Definition: The order of operations is the agreed sequence for evaluating an expression: grouping symbols, exponents, multiplication and division left to right, then addition and subtraction left to right.
What is the order of operations?
Without a shared rule, one expression could have several answers. Mathematicians agree on this order:
- Parentheses and other grouping symbols
- Exponents
- Multiplication and division, from left to right
- Addition and subtraction, from left to right
How does it look in action?
Evaluate 40 – 6 x (2 + 3) + 18 / 32.
- Parentheses: 2 + 3 = 5.
- Exponent: 32 = 9.
- Multiply and divide left to right: 6 x 5 = 30, and 18 / 9 = 2.
- Subtract and add left to right: 40 – 30 = 10, then 10 + 2 = 12.
What mistake is most common?
Treating multiplication as always before division, or addition as always before subtraction. They share a level, so move left to right. For 24 / 6 x 2, divide first to get 4, then multiply to get 8, not 2.
Example: 12 + 4 x 5 – 8 / 2 = 12 + 20 – 4 = 28.