Add, subtract, multiply, and divide fractions and mixed numbers without a calculator, at speed — the operations are simple, but each one has its own rule and its own way to slip. Every question comes with a written walkthrough of exactly which rule applied.
1/2 + 1/3 is not 2/5 — fractions can only combine directly once they share a denominator; a common denominator has to come first.
1/2 ÷ 1/3 means multiplying by the reciprocal of 1/3, which is 3/1 — flipping the first fraction instead of the second gives a completely different, wrong answer.
2 3/4 becomes 11/4, not 8/4 or 9/4 — multiply the whole number by the denominator, then add the numerator, over the same denominator.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Compute: 2/3 + 1/4
A — 11/12. Convert to a common denominator of 12: 2/3 = 8/12 and 1/4 = 3/12, so the sum is 8/12 + 3/12 = 11/12. 3/7 (B) comes from adding numerators and denominators straight across instead of finding a common denominator — a shortcut that never works for addition.
Compute: 1 1/2 ÷ 2/3
A — 2 1/4. Convert the mixed number first: 1 1/2 = 3/2. Dividing by a fraction means multiplying by its reciprocal: 3/2 ÷ 2/3 = 3/2 × 3/2 = 9/4, which is 2 1/4. 1 (B) comes from multiplying by 2/3 directly instead of flipping it to 3/2 first — skipping the reciprocal step entirely, which happens to land on a deceptively clean whole number.
Simplify: (2/5 + 1/3) ÷ (3/5 − 1/6)
A — 22/13. Simplify numerator and denominator separately first: 2/5 + 1/3 = 6/15 + 5/15 = 11/15, and 3/5 − 1/6 = 18/30 − 5/30 = 13/30. Dividing, 11/15 ÷ 13/30 = 11/15 × 30/13 = 330/195, which reduces to 22/13. 13/22 (D) is the reciprocal of the correct answer — the result of flipping the wrong fraction when converting the division to multiplication.
Fraction operations are where a rushed step compounds fastest — one flipped reciprocal or skipped common denominator changes the whole answer, not just part of it.
Never do the flip or the common-denominator conversion in your head — write it as its own step. Untimed practice is where that discipline gets built.
Move to timed sessions once each operation's rule is automatic. Fractions run a bit longer than whole-number arithmetic since there's a conversion step first.
Pair fraction operations with order of operations in a mock — multi-step expressions often mix both.
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