Reduce numerical and algebraic expressions to their simplest form efficiently — combining fraction, exponent, and order-of-operations rules into one problem. Every question comes with a written walkthrough of the sequence that got there fastest.
Reducing 24/36 to 12/18 is a real step, but it's not simplified — 12/18 still shares a factor of 6, so it isn't the final answer yet.
(6 + 9)/3 isn't 6/3 + 9 — the whole numerator has to be added before dividing, or every term in it needs to be divided by the same denominator, not just one of them.
On a long expression, redoing a step that's already been simplified — or skipping one that hasn't — is the most common way a multi-step simplification goes wrong.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Simplify: 48/72
A — 2/3. The greatest common factor of 48 and 72 is 24: dividing both by 24 gives 2/3. 4/6 (B) and 24/36 (C) are both real intermediate steps if you divide by a smaller common factor like 12 or 2 first, but neither is fully simplified since they still share a common factor.
Simplify: (6 + 9) / 3 + 2 × 4
A — 13. Resolve the parentheses first: 6 + 9 = 15, so 15/3 = 5. Then handle the multiplication: 2 × 4 = 8. Add the two results: 5 + 8 = 13. 28 (B) comes from ignoring the multiplication's priority and evaluating strictly left to right: 5 + 2 = 7, then 7 × 4 = 28.
Simplify: (3² × 4 − 6) / (2³ − 5) + 1/2
A — 21/2. Resolve each part in order: 3² = 9, so 9 × 4 − 6 = 30, and 2³ − 5 = 3. That gives 30/3 = 10 for the first term, and adding 1/2 gives 10 + 1/2 = 21/2. 10 (B) comes from dropping the final "+ 1/2" term entirely — a common slip on a long expression where the last piece gets forgotten after several steps of exponent and order-of-operations work.
Simplification problems are a stress test for every arithmetic rule at once — the fix isn't learning a new rule, it's not losing one you already know partway through.
Resist the urge to combine two steps in your head on a long expression. Untimed practice is where that patience gets built.
Move to timed sessions once multi-step expressions stop costing you a lost step. These run a bit longer since several rules are stacked in one problem.
Pair simplification with order of operations and fraction operations in a mock — all three are the same discipline applied to different building blocks.
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