Like Fractions Unlike Fractions

If a whole thing is divided into equal parts, then each part is said to be a fraction. In other words, a fraction is a part of the whole. A fraction is formed up of two parts - numerator and denominator. It is expressed as-  numerator/denominator. The numerator tells us how many of the total parts are taken and the denominator tells us the total number of equal parts.

For example, in 1/4 the top number ‘1’ is said to be the numerator and ‘4’ is said to be the denominator. Here we can say that 1 is taken from 4 equal whole parts. Fractions are very important to understand as it is used in our daily life. Depending on the numerator and denominator, fractions are divided into different types. These types are given as below:

• Proper fractions

• Improper fractions

• Mixed fractions

• Like fractions

• Unlike fractions

Here let us understand the concept of like fractions and unlike fractions in detail.

Like Fractions

In two or more fractions or a group of fractions when the denominator is the same then they are said to be like fractions.  In other words, you can say that ‘like’ fractions have the same number at the bottom. For example   2/4, 6/4, 8/4, 10/4.  Here, we can see that the denominator of all the fractions is 4, so these fractions are called like fractions. 

Some Important Points to Remember

• Fractions like 2/8, 25/20, 9/12, 8/32 are also like fractions though they have different denominators. It is because when they are written in the simplest form such as 1/4, 5/4, 3/4, 1/4, we get the same denominator here 4.

• Fractions like 4/2, 4/6, 4/10, 4 /13 are not like fractions. Here the numerators are the same but the denominators are different.

• Natural numbers like 2, 5, 6, 8  are called fractions because they have the same denominator 1. They are written as 2/1, 5/1, 6/1, 8/1.

Arithmetic Operations on Like Fractions

Mathematical operations like addition and subtraction can be carried out easily with like fractions. As the denominator is the same we have to just add or subtract the numerator accordingly.

Unlike Fractions

When the denominators of two or more fractions are different then they are said to be unlike fractions. We can define it as fractions with different denominators. You can also say that fractions that have different numbers in the denominator are called unlike fractions. For example  3/8, 1/13, 5/16

Arithmetic Operations on Unlike Fractions

Mathematical operations like addition and subtraction are not as easy as like fractions. It is because the denominator of unlike fractions is different. To carry out addition and subtraction with unlike fractions first we have to convert, unlike fractions into like fractions. There are two methods to convert unlike fractions to like fractions, and they are:

1. Cross multiplication method

2. LCM method

Cross Multiplication Method

To perform addition or subtraction of two unlike fractions, first, we have to simplify the fraction into the simplest form and make the denominators as co-prime or relatively prime. Then we have to follow the steps explained below in the cross multiplication method. 

Step 1: Multiply the numerator of the first fraction by the denominator of the second fraction. 

Step 2: Multiply the numerator of the second fraction by the denominator of the first fraction. 

Step 3: Multiply the denominators of both fractions and take it as a common denominator for the results of step 1 and step 2.

Step 4: After simplification, we will get the fractions with the same denominators and now we can carry out the given operation.

Example: Add 2/5 and 4/3

Solution: 

=2/5 + 4/3 

= (2x3) + (4x5)             

Applying cross multiplication method, we get;

=(2x3) + (4x5)/5 x 3

= (6 + 20)/15

= 26/15 

Lcm Method

To perform addition or subtraction of two unlike fractions, first, check if denominators of the fractions are not coprime (there is a common divisor other than 1), and then we have to apply this method. We have to follow these steps to use the LCM method. 

Step 1: Find the least common multiple of the denominators of the given fractions. 

Step 2: Using the least common multiple, make all the fractions like fractions.

Step 3: Now the denominator of all the fractions will be the same. So, we can carry out the necessary operations.

Example: Add 5/10 and 9/12

Solution: 

5/10 + 9/12

Now take the LCM of 10 and 12, we get;

LCM (10, 12) = 2 x 2 x 5 x 3 = 60

Now multiply the given fractions to get the denominators equal to 60, such that;

=(5x6)/(10x6) +  (9x5)/(12x5)

=(30/60) + (45/60)

=75/60

= 5/4