Fractions and ratios on the ACT reward clean arithmetic: reduce first, treat ratios as part-to-part comparisons, and use cross-multiplication to solve proportions. They connect directly to percent problems and show up inside word problems across the section.
Fraction operations
Add and subtract with a common denominator; multiply straight across; divide by multiplying by the reciprocal. Reduce before you multiply when possible—it keeps numbers small and cuts arithmetic errors. Example: (3/4) ÷ (9/16) = (3/4)(16/9) = 48/36 = 4/3.
Ratios as part : part
A ratio of 2:3 means two parts of one thing for every three parts of another—not necessarily two items and three items total. If the ratio of boys to girls is 2:3 and there are 30 students, the parts sum to 5. Each part is 30 ÷ 5 = 6, so there are 12 boys and 18 girls. Always find the whole by summing the parts when a total is given.
Proportions and cross-multiplication
If a/b = c/d, then ad = bc. Example: 3/5 = x/20 gives 3 × 20 = 5x, so x = 12. Set up the proportion carefully—matching units on both sides. A "per" statement (miles per hour, dollars per pound) is often a proportion in disguise; see ACT rate problems for the word-problem angle.
Link to percents
A percent is a ratio out of 100. 25% = 1/4, so a 25%-off sale and a 1/4-discount are the same math. When a problem mixes fractions and percents, convert to one form and stick with it. Our guide to ACT percent problems walks through the most common setups.
When you are stuck
Pick simple numbers and plug them in—see plugging in numbers on ACT Math. For a full topic map, check ACT Math topics.
Start practicing
Start with a free diagnostic, then drill your weak spots with 15-question quizzes and track how you're doing across Reading, English, and Math. Compare plans whenever you're ready to go further.
This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.