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Order of Arithmetic Operations


For a given arithmetic operation, the following order should be observed when solving:

1) Parentheses

2) Exponents (and Roots)

3) Multiplication & Division  (In order from left to right)

4) Addition & Subtraction  (In order from left to right)
This means that expressions within parentheses are evaluated first, then exponents (including roots, i.e. radicals), then multiplication and division (at the same level), and finally addition and subtraction (at the same level). If there are multiple operations at the same level on the order of operations, move from left to right.

Example #1:

Compute 4 − 8 x (3 + 2) + 42

Step 1:  Compute sum within parentheses

= 4 − 8 x 5 + 42

Step 2:  Compute exponent

= 4 − 8 x 5 + 16

Step 3: Compute product

= 4 − 40 + 16

Step 4: Compute difference

= −36 + 16

Step 5: Compute remaining sum to attain answer

= −20


Example #2:

Compute 5 + 6 / 2 + 9

Step 1: Compute divsion operation

= 5 + 3 + 9

Step 2: Compute remaining sum

= 17

(Note: It would be easy to accidentally provide an incorrect answer of 11/11 = 1 in the event addition operations were performed first)