A.3 Order of Operations

Equations and formulas often include a number of mathematical operations combining addition, subtraction, multiplication, and division. Some also include exponents and square roots. In complex equations with more than one operation, it is important to perform the operations in a specific sequence. Deviating from this sequence can produce a wrong answer. Table A.2 lists the order of operations for quick reference.

Table : TABLE A.2 Order of Operations
Rule of Operation Example
1. Complete any calculations within parentheses first. 1a. (6 + 2) − 4 × 3/22 + 6 =
1b. 8 − 4 × 3/22 + 6 =
2. Complete any squaring (or raising to another exponent) second. 2a. 8 − 4 × 3/22 + 6 =
2b. 8 − 4 × 3/4 + 6 =
3. From left to right, complete all multiplication and division operations. This may require multiple steps. 3a. 8 − 4 × 3/4 + 6=
3b. 8 − 12/ 4 + 6 =
3c. 8 − 12/4 + 6 =
3d. 8 − 3 + 6 =
4. Last, complete all the addition and subtraction operations. 4a. 8 − 3 + 6 =
4b. 5 + 6 =
4c. 11 = 11

Order of Operations: Worked Examples

Self-Quiz #2: Order of Operations

(Answers to this quiz can be found in section A-6.)

  1. 3(7) − 12/3 + 2 =
  2. 4/2 + 6 − 2(3) =
  3. −5(4) + 16 =
  4. 8 + (−16)/4 =
  5. 6 − 3 + 5 − 3(5) + 10 =
  6. 42/8 − 4(3) + (8 − 3) =
  7. (14 − 6) + 72/9 + 4 =
  8. (54 − 18)/4 + 7 × 3 =
  9. 32 − 4(3 + 4) + 8 =
  10. 100 × 3 − 87 =