ACT Math · Pre-Algebra
Ratios, proportions, and percentages
Setting up proportions and percent computations.
What's tested in this subtopic
These items mirror the SAT's ratio and percent items closely. The ACT tends to dress them in slightly more textbook-like phrasing, but the underlying math is identical.
Tactics that actually move your score
Set up the proportion in the same units on each side. For percent change, the formula is (new − old)/old × 100%. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy A class has boys and girls in the ratio 6:8. If there are 84 students in the class, how many are boys?
- Easy The price of an item increased from $50 to $56. What was the percent change?
- Medium A class has boys and girls in the ratio 4:3. If there are 63 students in the class, how many are boys?
- Medium The price of an item decreased from $81 to $72. What was the percent change?
- Medium A class has boys and girls in the ratio 2:5. If there are 63 students in the class, how many are boys?
- Hard The price of an item decreased from $111 to $75. What was the percent change?
- Easy A class has boys and girls in the ratio 3:9. If there are 108 students in the class, how many are boys?
- Easy The price of an item increased from $103 to $128. What was the percent change?
- Medium A class has boys and girls in the ratio 2:9. If there are 132 students in the class, how many are boys?
- Medium The price of an item increased from $140 to $185. What was the percent change?
- Medium A class has boys and girls in the ratio 8:8. If there are 128 students in the class, how many are boys?
- Hard The price of an item decreased from $129 to $92. What was the percent change?
- Easy A class has boys and girls in the ratio 6:7. If there are 130 students in the class, how many are boys?
- Easy The price of an item increased from $100 to $106. What was the percent change?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in ACT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.