Proportions and probability questions are common in ACT math sections. The can be expressed in algebraic equations, fractions or as word problems. They’re tough. These problems include ratios, proportions, rates, averages, probability, permutations and combinations. There are basic formulas you can memorize to help you through.
For example, ratios compare two quantities by division. So, it will be written fraction form x/y or with a colon x:y.
Proportions are two equal ratios written as fractions with one term missing: 4/12=x/36. To solve you cross-multiply 12x times 36 then divide by 4 so your answer for the missing term is 12.
A rate is something per something. That’s really vague, better illustrated with examples like distance/time as in miles per hour or feet per second.
Probability questions are solved using a three-part formula that looks like this:
probability = # of desired outcomes/ # of possible outcomes
So the most common types of probability questions on the ACT math section will ask you to find the probability of something happening.
Be aware that there are common traps intentionally built into proportion and probability questions to trip you up. With rate problems, for example, the most common mistake is problems that involve average speeds when multiple speeds are involved. Students will average two separate trips together instead of the average speed for the whole trip. The best way to prepare for “traps” is to consult a prep course and do practice math problems like those outlined here.