1.8 Order of Operation

ORDER OF OPERATION

Some math problems are a mixture of addition, subtraction, division, and multiplication. An operation to be performed might be true for one item but not another, so parentheses are used () for clarification.

There is a specific order to follow when making calculations.

The order in which operations are performed is:

  1. Parentheses: ( )
  2. Exponents: 23
  3. Multiplication and division
  4. Addition and subtraction
  5. Left to right

Note: It is always useful to add parentheses to clarify the order.

Example 1 - Solve 10 + 10 ÷ 10

Step 1. Division is performed before addition.
10 ÷ 10 = 1

Step 2. Add.
10 + 1 = 11

10 + 10 ÷ 10 = 11

The same example can be rewritten:
10 + 10 ÷ 10
10 + (10 ÷ 10). Using the parentheses helps clarify the order of operation.

Example 2 - Solve 63 ÷ (10 - 8)2 ÷ 2 + 2

Step 1. Parentheses.
63 ÷ (10 - 8)2 ÷ 2 + 2 = 63 ÷ 22 ÷ 2 + 2

Step 2. Exponents.
216 ÷ 4 ÷ 2 + 2

Step 3. Division in order from left to right.
216 ÷ 4 = 54
54 ÷ 2 = 27

Step 4. Addition.
27 + 2 = 29

63 ÷ (10 - 8)2 ÷ 2 + 2 = 29