Ratio and Proportion Table
A ratio compares two quantities (written a:b), while a proportion states that two ratios are equal. This reference table converts common ratios to fractions, decimals, and percentages, shows equivalent ratios at a glance, and explains how to solve for an unknown value in a proportion.
Ratio Simplifier
Enter a ratio a:b to reduce it to lowest terms and see its fraction, decimal, and percentage.
Common Ratios as Fractions, Decimals, and Percentages
Each ratio a:b below is expressed as the fraction a/b, its decimal equivalent, and its percentage. Repeating decimals are marked with an ellipsis (…).
| Ratio | Fraction | Decimal | Percentage |
|---|---|---|---|
| 1:2 | 1/2 | 0.5 | 50% |
| 1:3 | 1/3 | 0.3333… | 33.33% |
| 2:3 | 2/3 | 0.6667… | 66.67% |
| 1:4 | 1/4 | 0.25 | 25% |
| 3:4 | 3/4 | 0.75 | 75% |
| 1:5 | 1/5 | 0.2 | 20% |
| 2:5 | 2/5 | 0.4 | 40% |
| 3:5 | 3/5 | 0.6 | 60% |
| 4:5 | 4/5 | 0.8 | 80% |
| 1:8 | 1/8 | 0.125 | 12.5% |
| 3:8 | 3/8 | 0.375 | 37.5% |
| 5:8 | 5/8 | 0.625 | 62.5% |
| 7:8 | 7/8 | 0.875 | 87.5% |
| 1:10 | 1/10 | 0.1 | 10% |
| 3:10 | 3/10 | 0.3 | 30% |
| 7:10 | 7/10 | 0.7 | 70% |
| 9:10 | 9/10 | 0.9 | 90% |
| 1:100 | 1/100 | 0.01 | 1% |
For a broader lookup of fraction-decimal-percentage equivalents beyond simple ratios, see the Fractions to Decimals Table and the Percentage Table.
Equivalent Ratios
Multiplying (or dividing) both terms of a ratio by the same number produces an equivalent ratio. The table below scales four common base ratios by 2×, 3×, 4×, and 5×.
| Base Ratio | ×2 | ×3 | ×4 | ×5 |
|---|---|---|---|---|
| 1:2 | 2:4 | 3:6 | 4:8 | 5:10 |
| 2:3 | 4:6 | 6:9 | 8:12 | 10:15 |
| 3:4 | 6:8 | 9:12 | 12:16 | 15:20 |
| 1:5 | 2:10 | 3:15 | 4:20 | 5:25 |
Solving a Proportion
A proportion sets two ratios equal: a/b = c/d. To solve for an unknown term, cross-multiply: a × d = b × c.
Example: If 3 kg of flour costs $6, how much do 5 kg cost? Set up the proportion 3/6 = 5/x. Cross-multiplying gives 3x = 30, so x = 10 — 5 kg costs $10.
Proportion Solver
Solve a/b = c/x for the missing term x.