Comparing Fractions Calculator

Our comparing fractions calculator will give you the answer and show the work to compare fractions. This can be helpful if you want to know how to compare fractions or just need a little help with your math homework.

What is a fraction?

When you look at a fraction, it’s easy to see that the top number is called the numerator and the bottom number is called the denominator. A specific type of fraction where both numbers are equal is called an equal or unit fraction. For example, 1/2 and 2/4 are equal fractions.

When you write out a fraction in word form, you can say “four fifths” instead of “4/5” or “one third” instead of “1/3″.

How to compare fractions

To compare fractions means to observe two fractions and find out which one is larger than the other. To be able to do this, you need to know some rules.

Comparing fractions with different denominators

Let me show you with an example.

\frac {1}{3} \text { and } \frac {1}{2}

To find out which one is larger, we need to have the same denominators on both of these. To do that, we need to find their common denominator, and expand them. Usually, the best way to find a common denominator is to multiply the two denominators with each other. In this case, the result would be 6.

Then, we need to expand the first one. We do this by dividing the common denominator by its denominator. This would get us 2. Then, we need to multiply the numerator by 2 as well. Once we do this, we have expanded the fraction. Then, we need to do the same with the second fraction.

Now, when they have the same denominators, the one that has the larger numerator is larger.

\frac {2}{6} < \frac {3}{6}

Comparing fractions with the same numerators

For this purpose, the numerators are not important. The process is the same as in the previous example.

Comparing fractions with the same denominators

If they have the same denominators, the larger one is the one with the larger numerator.

Comparing improper and mixed fractions

Improper fractions are fractions in which the numerator is larger than the denominator. Those fractions can be turned into mixed fractions, which are a mixture of whole numbers and fractions, for example:

\frac {5}{4}= 1 \frac {1}{4}

Essentially, the process is the same. If you have a mixed fraction, you turn it into an improper fraction, and repeat the process from before. You turn a mixed fraction into an improper fraction by multiplying the number in the front by the denominator, and then adding the result to the numerator.

How to use the comparing fractions calculator

Of course, the simplest way to compare fractions is using our calculator. All you need to do, is input both fractions into the calculator, and the calculator will tell you which one is larger, or if they are equal. It will also show you the process it used, as well as the expanded versions of the fractions.

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