ACT Math: Solve Ratio and Proportion Problems Efficiently

Ratios compare two quantities. A proportion is an equation that says two ratios are equal. To solve any ratio problem: Step 1, identify the ratio given (e.g., 3:5 means for every 3 of one thing, there are 5 of another). Step 2, determine what you're solving for. Step 3, set up a proportion by writing the known ratio equal to an unknown ratio with a variable. Step 4, cross-multiply and solve. This method works for every ratio problem on the ACT, from mixture problems to scale problems to probability.

Example: If the ratio of girls to boys is 3:5, and there are 12 girls, how many boys? Set up: 3/5=12/x. Cross-multiply: 3x=60. Solve: x=20. There are 20 boys. This method is mechanical once you understand the four steps.

Error 1: Mixing up which number goes in which part of the ratio. Example: If the ratio of boys to girls is 2:3, writing it as 3:2 will give the wrong answer. Fix: Write the ratio exactly as it's described in the problem. Error 2: Forgetting that the ratio means all parts must scale by the same factor. Example: If you know one part changed, all parts change by that same scale factor. Error 3: Confusing part-to-whole ratios with part-to-part ratios. Example: "The ratio of boys to girls is 2:3" (part-to-part) vs. "Boys make up 2 out of 5 students" (part-to-whole). Always identify upfront whether the ratio compares two parts or a part to the whole.

Self-check: After you solve, plug your answer back into the original ratio. Does it simplify to the given ratio? If yes, you're correct. If no, you made a setup error.

Problem 1: The ratio of dogs to cats in an animal shelter is 4:7. If there are 16 dogs, how many cats? Problem 2: A recipe calls for sugar and flour in a 2:5 ratio. If you use 10 cups of flour, how much sugar? Problem 3: In a class, the ratio of students who passed to students who failed is 5:2. If 14 students failed, how many passed? Problem 4: A map scale is 1:50,000 (1 inch on the map represents 50,000 inches in reality). If two cities are 3 inches apart on the map, how many inches apart are they in reality? For each, write the proportion, cross-multiply, and solve. Then verify by checking the ratio. Show every step; don't skip the verification.

Answers: P1: 28 cats (4/7=16/x; 4x=112; x=28). P2: 4 cups sugar (2/5=x/10; 5x=20; x=4). P3: 35 passed (5/2=x/14; 2x=70; x=35). P4: 150,000 inches (1/50,000=3/x; x=150,000). If you missed any, redo the setup carefully and verify with the original ratio.

Ratio and proportion questions appear on every ACT Math test (questions 20-45) and are worth the same as harder algebra problems, but they're faster to solve if you use the scaling method. Once you master the four-step method and avoid the three setup errors, you'll solve every ratio problem in under 2 minutes, earning reliable points that feel effortless.

Spend this week drilling the four-step method daily. By test day, ratio problems will feel like automatic points, freeing up mental energy for geometry and trigonometry questions.