How to solve a proportion
Cross-multiply, then divide by the known factor beside the missing value.
Direct: A × D = B × C. Inverse: A × B = C × D.
- Write the two ratios in the same order: A / B = C / D.
- Multiply across the equality to get A × D = B × C.
- Divide the known product by the missing value's partner to find x.
- Substitute the answer into the original equation to check both sides.
- For inverse proportion, keep the products equal: A × B = C × D.
Worked example: 2 / 3 = 4 / x gives 2 × x = 3 × 4. Therefore x = 3 × 4 ÷ 2 = 6. Both ratios simplify to 2 : 3.
Common proportion examples
| A | B | C | D | Missing value (D) |
|---|---|---|---|---|
| 2 | 3 | 4 | x | 6 |
| x | 5 | 12 | 20 | 3 |
| 3 | 4 | x | 16 | 12 |
| 1.5 | 2 | 6 | x | 8 |
| 1/2 | 3 | x | 9 | 3/2 |
Swipe the table sideways to see the rest.
Things to consider
- Keep matching quantities in the same position in both ratios.
- B and D cannot be zero in direct mode.
- Use fractions such as 1/2 when an exact answer matters.
- Inverse example: 4 workers take 6 days. At the same work rate, 3 workers take 4 × 6 ÷ 3 = 8 days.
Frequently asked questions
What is a proportion?
A proportion states that two ratios are equal. For example, 2 / 3 = 4 / 6 because both simplify to 2 : 3.
How does cross-multiplication work?
Multiplying A / B = C / D by the non-zero denominators B and D gives A × D = B × C. Divide by the known partner of x to solve the equation.
How do I check if two ratios are proportional?
Enter all four values in direct mode. The ratios are proportional when A × D equals B × C exactly, provided B and D are non-zero.
What is the difference between direct and inverse proportion?
In direct proportion, quantities change by the same factor and their ratio stays constant. In inverse proportion, one increases as the other decreases and their product stays constant. For a fixed job at equal work rates, 4 workers taking 6 days corresponds to 3 workers taking 8 days.
Where are proportions used?
Use proportions to scale recipes, interpret map scales and compare unit pricing. Keep units consistent. Work-rate problems can use inverse proportion when the total work and each worker's rate stay constant.
Can I enter fractions or decimals?
Yes. Values such as 1/2 and 1.5 are parsed as exact fractions. The exact result is shown alongside a decimal rounded to at most 4 places.
Results are estimates for general information only, not financial, medical or professional advice.