Comparing fractions means looking at two fractions and figuring out which one is bigger. To compare fractions, all you need to do is leave them with the same denominator and see which one has the higher numerator, so you'll tell which one is higher. The hardest part is knowing how to make sure the fractions have common denominators, but it's not that complicated. If you want to know how to compare fractions, follow the Steps below.
Step 1. See if the fractions have the same denominators
This is the first step to compare them. The denominator is the bottom number of the fraction and the numerator is the top number. For example, the fractions 5/7 and 9/13 don't have the same denominator because 7 doesn't equal 13. So you need to do some things to compare them.
If the denominator of the fractions is the same, you just need to look at the numerator to see which one is bigger. For example, with the fractions 5/12 and 7/12, you know that 7/12 is greater than 5/12 because 7 is greater than 5
Step 2. Find a common denominator to know which fraction is larger
To add and subtract fractions, you must find the lowest common denominator between them, but since you're just comparing them, you can cut your way and multiply the denominators of the two fractions to find a common denominator.
7 x 13 = 91, so the common denominator between these two fractions will be 91
Step 3. Change the fraction numerators
Now, you will need to change the numerators so that the fraction values stay the same. To do this, you'll need to multiply the numerator of each fraction by the same number that multiplied the denominator to get 91.
- With the original 5/7 fraction, you've multiplied 7 by 13 to get the denominator 91, so you'll need to multiply 5 by 13 to get the new numerator. Basically, you'll be multiplying the numerator and denominator of the fraction by 13/13 (which equals 1). 5/7 x 13/13 = 65/91.
- With the original 9/13 fraction, you've multiplied 13 by 7 to get the denominator 91, so you'll need to multiply 9 by 7 to get the new numerator. 9 x 7 = 63, so the new fraction is 63/91.
Step 4. Compare the fraction numerators
The fraction with the highest numerator is the largest. So 65/91 is greater than 63/91 because 65 is greater than 63. This means that the original fraction, 5/7, is greater than 9/13.