How It Works

Each ratio term is treated as a fraction, with a whole number treated as that number over 1. For a ratio a/b : c/d, multiply the first term by the second denominator and the second term by the first denominator to obtain the equivalent whole-number ratio (a × d) : (c × b). The resulting terms are then reduced to lowest terms using their greatest common divisor (GCD).

For a/b : c/d, the equivalent whole-number ratio is (a × d) : (c × b). Divide both terms by their greatest common divisor (GCD) to obtain the simplest ratio.

Example

For example, 1/2 : 3/4 becomes 4 : 6 after multiplying by the opposite denominators. Dividing both terms by their GCD, 2, gives the simplest ratio 2 : 3.

Frequently Asked Questions

Can I mix a whole number and a fraction in a ratio?

Yes. Either ratio term can be a whole number or a fraction. A whole number is treated as a fraction with a denominator of 1, allowing the calculator to simplify mixed ratios such as 3 : 1/2.

How do you simplify a ratio of fractions?

For a ratio a/b : c/d, multiply the first term by d and the second term by b to obtain (a × d) : (c × b). Then divide both terms by their greatest common divisor to reduce the ratio to its simplest whole-number form.

What is 1/2 : 3/4?

The ratio 1/2 : 3/4 simplifies to 2 : 3. Multiplying by the opposite denominators gives 4 : 6, and dividing both terms by their greatest common divisor, 2, gives 2 : 3.

What is the difference between a ratio calculator and a ratio calculator with fractions?

A standard ratio calculator typically works with whole-number terms, while this calculator accepts fractions as either ratio term and converts the result into the simplest whole-number ratio.

Can a ratio contain two fractions?

Yes. Both terms can be fractions. For example, the ratio 2/3 : 4/5 can be converted to 10 : 12 and then simplified to 5 : 6.

Can a ratio contain a whole number and a fraction?

Yes. For example, 3 : 1/2 can be written as 3/1 : 1/2, which becomes 6 : 1 after multiplying by the opposite denominators.