Comparing fractions means looking at two fractions and determining which is larger. To compare fractions, all you have to do is make the two fractions have the same denominator, then see which fraction has the larger numerator -- it lets you know which fraction is bigger. The tricky part is changing the fractions to have the same denominator; but not very difficult. If you want to know how to compare fractions, just follow these steps.
Step
Step 1. See if both fractions have the same denominator or not
That is the first step in comparing fractions. The denominator is the number at the bottom of the fraction, while the numerator is the number at the top. For example, the fractions 5/7 and 9/13 don't have the same denominator, because 7 isn't the same as 13. So you'll need to take several steps to compare the two fractions.
If the denominators of both fractions are the same, all you have to do is look at the numerator to see which fraction is larger. For example, when comparing the fractions 5/12 and 7/12, it appears that 7/12 is greater than 5/12, because 7 is greater than 5
Step 2. Find the common denominator
To be able to compare fractions, you have to find a common denominator, so you know which fraction is larger. If you're adding and subtracting fractions with different denominators, it's best to find the smallest common denominator. But since it only compares fractions, you can take a shortcut, and multiply the denominators of both fractions to find a common denominator.
7 x 13 = 91. So, the new denominator is 91
Step 3. Change the numerator of both fractions
Now that the denominator has been changed, the numerator also needs to be changed, so that the fraction value remains the same. To do this, you'll need to multiply the numerator of each fraction by the same number you used to multiply the denominator which results in the number 91. Here's how:
- In the original 5/7, you multiply 7 by 13 to get the new denominator, which is 91. So you need to multiply 5 by 13 to get the new numerator. Basically, you multiply both the numerator and denominator by the fraction 13/13 (which equals 1). 5/7 x 13/13 = 65/91.
- In the original 9/13, you multiply 13 by 7 to get the new denominator, which is 91. So you 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 numerators of the two fractions
The fraction that has the larger numerator is the larger fraction. So, the fraction 65/91 is greater than 63/91 because 65 is greater than 63. That means, the original fraction is 5/7 greater than 9/13.
