Ratio To Fraction Calculator

What this calculator does

So, you have a ratio and you want it written as a fraction in simplest form. This tool converts it. Enter the two parts of the ratio and it returns the ratio as a fraction, reduced to lowest terms, and as a mixed number when that fits better.

You enter Ratio A and Ratio B, the two parts, and the tool does the conversion and the simplifying together.

How to use it

1. Enter Ratio A, the first part.
2. Enter Ratio B, the second part.
3. Press Calculate.

Both parts should be positive numbers.

A ratio written as a fraction

Turning a ratio into a fraction is direct: the ratio A to B becomes the fraction A over B. So the ratio 3 to 4 is the fraction 3 over 4, and the ratio 10 to 15 is 10 over 15. The tool then reduces that fraction to lowest terms using the greatest common divisor of the two parts, exactly as you would simplify any fraction. So 10 over 15 comes back as 2 over 3. The conversion and the simplification happen in one go, giving you the tidiest fraction that matches the ratio.

Whole numbers, fractions, and mixed numbers

The answer can take a few shapes depending on the numbers, and the tool picks the natural one. If the second part divides the first exactly, the ratio is really a whole number: the ratio 6 to 2 is 6 over 2, which is just 3. If the first part is larger than the second but does not divide evenly, the fraction is top-heavy, and the tool writes it as a mixed number, a whole number alongside a proper fraction, such as 3 to 2 becoming one and a half. And if the first part is smaller, you get a proper fraction, like 2 over 3. Each form is the clearest way to show that particular result.

How a ratio and a fraction differ

It is worth pausing on why this is a conversion at all, since a ratio and a fraction look so alike. A ratio compares two separate quantities to each other, two parts side by side. A fraction usually names a part of a single whole, or the result of a division. The ratio 3 to 2 compares two amounts; the fraction three over two is a single number, one and a half. The same pair of numbers, read two ways. This tool takes the comparison and expresses it as that single number. To keep the answer in ratio form instead, the ratio simplifier calculator reduces it while leaving the colon in place.

A worked example

Enter Ratio A as 3 and Ratio B as 2. The ratio 3 to 2 becomes the fraction 3 over 2. Since 3 is bigger than 2 and does not divide evenly, the tool writes it as the mixed number one and one half. Enter 10 and 15 instead, and since 2 over 3 is already a proper fraction in lowest terms, it returns 2 over 3.

Questions people ask

How is a ratio turned into a fraction?

The ratio A to B becomes the fraction A over B, which the tool then reduces to lowest terms.

When do I get a mixed number?

When the first part is larger than the second but does not divide it evenly, so the fraction is top-heavy. The ratio 3 to 2 becomes one and a half.

When is the answer a whole number?

When the second part divides the first exactly. The ratio 6 to 2 is simply 3.

Isn't a ratio the same as a fraction?

They share notation but differ in meaning. A ratio compares two parts; a fraction is a single number or a part of a whole. This tool expresses the ratio as that single number.

What if I want to keep it as a ratio?

The ratio simplifier calculator reduces the ratio and keeps it in colon form.

References

On ratios and fractions. The ratio A to B corresponds to the fraction A over B, which can be reduced and written as a proper, improper, or mixed form.

1. Eric W. Weisstein, "Ratio," from MathWorld, a Wolfram resource, on the ratio of two numbers as equivalent to their quotient.
2. Eric W. Weisstein, "Fraction," from MathWorld, a Wolfram resource, on fractions and their reduced and mixed forms.