Ratio vs. Fraction vs. Percentage: How to Convert Between Them
Ratios, fractions and percentages describe relationships in different ways. Learn when each is used and how to convert part-to-part and part-to-whole correctly.
"Three out of five dentists," "a 3 : 2 ratio" and "60%" can all describe the same situation, or completely different ones. The key question is always: is this comparing a part to another part, or a part to the whole?
Part-to-part and part-to-whole
A class has 12 girls and 18 boys.
- Part to part: girls to boys is 12 : 18, or 2 : 3.
- Part to whole: girls to all students is 12 : 30, or 2 : 5.
Fractions and percentages are almost always part-to-whole. Ratios can be either, so read them carefully.
Converting a part-to-part ratio to fractions and percentages
Add the terms to get the whole, then divide each term by it.
| Ratio | Total parts | Fractions | Percentages |
|---|---|---|---|
| 2 : 3 | 5 | 2/5 and 3/5 | 40% and 60% |
| 1 : 3 | 4 | 1/4 and 3/4 | 25% and 75% |
| 3 : 5 : 2 | 10 | 3/10, 5/10, 2/10 | 30%, 50%, 20% |
| 7 : 1 | 8 | 7/8 and 1/8 | 87.5% and 12.5% |
A very common mistake is to turn 2 : 3 into 2/3. That fraction compares the first part to the second part, not to the whole, and it's only correct if the question asks "how many times larger."
Converting a fraction or percentage to a ratio
If 35% of a budget goes to rent, the rest is 65%. Rent to everything else is 35 : 65, which simplifies to 7 : 13. Rent to the whole budget is 35 : 100, or 7 : 20.
Ratios as "times as many"
A part-to-part ratio can also be read as a multiplier. In 2 : 3, the second quantity is 3 ÷ 2 = 1.5 times the first, and the first is 2 ÷ 3 ≈ 0.67 times the second. The ratio calculator shows this decimal for two-term ratios.
Odds are part-to-part
Betting odds of 3 : 1 against an event mean 3 ways to lose for 1 way to win, so the probability of winning is 1 out of 4, or 25%. Probability is part-to-whole; odds are part-to-part. Confusing them is a classic error in statistics classes.
Rates are ratios with units
A rate compares quantities with different units: 60 miles per hour, $3.50 per pound, 30 miles per gallon. Unit rates have 1 as the second term. Comparing prices by unit rate is a proportion problem; see unit rates and best buys.
When to use which
- Ratios: recipes, mixes, scale drawings, aspect ratios, sharing amounts.
- Fractions: exact parts of a whole, especially in math and measurement.
- Percentages: comparisons across different totals, such as test scores or market share.
Quick practice
A bag holds red and blue marbles in the ratio 4 : 5. What fraction is red? 4/9. What percentage is blue? 5 ÷ 9 ≈ 55.6%. If there are 72 marbles, how many are red? 72 × 4/9 = 32. The last question is a sharing problem; see dividing an amount in a ratio.
Further reading from official sources
- Ratios, rates and percentages (Grade 6 math) – Khan Academy
