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

MORE EXAMPLES ON NEXT PAGE

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