Evaluate multi-step numerical expressions in the correct order — parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right. The rules are simple; the exam just gives you more steps than you expect to track at once. Every question comes with a written walkthrough of the order applied.
Multiplication doesn't outrank division, and addition doesn't outrank subtraction — each pair is a tie broken by reading left to right, not by the order the letters appear in the acronym.
3(4 + 5²) requires resolving 5² and the addition inside the parentheses completely before multiplying by 3 — not distributing the 3 across each term first.
−3² is −9, not 9 — the exponent applies only to the 3 unless the negative sign is also inside parentheses, like (−3)².
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Evaluate: 6 + 4 × 3 − 2
A — 16. Multiplication happens before addition and subtraction: 4 × 3 = 12 first, then 6 + 12 − 2 = 16. 28 (B) comes from evaluating strictly left to right — computing 6 + 4 = 10, then 10 × 3 = 30, then 30 − 2 = 28 — ignoring that multiplication takes priority over the addition and subtraction around it.
Evaluate: 2(3 + 4)² − 10
A — 88. Resolve the parentheses first: 3 + 4 = 7. Apply the exponent next: 7² = 49. Then multiply by 2: 98, and subtract 10: 88. 39 (B) comes from forgetting the leading 2 entirely — squaring the parentheses and subtracting 10 without ever multiplying by the coefficient out front. 186 (C) comes from distributing the 2 into the parentheses before applying the exponent, squaring 14 instead of 7.
Evaluate: 2 + 3 × 4² ÷ 6 − 1
A — 9. Handle the exponent first: 4² = 16. Then multiplication and division at equal priority, left to right: 3 × 16 = 48, then 48 ÷ 6 = 8. Finally addition and subtraction, left to right: 2 + 8 = 10, then 10 − 1 = 9. 25 (B) comes from applying the exponent to the whole "3 × 4" instead of just the 4 — squaring 12 to get 144, dividing by 6 to get 24, then adding and subtracting to reach 25.
PEMDAS problems are rarely about not knowing the rule — they're about tracking four or five steps without losing one along the way.
Never combine two steps in your head. Write the expression again after each operation, even when it feels slow. Untimed practice is where that habit gets built before speed tempts you to skip it.
Move to timed sessions once you're not losing steps. Multi-step expressions run a little longer than single-operation problems.
Pair order of operations with simplification in a mock — both reward the same step-by-step discipline.
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