Percentages on the ACT: Every Type, Named and Explained

Because the 20% decrease is applied to a larger number than the original. After a 20% increase, the new value is 120% of the original — a bigger base. When you take 20% off that bigger base, you remove more absolute value than the increase added. The result is always slightly below the original.

The exact math: a 20% increase gives multiplier 1.20. A 20% decrease gives multiplier 0.80. Combined: 1.20 × 0.80 = 0.96. That means you end up at 96% of where you started — a net 4% decrease, not zero. For any equal-opposite percentage pair, the net result is always a small decrease. For a 10% pair: 1.10 × 0.90 = 0.99 (1% loss). For a 50% pair: 1.50 × 0.50 = 0.75 (25% loss). The larger the percentage, the bigger the net loss.

On the ACT, always set these up using the Sequential Multiplier. Multiply the multipliers — do not add or subtract the percentages. The answer “same as the original” is always wrong when a percentage increase is followed by the same percentage decrease.

Use the Divide-by-the-Multiplier Method: divide the final value by the multiplier that was applied. For a 15% increase, the multiplier is 1.15. For a 30% decrease, the multiplier is 0.70. Dividing the final value by that multiplier gives you the original.

The trap the ACT sets: instead of dividing by 1.15, students multiply by 0.85 (subtracting 15% from the final). This gives a wrong answer — and the ACT includes it as a specific choice. Here is why it is wrong: if the original was $80 and a 15% increase was applied, the new value is $92. If you multiply $92 by 0.85, you get $78.20 — not $80. But if you divide $92 by 1.15, you get $80 exactly. Always divide.

The verify step makes this foolproof: whatever answer you compute, multiply it by the multiplier and confirm it equals the given final value. $80 × 1.15 = $92 ✓. If it does not match, you used the wrong operation. This check takes ten seconds and catches every reverse percentage error.

The Decimal Multiplier is the fastest method for most ACT percentage questions — convert the percentage to a decimal and multiply (or divide for reverse problems). It requires no setup, works for every question type on this page, and produces exact answers with a calculator in under 15 seconds.

The “pick a number” approach — assuming the total is 100 or a similar round number — works well when a question asks for a percentage of an unspecified total, or when the answer choices are expressed as percentages rather than specific values. For example, “a price increases by 20% and then decreases by 10% — what is the net percent change?” Start with $100: after 20% increase it is $120; after 10% decrease it is $108. Net change = 8%. This approach turns an abstract percentage question into a concrete arithmetic problem and is genuinely faster than algebraic setup on some question types.

Proportions are the slowest of the three approaches for percentage problems specifically — they add a setup step that the Decimal Multiplier does not require. Use proportions when the problem is framed as a direct comparison (X/Y = A/B), but default to the Decimal Multiplier for everything else.

Apply the Part-Over-Whole Rule: the value immediately after the word “of” is the whole — it goes on the bottom (denominator). The value being expressed as a percentage of that whole goes on top (numerator). The phrase always reads as “[part] is what percent of [whole].”

“18 is what percent of 45?” → 18 goes on top (it is what percent), 45 goes on the bottom (it follows “of”): 18/45 = 0.40 = 40%. “What percent of 45 is 18?” — same answer, different phrasing: the “of” still marks 45 as the denominator.

The sanity check confirms you have it right: if the part is smaller than the whole, the percentage should be less than 100%. If the part is larger, the percentage should exceed 100%. In “18 is what percent of 45,” 18 is smaller than 45, so the answer must be under 100%. If your computation gives something above 100%, you inverted the fraction.

Yes — percentage questions appear across the full difficulty range, and the harder ones use the same six types covered in this guide. What changes is not the underlying math but the presentation: harder percentage questions embed two or more percentage operations in a single word problem, include extra numbers that are irrelevant to the percentage calculation (distractors), or require you to recognize that a percentage is involved before you can begin solving.

The most common harder-question structure: multi-step word problems where the output of one percentage calculation becomes the base for the next. A price is marked up by one percentage, and then a discount is applied to the marked-up price — and the question may ask for the final price, or for the overall percent change from the original wholesale price. Both require recognizing the correct base at each step and applying the Sequential Multiplier, not combining percentages arithmetically.

A second harder structure: reverse percentage buried inside a word problem where you must first identify that a reverse percentage is needed. The question will give you a final value and a percentage and ask for the original — but disguised as a “how much did it cost before the sale?” scenario with irrelevant details about other items or quantities. The Distractor Scan and the Divide-by-the-Multiplier Method apply identically regardless of how much extra context surrounds the core percentage operation.

“Percent of” asks what fraction one value is of another, expressed as a percentage. No change is implied — you are simply expressing a relationship between two existing numbers. Formula: (part ÷ whole) × 100. “18 is what percent of 45?” → (18/45) × 100 = 40%.

“Percent change” asks how much a value has changed relative to where it started. Change is implied — there is a before and an after. Formula: (amount of change ÷ original value) × 100. “A price went from $45 to $36 — what is the percent change?” → (9/45) × 100 = 20% decrease.

The practical distinction on the ACT: if the problem gives you two values and describes a before-and-after situation (sale price, population growth, test score increase), it is a percent change question. If the problem gives you two values and asks how one compares to the other without implying a change over time, it is a “percent of” question. The signal words: “decreased by,” “increased by,” “grew,” or “fell” all indicate percent change. “Is what percent of,” “what fraction of,” or “compared to” indicate percent of.