Addition of Unlike Fraction(Different Denominators)

Adding Fractions With Different denominators

We learned how to add like fractions(same denominators).

In this tutorial we will learn addition of fractions with different denominators.

When denominators are different the fractions are called unlike fractions.

When we add unlike fractions, first we convert them to like fractions by finding the LCM of the denominators, so the denominators becomes same and then add them.

Let us see the steps of addition of unlike fractions with the help of an example given below.

Example: Add 1/4 and 2/3

Step 1: To add unlike fractions, First we convert them into like terms.

So, to make a common denominator, we find the LCM (least common multiple) of the different denominators of the given fractions.

So, the denominators becomes same and then add them.

In the given fraction denominators are different, as 4 and 3.

LCM of 4 and 3 is 12.

Now we need to find fractions equivalent, to 1/4 and 2/3, which have 12 in the denominators.

Step 2: Now multiply the numerator and denominator of 1/4 with 3

(1/4) x (3/3) = 3/12 and

multiply the numerator and denominator of 2/3 with 4

(2/3) x (4/4) = 8/12

Step 3: Denominators of both fractions are same as 12.

We get two new fractions with common denominators are 3/12 and 8/12.

So, we add the numerators of the fractions and write the sum over the common denominator.

So, the result is 3/12 + 8/12 = (3 + 8)/12 = 11/12

Simplify the fraction to its lowest form, if needed.

Example: Add 2/3 and 3/4

Solution: In the given fraction denominators are 3 and 4.

First we finding the LCM (least common multiple) of the denominators.

LCM of 3 and 4 is 12.

So we need to find fractions equivalent to 2/3 and 3/4 which have 12 in the denominator.

Now multiply the numerator and denominator of 2/3 with 4

(2/3) x (4/4)

= 8/12 and

multiply the numerator and denominator of 3/4 with 3

(3/4) x (3/3) = 9/12

We get two new fractions with common denominators are 8/12 and 9/12.

Now denominators of both fractions are same as 12. So we add the numerators and write the sum over the common denominator.

So, the sum is 8/12 + 9/12

= (8 + 9)/12

= 17/12

Example: Add 7/8 and 3/2

Example: Add 9/5 and 7/4

Solution: Two denominators are 5 and 4

LCM of the denominators 5 and 4 is 20

Therefore, multiplying 9/5 with 4/4 and 7/4 with 5/5 we get;

9/5 = (9 x 4)/(5 x 4) = 36/20

7/4 = (7 x 5)/(4 x 5) = 35/20

= 36/20 + 35/20

= (36 +35)/20

= 71/20

Answer is 71/20