When dealing with expressions that have more than one operation, there are rules to the order in which you perform those operations.
- Evaluate all items in parentheses first.
- Evaluate all exponents and roots
- Evaluate all multiplication and division from left to right
- Evaluate all addition and subtraction from left to right
There is a saying that many people use to remember this order: Please Excuse My Dear Aunt Sally. If you use the first letters of each words, they correspond to the different operations:
| Please |
Parentheses |
| Excuse |
Exponents (and roots) |
| My |
Multiplication |
| Dear |
Division |
| Aunt |
Addition |
| Sally |
Subtraction |
Examples
Evaluate 4 + 2 × 3
First we evaluate 2 × 3 = 6 and then we add 4
Answer: 4 + 2 × 3 = 10
Evaluate 12 / (6 - 2)
This expression can also be written with the fraction upright and the 6 - 2 in the denominator. If we see an expression in a numerator or denominator, we act as if there are parentheses around it:
