Convert between fractions, decimals, and percentages, and apply that fluency to percentage change, markup, and discount problems — the numbers rarely come pre-simplified. Every question comes with a written walkthrough of the conversion step, not just the final answer.
A price that rises 20% then falls 20% doesn't return to its original value — the second 20% is taken from the new, larger amount, not the original.
Going from 20% to 25% is a 5 percentage-point increase, but a 25% increase relative to the original 20% — mixing these up is a common source of wrong answers on change problems.
3/8 and 0.4 can't be compared directly by eye — convert both to the same form first, or the larger-looking number can trick you.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Write 7/8 as a percentage.
A — 87.5%. Divide 7 by 8 to get 0.875, then multiply by 100 to convert to a percentage: 87.5%. 78% (B) comes from reading the fraction's digits in the wrong order instead of dividing. 875% (C) comes from forgetting to divide the decimal by 100 after converting — leaving the decimal point in the wrong place.
A jacket originally priced at $80 is marked up 25%, then put on sale for 10% off the marked-up price. What is the final price?
A — $90. Apply each percentage to the current price, not the original: the markup takes $80 to $80 × 1.25 = $100, and the discount is then taken from that $100, giving $100 × 0.9 = $90. $80 (B) comes from assuming the two percentages offset each other, which only works if they were the exact same percentage in opposite directions — 25% and 10% don't cancel. $72 (D) comes from applying the discount to the original $80 instead of the marked-up price: 80 × 0.9 = 72, reusing the wrong base.
A population increased by 10% one year, then decreased by 10% the next. If the population is now 19,800, what was the population two years ago?
A — 20,000. A 10% increase followed by a 10% decrease doesn't return to the original — it multiplies by 1.1 × 0.9 = 0.99, a net 1% decrease. So 0.99P = 19,800, giving P = 19,800 / 0.99 = 20,000. 19,800 (B) comes from assuming the two 10% changes cancel out exactly, treating the net multiplier as 1 instead of 0.99.
Percent problems are arithmetic wearing new clothes — the fastest gains come from locking in which number is the base before doing any multiplication.
For every percent problem, name which number the percentage applies to before doing any arithmetic. Untimed practice is where that habit gets built.
Move to timed sessions once base-identification is automatic. Percent problems should be some of the fastest in the section once the habit sticks.
Pair percentages with ratio and proportion in a mock — both are about relationships between two changing quantities.
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