"Adding unlike fractions" is sometimes difficult job for some students who study math in school level.

Actually it is not a difficult one, once we have understood the concept.

Here, we explain two methods to add two fraction with different denominators.

Here students may have a question.

That is, "When do we have to use the appropriate method to add two fractions with different denominators? "

Answer for the above question is given with detailed explanation.

Cross-multiplication method

If the denominators of the fractions are co-prime or relatively prime, we have to apply this method.

Fro example, let us consider the two fractions 1/8, 1/3.

In the above two fractions, denominators are 8 and 3.

For 8 and 3, there is no common divisor other than 1. So 8 and 3 are co-prime.

Here we have to apply cross-multiplication method to add the two fractions 1/8 and 1/3 as given below.

L.C.M method

If the denominators of the fractions are not co-prime (there is a common divisor other than 1), we have to apply this method.

Fro example, let us consider the two fractions 5/12, 1/20.

In the above two fractions, denominators are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

2 & 4

So 12 and 20 are not co-prime.

In the next step, we have to find the L.C.M (Least common multiple) of 12 and 20.

12 = 2² x 3

20 = 2² x 5

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20.

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 = 2² x 3 x 5

= 4 x 3 x 5

= 60

Now we have to make the denominators of both the fractions to be 60 and add the two fractions 5/12 and 1/20 as given below.

After having gone through the stuff and examples, we hope that the students would have understood "How to add two fractions with different denominators".

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