Ratios & Proportions Practice
20 questions · 60 seconds · simplify ratios, solve proportions & unit rates
Free · no login · instant feedback on every answer
Train the skill that connects fractions to real-world comparisons: ratios and proportions. Twenty questions in sixty seconds mix three tasks — simplify a ratio like 12:18, solve a proportion such as 3:4 = x:12, and find a unit rate from a real quantity — each checked instantly so you know right away whether the reasoning held.
Ratios and proportions are the bridge from arithmetic to algebra: the same cross-multiplication move that solves 3:4 = x:12 reappears in scale drawings, percent problems, unit conversions, and eventually slope and similar triangles. Getting comfortable simplifying and solving now means one less new idea to learn when those topics show up in middle and high school.
Tips That Make It Stick
- Divide out the common factor. 12:18 simplifies to 2:3 once you find the greatest common factor (6) and divide both terms by it — a ratio reduces the same way a fraction does.
- Cross-multiply to solve for x. In 3:4 = x:12, multiply the outer and inner terms (3 × 12 = 4 × x) and divide to get x = 9. The same move works no matter which term is missing.
- Divide to find the unit rate. 240 miles in 4 hours means dividing 240 by 4 to get 60 miles per hour — a unit rate is just a ratio scaled down to a denominator of 1.
Frequently Asked Questions
What grade learns ratios and proportions?
Ratios are introduced in 6th grade, where students learn to write, compare, and simplify them. Proportions and unit rates build on that in 6th and 7th grade, forming the foundation for percent and slope problems later on.
How do you solve a proportion like 3:4 = x:12?
Cross-multiply the two ratios: 3 × 12 = 4 × x, so 36 = 4x, and dividing both sides by 4 gives x = 9. Cross-multiplication works because equal ratios always have equal cross products.
What is the difference between a ratio and a unit rate?
A ratio compares two quantities, like 12 red marbles to 18 blue marbles, and can share or differ in units. A unit rate is a special ratio written with a denominator of 1, such as 60 miles per hour from 240 miles in 4 hours.
📝 Matching Printable Worksheets
Prefer paper practice? These free PDF worksheets cover the same skill — each includes an answer key: