ACT rates and percentages strategies
ACT Math tests rates, ratios, and percentages throughout the 60-question, 60-minute section. These questions appear in pre-algebra and elementary algebra items and reward students who can set up a proportion quickly and identify the correct base for each percent. These strategies cover the ratio backbone, percent change with the right denominator, the trap of applying a percent to the wrong base, and a step-by-step walkthrough.
The core principle
Rates and percentages are both ratios. A rate compares two quantities with different units, like miles per hour. A percentage compares a part to a whole, scaled to 100. Every rate or percent question reduces to the same move: set up a ratio, identify which quantity is the base (the denominator), and solve. For rates, the base is the unit of time or the unit being counted. If a car travels 240 miles in 4 hours, the rate is miles per hour. For percentages, the base is the original value, the whole you are taking a percent of. If a price increases from $80 to $100, the percent change is . The denominator is always the original, never the new value.
The most common trap
Applying a percent to the original instead of the current value
A price increases by 30%, then decreases by 30%. You apply both percents to the original and conclude the net change is zero. The decrease applies to the new, higher price, not the original, so the net change is a 9% decrease: \(1.30 \times 0.70 = 0.91\). The answer choices include "no change" because the test writers know this mistake. Identify the base for each percent before applying it. The base shifts after every change.
Step-by-step strategy
When to use: any question involving rates, unit conversions, percent change, percent increase or decrease, or successive percents.
- 1Identify the base: which value is the percent or rate acting on? For percent change, the base is the original. For successive percents, the base shifts to the current value after each step.
- 2Convert the percent to a multiplier: a 20% increase is 1.20, a 20% decrease is 0.80.
- 3For rates, set up the ratio as \(\frac{\text{quantity}}{\text{unit}}\) and cross-multiply to solve for the unknown.
- 4Check the answer choices. If one matches the result of applying every percent to the original, that is the trap answer.
When not to use: when the question gives a ratio or fraction rather than a percent, unless you convert first.
Related pages
Rates and percentages practice questions
Free practice questions with full explanations.
Linear equations strategies
Isolating the variable and avoiding sign errors.
Proportional reasoning strategies
Setting up proportions and cross-multiplying.
ACT Math practice
Browse practice questions for every ACT Math topic.
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