Like Fractions :
In two or more fractions, the denominators (bottom numbers) are same, they are called as like fractions.
Examples :
3/5 , 6/5, 2/5, 7/5
In the above fractions, all the denominators are same. That is 5.
Unlike Fractions :
In two or more fractions, the denominators (bottom numbers) are different, they are called as unlike fractions.
Examples :
3/5 , 6/7, 2/9, 7/2
In the above fractions, all the denominators are different. They are 5, 7, 9 and 2.
When adding or subtracting fractions, we must be knowing the difference between like
fractions and unlike fractions.
Because, adding or subtracting two or more like fractions is always easier. But when we want to add or subtract two or more unlike fractions, we have to use either cross-multiplication method or LCM (Least common multiple) method to add or subtract two or more fractions.
Addition or Subtraction of Two Like Fractions :
We have to follow the steps given below to add or subtract two like fractions.
Step 1 :
When two fractions with the same denominator are added or subtracted, take the denominator once.
Step 2 :
Now, add or subtract the numerators and simplify the resulting fraction, if required.
Example :
Find the value of :
1/5 + 2/5
Solution :
1/5 + 2/5
The given two fractions have the same denominator. That is 5.
So, take the denominator once and add the numerators.
= (1 + 2)/5
= 3/5
Therefore,
1/5 + 2/5 = 3/5
Addition or Subtraction of Two Unlike Fractions :
We can use one of the following methods to add or subtract two fractions with unlike denominators.
1. Cross-Multiplication method
2. LCM Method.
Cross - Multiplication Method :
If the denominators of the fractions are co-prime or relatively prime, we have to apply this method.
For example, let us consider the addition of two fractions given below.
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 shown below.
LCM 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.
For example, let us consider the addition of two fractions given below.
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 and 4
So 12 and 20 are not co-prime.
In the next step, we have to find the LCM (Least common multiple) of 12 and 20.
12 = 2^{2} x 3
20 = 2^{2} 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, the LCM of 12 and 20 is
= 2^{2} x 3 x 5
= 4 x 3 x 5
= 60
Now, make the denominators of both the fractions as 60 using multiplication and then add them as shown below.
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