Comparing Fractions With Different Denominators

As the denominators in unlike fractions are different, therefore for comparing unlike fractions, we need to make the denominators the same.

Let us take an example to understand the method of comparison of unlike fractions.

Consider the fractions, 3/8 and 5/12. The given fractions are unlike as the numerators and denominators are different. To compare them following steps are followed:

Step 1: Take LCM of denominators of given fractions i.e. 8 and 12 respectively.

(LCM is the smallest number which is a common multiple of given numbers)

24 is the least common multiple of  8 and 12.

Step 2: To convert the given fractions into like fractions, multiply the numerator and denominator by the ratio of LCM and denominator of the fraction

In 3/8, multiply the numerator and denominator by 3 = (3 ×3)/(8 ×3) = 9/24

In 5/12, multiply the numerator and denominator by 2 = (5 ×2)/ (12  × 2) = 10/24

Step 3: Now, the denominators of both fractions are the same.

i.e., 9/24 and 10/24

Now, the same method is followed for comparison i.e. method of comparison of like fractions.

As the numerator 10 in the fraction 10/24  is greater than the numerator 9 in the fraction 9/24.

Therefore, 10/24 is greater than 9/24

⇒ 5/12 is greater than 3/8.

These are the different methods of comparing fractions.