Ratios and Proportions — ACT Math Guide
Ratios and proportions ACT questions appear regularly on the ACT Math section, testing your ability to compare quantities and solve for unknown values. These problems involve comparing two or more quantities using fractions, decimals, or the colon format (like 3:4). You'll encounter about 3-4 ratio and proportion questions among the 60 questions in 60 minutes on the ACT math section. The good news is that these problems follow predictable patterns once you master the key techniques.
What You Need to Know
Ratio: A comparison of two quantities (can be written as 3:4, 3/4, or "3 to 4")
Proportion: An equation stating that two ratios are equal (3/4 = 9/12)
Cross multiplication: Multiply diagonally across the equal sign to solve proportions
Unit rates: Ratios that compare quantities with different units (miles per hour, cost per item)
Scale factors: Ratios used in similar figures and map problems
Direct variation: When one quantity increases, the other increases proportionally
📐 KEY FORMULA: If a/b = c/d, then ad = bc (cross multiplication)
⏱️ ACT TIME TIP: Set up proportions quickly by identifying what you know and what you're solving for — this saves precious seconds in your 60-minute time limit.
How to Solve Ratios and Proportions on the ACT
Example Question 1 — Easy/Medium Difficulty
A recipe calls for 2 cups of flour for every 3 cups of sugar. If Maria uses 8 cups of flour, how many cups of sugar does she need?
A) 6
B) 10
C) 12
D) 14
E) 16
Solution:
Step 1: Set up the proportion with flour on top: 2/3 = 8/x
Step 2: Cross multiply: 2x = 3 × 8 = 24
Step 3: Solve for x: x = 24 ÷ 2 = 12
✅Answer: C — Maria needs 12 cups of sugar to maintain the same ratio.
Example Question 2 — Hard Difficulty
On a map, 1.5 inches represents 60 miles. If two cities are 4.5 inches apart on the map, and a car travels from one city to the other at an average speed of 45 miles per hour, how long will the trip take?
A) 4 hours
B) 5 hours
C) 6 hours
D) 8 hours
E) 9 hours
Solution:
Step 1: Find the actual distance using the map scale: 1.5/60 = 4.5/x
Step 2: Cross multiply: 1.5x = 60 × 4.5 = 270
Step 3: Solve for distance: x = 270 ÷ 1.5 = 180 miles
Step 4: Calculate time: 180 miles ÷ 45 mph = 4 hours
✅Answer: A — The trip will take 4 hours at 45 miles per hour.
Common ACT Math Mistakes to Avoid
❌Mistake: Mixing up which quantities go together in your proportion setup
✅Fix: Always label your ratios clearly and keep like quantities in the same position
❌Mistake: Forgetting to cross multiply when solving proportions
✅Fix: Remember the cross multiplication rule: if a/b = c/d, then ad = bc
❌Mistake: Not checking if your answer makes logical sense
✅Fix: Quick mental check — if the ratio increases one quantity, the other should increase proportionally
❌Mistake: Confusing direct and inverse relationships in word problems
✅Fix: Direct variation means both quantities change in the same direction (more workers, more output)
Practice Question — Try It Yourself
A school's student-to-teacher ratio is 24:1. If there are 18 teachers at the school, how many students are there?
A) 332
B) 392
C) 432
D) 456
E) 482
Show Answer
Answer: C — Set up the proportion 24/1 = x/18, cross multiply to get x = 24 × 18 = 432 students.
Key Takeaways for the ACT
Set up proportions by keeping like quantities in the same positions (top with top, bottom with bottom)
Cross multiplication is your fastest tool for solving proportion equations on the ACT
Always double-check that your answer makes sense in the context of the problem
Unit rates help you solve complex word problems by breaking them into simpler steps
ACT math ratios and proportions often appear in geometry problems involving similar figures
Related ACT Math Topics
Strengthen your ACT math prep with these related topics:
Percentages →
Similar triangles →