What is a ratio?
A ratio compares quantities in a fixed order. The ratio 18:24 says that the first quantity has 18 units for every 24 units of the second. It can also be written 18 to 24 or as the fraction 18/24 when there are two parts. Dividing both quantities by 6 gives 3:4, which describes the same relationship with smaller whole numbers.
Ratios may compare two or more parts. A paint mixture of 12:18:30 keeps three quantities in order, and dividing all parts by 6 simplifies it to 2:3:5. Changing only one part would change the mixture, so every valid ratio transformation must multiply or divide all parts by the same positive scale factor.
How to use the ratio calculator with steps
Enter two to six quantities separated by colons, such as 18:24 or 12:18:30. You can write the word to instead of a colon. Fractions and terminating decimals are accepted, so inputs such as 1/2:3/4 and 1.5:2.25 can be converted into simplest whole-number form without early rounding.
- Read each part as an exact nonnegative quantity.
- Find a least common denominator if any part is fractional.
- Multiply every part by that denominator to make whole numbers.
- Find the greatest common factor of all whole-number parts.
- Divide every part by the same greatest common factor.
- Rebuild the original whole-number ratio to verify the common scale.
Worked example: simplify 18:24
The parts 18 and 24 are already whole numbers. Their common factors are 1, 2, 3, and 6, so the greatest common factor is 6. Divide both parts by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The simplest ratio is therefore 3:4.
Verification reverses the reduction. Multiplying 3 and 4 by the shared scale factor 6 rebuilds 18 and 24 exactly. Other equivalent ratios come from multiplying the simplified pair by another positive number: 6:8, 9:12, and 12:16 all express the same 3-to-4 comparison.
Simplify ratios containing fractions or decimals
A ratio of fractions should be cleared before finding a whole-number GCF. For 1/2:3/4, the denominators 2 and 4 have LCD 4. Multiplying both parts by 4 gives 2:3, which is already simplest. The multiplication applies to every part, so the comparison remains equivalent.
Decimals are converted to exact fractions first. For 1.5:2.25, the values are 3/2 and 9/4. Multiplying both by 4 produces 6:9, and dividing by GCF 3 produces 2:3. An exact simplify ratio calculator avoids treating rounded decimal approximations as if they were the original quantities.
Ratios, rates, and proportions are related but different
A ratio compares quantities. A rate is a ratio whose quantities use different units, such as 150 kilometres in 3 hours. A unit rate simplifies the second quantity to one, giving 50 kilometres per hour. This calculator simplifies numeric parts but does not attach, convert, or cancel measurement units, so keep unit labels in your written work.
A proportion is an equation stating that two ratios are equivalent, such as 3/4 = 9/12. Simplifying both sides can help check a proportion, but solving for an unknown part requires a proportion-solving method. Use this calculator when the parts are known and the goal is simplest whole-number comparison.
Common ratio mistakes and exact checks
Keep the part order unchanged. A ratio of red to blue objects is not interchangeable with blue to red. Divide every part by the same factor, and do not reduce one pair inside a three-part ratio while leaving the remaining part untouched. A ratio whose every part is zero has no useful scale and is rejected.
To check the simplified result, multiply each simplified part by the recorded scale factor and confirm that every original whole-number part returns. The proportional bars provide a visual comparison, while the exact working supplies the proof. The visual length is explanatory; the reduced integers and scale reconstruction are authoritative.