Different Cases of Adding Fractions


We learn about the concept of fractions in our lower classes. In a layman’s language, fractions are a fragmented part of a number expressed in the form of p/q. We use fractions in our everyday life without even noticing it. Some of the examples of fractions are 2/3 of the birthday cake, 1/3 of the pineapple pizza, 3/4 of the pie chart, etc. We perform various arithmetic operations on fractions like adding fractions, subtracting fractions, multiplying fractions, and dividing fractions. Performing these arithmetic operations on fractions is quite easy. In this article, we will discuss in detail adding fractions.

Addition of Fractions in Different Cases

The process of adding fractions is different in different cases. Let us learn each of the cases of adding fractions with the help of an example in each case.

When We Have Same Denominators

One of the easiest cases of addition is when we operate by adding fractions when the denominators are the same. In this case, we add different values of the numerators over the same denominator. Let us understand this case of adding fractions with the help of an example.

  1. Add 26/33 and 5/33. 

Solution: We see that both the fractions have the same denominator.

Thus, we will add the different values of the numerator over the common denominator. 

So, (26 + 5)/33 = 31/33.

Thus, we have the answer as 31/33.

When We Have Different Denominators

While adding fraction, when we have different values of denominators, it should first be converted into the same value so that adding fraction can become possible. This is done by finding out the Lowest Common Multiple of the two different values of the denominators. Let us understand this case of adding fraction with the help of an example.

Read More: The Amazing Benefits of NCERT Solutions

  1. Add 12/5 and 7/6.

Solution: We see that the values of denominators are different. Thus, we need to convert it into a single value by finding out the LCM of the two numbers. 

We have the LCM of 6, 5 as 30 which becomes our denominator.

Now, we multiply 12/5 with 6/6, 12/5 * 6/6 = 72/30, and multiply 7/6 with 5/5, 7/6 * 5/5 = 35/30. 

We see that both the numbers now have the same denominator which is 30. 

We will now perform the operation of addition as we did in the first case.

(72 + 35)/30 = 107/30.

Thus, we have the answer as 107/30.

When We Have Fraction With Whole Numbers

This case of adding fraction is also very easy. In this case, we simply write the given numbers in the form of a mixed fraction to add them. Let us understand this case of adding fraction with the help of an example.

  1. Add 3 and 36/61.

Solution: Since we have a whole number and a fraction here, we will simply write them in the form of a mixed fraction to add it.

So, 3 + 36/61 = 3 36/61.

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