Order of Operations
Students who calculate 3 + 4 × 2 as 14 instead of 11 have fallen into the classic order of operations trap. Teaching PEMDAS correctly prevents calculation errors that compound throughout middle school algebra. The acronym provides a reliable framework that transforms confusing expressions into step-by-step solutions.
Why it matters
Order of operations appears everywhere students encounter multi-step calculations. When splitting a $60 dinner bill among 4 friends with a $12 tip, students must calculate (60 + 12) ÷ 4 = $18 per person, not 60 + 12 ÷ 4 = $63. Scientific formulas like calculating area of composite shapes require precise operation sequencing. A rectangular garden with a 3 × 5 foot section plus a 2 × 4 foot extension needs (3 × 5) + (2 × 4) = 23 square feet of mulch. Programming and spreadsheet formulas follow identical rules, making PEMDAS essential for technology literacy. Students who master order of operations in elementary grades avoid algebraic confusion later, building confidence for expressions like 2x + 3(x - 1) where parentheses and distribution follow predictable patterns.
How to solve order of operations
Order of Operations (PEMDAS)
- Parentheses first.
- Then exponents.
- Then multiplication and division (left to right).
- Then addition and subtraction (left to right).
Example: 3 + 4 × 2 = 3 + 8 = 11 (not 14).
Worked examples
3 + 3 × 2 = _______
Answer: 9
- Multiply first → 3 × 2 = 6 — Multiplication before addition (PEMDAS).
- Then add → 3 + 6 = 9 — Now add the remaining term.
- Verify → 3 + 3 × 2 = 9 ✓ — Check the answer.
True or false: 2 + 9 × 9 = 99
Answer: False (83)
- Multiply first → 9 × 9 = 81 — Multiplication before addition.
- Then add → 2 + 81 = 83 — Add the remaining.
- Verify → 2 + 9 × 9 = 83 ✓ — Check.
Add parentheses to make it true: 3 × 5 + 4 − 4 = 23
Answer: 3 × (5 + 4) − 4
- Without parentheses → 3 × 5 + 4 − 4 = 15 — Without parentheses we get 15, not 23.
- Try grouping addition → 3 × (5 + 4) − 4 — Parentheses around the addition changes the order.
- Verify → 3 × (5 + 4) − 4 = 23 ✓ — Check.
Common mistakes
- Working left to right without considering operation priority, calculating 6 + 2 × 3 as 8 × 3 = 24 instead of 6 + 6 = 12.
- Forgetting parentheses change everything, solving 4 × 3 + 2 = 14 but missing that 4 × (3 + 2) = 20.
- Treating multiplication and division as having different priorities, calculating 12 ÷ 3 × 2 as 12 ÷ 6 = 2 instead of 4 × 2 = 8.
- Ignoring exponents in the sequence, computing 2 + 3² × 4 as 5² × 4 = 100 instead of 2 + 9 × 4 = 38.