Ratio Problem Generator
A ratio compares two or more quantities directly: the flour to sugar in a recipe, wins to losses in a season, or the mix of sand to cement in a batch of mortar. Ratios are one of the highest-leverage topics in middle school and GCSE-level math because they feed straight into fractions, percentages, scale drawings, unit rates, and probability.
This free ratio problem generator creates unlimited practice questions across the three ratio skills that show up most often on homework and exams: simplifying a ratio, finding a missing value in an equivalent ratio, and dividing a total quantity according to a given ratio. Every set is randomly generated, self-grading, and printable.
How the difficulty levels work
| Level | Skill | Example |
|---|---|---|
| Easy | Simplify a ratio | Simplify 12 : 36 |
| Medium | Find the missing value | 11 : 8 = ? : 72 |
| Hard | Divide a quantity in a ratio | Divide 209 in 3 : 9 : 7, largest share? |
Easy: simplifying ratios. You reduce a ratio to its lowest terms exactly the way you simplify a fraction: divide every part by the greatest common divisor (GCD). For 12 : 36, the GCD is 12, so the answer is 1 : 3. The relationship is unchanged, only the numbers get smaller. Watch for ratios that are already fully simplified, since spotting a GCD of 1 (like 11 : 36) is a skill in itself.
Medium: equivalent ratios and missing values. You get one complete ratio and one incomplete ratio, and you find the value that keeps the two proportional. In 11 : 8 = ? : 72, compare the parts you know: 8 becomes 72, which is a scale factor of 9. Apply the same factor to the other side: 11 × 9 = 99. This is the foundation of proportional reasoning and it is the same mechanic behind recipe scaling, map scales, currency conversion, and unit pricing.
Hard: dividing a quantity in a ratio. You split a total into three parts according to a given ratio, then report one specific share (usually the largest). This requires two steps rather than one, which is why it trips students up: find the value of a single part first, then scale each ratio number up.
Using the generator
Pick a difficulty level and a question count, and a fresh set appears instantly. No sign-up, no limits.
- Type ratio answers with a colon, like
2:3. Use plain numbers for missing-value and share problems. - Check Answers grades the entire set at once and flags exactly which questions need another look.
- Show Answers reveals every full solution when you want to review the method rather than test yourself.
- Print Worksheet outputs a clean, ink-friendly page (no navigation, no clutter) for classroom or paper practice.
Teachers: regenerate the set to hand out different versions of the same worksheet and cut copying between desks.
Worked example: solving a “divide in this ratio” problem
Problem: Divide 209 in the ratio 3 : 9 : 7. What is the largest share?
- Add the parts. 3 + 9 + 7 = 19 total parts.
- Find one part. 209 ÷ 19 = 11. Every single “part” is worth 11.
- Scale each share. 3 × 11 = 33, 9 × 11 = 99, 7 × 11 = 77.
- Check. 33 + 99 + 77 = 209. The shares add back to the original total, so the answer holds.
The largest share is 99.
That final check is the habit worth building. If your shares do not sum back to the original quantity, you divided by the wrong number of parts, and you will catch it in five seconds instead of losing the mark.
Common mistakes to avoid
- Dividing the total by the number of terms instead of the number of parts. In 3 : 9 : 7 there are three terms but 19 parts. Always sum the ratio.
- Reversing the order. A ratio of 3 : 9 is not the same as 9 : 3. Match your answer to the order given in the question.
- Mixing up ratio and fraction notation. In the ratio 3 : 7, the first quantity is 3/10 of the total, not 3/7. Part-to-part and part-to-whole are different comparisons.
- Stopping halfway on a simplification. 12 : 36 reduces to 2 : 6 if you divide by 6, but that is not lowest terms. Keep going to 1 : 3.
- Forgetting units. If the total is 209 liters, the shares are in liters too.
Related practice
Ratios, fractions, and percentages all describe the same underlying idea: a part compared to a whole, or one quantity compared to another, just written in different notation. Once ratios click, the other two get noticeably easier, so it is worth drilling all three back to back.