Compare Fractions Calculator
Enter your fractions, using a slash (/) symbol as the separator, and compare fractions to find which is greater than, less than, or if they are equal.
Steps to Compare Fractions
Step One: convert mixed numbers to a fraction, if there are any1 23=53
Step Two: find the least common denominator of the two fractions
Least common denominator = 12
Check out our least common denominator calculator for help on finding this.
Step Three: rewrite each fraction to an equivalent fraction using the denominator 12
To do this, start by dividing 12 by the denominator of the first fraction. Next, multiply the result by the numerator to find the new numerator. To rewrite, put the new numerator over 12. Repeat this for the second fraction20122112
Step Four: compare the numerators
At this point to compare the fractions we can simply compare the numerators to see which is larger20<21
Step Five: rewrite each fraction as the original fraction1 23<1 34
How to Compare Fractions
Comparing fractions might seem challenging, it seems a bit like comparing apples and oranges. Fortunately, there are a few methods for comparing one fraction to another.
Method One: Compare Fractions by Converting to Decimal First
The first way to compare fractions is to convert them to a decimal value. Simply divide the numerator of each fraction by the denominator, then compare the decimal values.
Method Two: Compare Fractions By Finding the Common Denominator
Another way to compare fractions is to rewrite all the fractions to equivalent fractions with the same denominator. To do this, find the greatest common denominator, then make the denominators of each fraction equal.
Start by finding the lowest common denominator, which is often referred to as the least common denominator. This is the smallest number that each denominator divides equally into. If you’re not sure how to do this, our lowest common denominator calculator will help you find it.
For example, let’s find the lowest common denominator of 6 and 9.
6 × 3 = 18
9 × 2 = 18
LCD = 18
Next, divide the lowest common denominator by the denominator of the fraction to find the multiple. Then, multiply the numerator by the multiple to get the new numerator. Put the new numerator over the lowest common denominator to get the new fraction.
For example, convert 16 to a fraction with a denominator of 18.
18 ÷ 6 = 3
3 × 1 = 3
16 = 318
You’ll want to repeat this step for each fraction until they all have the same denominator.
Also see our equivalent fraction chart to see equivalents for common fractions which might help shortcut the conversion.
Finally, compare the numerators to find which fraction is largest or smallest. The fraction with the larger numerator is the larger number.
For example, compare 318 to 218 to see which is largest.
numerator #1 = 3
numerator #2 = 2
3 > 2
Thus, 318 is greater than 218
Method Three: Compare Fractions With the Same Numerator
When fractions have the same numerator they can be compared by comparing the denominators. When the numerators are the same, the fraction with the smaller denominator is larger. Saying this a different way, the larger the denominator the smaller the number is.
You might also find our ordering fractions calculator interesting.