"Subtracting fractions with unlike denominators" is sometimes a difficult job for the children who study math in primary level.
Actually it is not a difficult one, once we have understood the concept.
Here, we explain two methods to subtract fractions with unlike denominators.
Here students may have a question.
That is, "When do we have to use the appropriate method to subtract fractions with unlike denominators?
Answer for the above question is given with detailed explanation.
If the denominators of the fraction parts are co-prime or relatively prime, we have to apply this method.
For example, let us consider the two fractions 1/8 and 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 subtract the two fractions 1/8 and 1/3 as given below.
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
Now we have to make the denominators of both the fractions to be 60 and subtract 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 subtract two fractions with different denominators".
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