 + 4 x 2 – 9 x 2 =
10 + 8 – 18 =
18 – 18 = 0
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Example: Evaluate 10 + 4 – 2 x 3 – (4 - 3)2 + 2 x 5
10 + 4 – 2 x 3 – (4 - 3)2 + 2 x 5 =
10 + 4 – 2 x 3 – (1)2 + 2 x 5 =
10 + 4 – 2 x 3 – 1 + 2 x 5 =
10 + 4 – 6 – 1 + 10 =
14 – 6 - 1 + 10 =
8 - 1 + 10 =
7 + 10 = 17
Example: Evaluate ((12 - 5 x 2)3 + 1)2
((12 - 5 x 2)3 + 1)2 =
((12 - 10)3 + 1)2 =
((2)3 + 1)2 =
(8 + 1)2 =
(9)2 =
9 x 9 = 81
REMEMBER:
PEMDAS = Parentheses Exponents Multiply/Divide Add/Subtract