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Ratio calculator
Simplify a ratio and find the missing number in an equal ratio.
Quick answer
A ratio compares two quantities, and simplifying it divides both by their greatest common divisor. Formula: Simplify by dividing A and B by their greatest common divisor. The ratio 12 : 18 simplifies to 2 : 3, and 10 : 15 is equal to it.
Read the guide: How to simplify a ratio and solve proportions
Simplest ratio
2 : 3
- D, so that 12 : 18 = 10 : D
- 15.0000
- A ÷ B as a decimal
- 0.6667
How is a ratio calculated?
A ratio compares two quantities. Dividing both by the same number does not change it, so 12 : 18 and 2 : 3 are the same ratio.
To scale a recipe or a map, keep the ratio and solve for the missing number.
Cross-multiplying is the shortcut: A × D = B × C.
What is the formula for a ratio?
- Simplify by dividing A and B by their greatest common divisor
- A : B = C : D gives D = C × B ÷ A
Can you show a worked example of a ratio?
12 : 18: the greatest common divisor is 6, so the ratio is 2 : 3. If C = 10, then D = 10 × 18 ÷ 12 = 15, so 12 : 18 = 10 : 15.
What do common ratios simplify to?
A ratio in lowest terms, and A ÷ B as a decimal.
| Ratio | Simplest form | As a decimal |
|---|---|---|
| 12 : 18 | 2 : 3 | 0.6666666667 |
| 25 : 100 | 1 : 4 | 0.25 |
| 45 : 60 | 3 : 4 | 0.75 |
| 8 : 12 | 2 : 3 | 0.6666666667 |
| 100 : 250 | 2 : 5 | 0.4 |
Common questions
How do I simplify a ratio?
Divide both numbers by their greatest common divisor. For 12 : 18 that is 6, giving 2 : 3.
How do I split an amount in a ratio?
Add the parts, divide the total by that sum and multiply by each part. ₹500 in 2 : 3 is ₹200 and ₹300.
Can ratios use decimals?
Yes. The calculator scales decimals to whole numbers before simplifying.
What is a proportion?
A statement that two ratios are equal, such as 12 : 18 = 10 : 15.