Order of Operations
Why does 2 + 3 × 4 equal 14, not 20? Calculators and mathematicians follow one agreed order. Learn it once and you'll never be tricked by a viral math puzzle again.
The agreed order
When a calculation has several operations, do them in this order:
| Step | Examples | |
|---|---|---|
| P | Parentheses (brackets) first | ( ), [ ] |
| E | Exponents (powers and roots) | 3², √9 |
| MD | Multiplication and Division, left to right | ×, ÷ |
| AS | Addition and Subtraction, left to right | +, − |
Common memory aids: PEMDAS (US), BODMAS or BIDMAS (UK and elsewhere). They're the same rule with different words.
- Multiplication before addition: 3 × 4 = 12
- Then 2 + 12
- = 14
The rule most people get wrong
Multiplication does not always come before division, and addition doesn't always come before subtraction. They're equal partners: work left to right.
- Same level, so go left to right
- 12 ÷ 3 = 4
- 4 × 2
- = 8 (not 2)
- Left to right: 10 − 4 = 6
- 6 + 3
- = 9 (not 3)
This is why “PEMDAS” misleads people: the letters suggest M before D and A before S. Think of it as P · E · MD · AS, four levels, not six.
Viral puzzles and good habits
Puzzles like 8 ÷ 2(2 + 2) go viral because they're written ambiguously on purpose. Following the standard rules: brackets give 4, then left to right, 8 ÷ 2 = 4, then 4 × 4 = 16. Some people (and some older textbooks) treat “2(4)” as a single unit and get 1.
Real mathematicians avoid the argument by writing clearly: use extra brackets or a fraction bar so there's only one way to read it.
Negative numbers and powers: −3² is −9 (the power applies to 3 first), but (−3)² is 9.
Use * or × for multiply, / or ÷ for divide, and ^ or ² for powers.