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# Adding Fractions – Introduction and Definition

HomeEducationAdding Fractions - Introduction and Definition

A fraction is a portion of the whole. The upper portion of the fraction is the numerator and the bottom portion is the denominator. For example, if the child has a bar of chocolate and he has to equally divide it between himself and his sister then the fraction of the chocolate each will get half of the chocolate. Proper fraction, improper fraction, mixed fractions, Like and Unlike Fractions. Adding fractions teaches us how to combine two or more fractions with the same or different denominators. The addition of fractions is conditional on two fundamental factors: The denominators are the same or different.

Fraction addition teaches us how to calculate the sum of two or more fractions with the same or different denominators. The addition of fraction can be performed on two conditions

• Fractions with same denominators
• Fraction with different denominators

## Adding Fractions with Same Denominators

For the addition of  fractions with the same denominators,  we just need to add the numerators of the fractions
Example 1: Add 315 and 815

Solution: Since the denominators are the same we can just add the numerators

315 +815

=3 +815 =1115

## Adding Fractions with Different  Denominators

When two or more fractions with distinct denominators are combined, the numerators cannot be directly added.

First, find the lcm of the denominators and rationalize them to make the denominators of the fractions the same. Add the numerators of the fractions while keeping the denominator the same. To find the final sum, simplify the fraction.

Solution:

To solve this problem, we need to make the denominator of the fractions equal, which we can do by finding the lcm of 4, 8 and 16. The lcm of the denominators is 16. Therefore,

1 +3 +516 = 916

So adding 14 38516 we get 916

A mixed fraction is a number that contains both whole numbers and fractions. To combine two mixed fractions, first convert them to improper fractions, then add them together.

Example 1: Add: 2 15  + 3 13

Solution:

First, we have to convert the given mixed fractions to improper fractions.

2 15115

3 13103

We will now make the denominators the same by taking the lcm and multiplying the suitable fractions for both.

LCM of the denominators 5 and 3 is 15

So,.115103 = 11 * 3 + 10 * 515

= 33 + 5015 = 8315

Therefore, 2 15  + 3 138315 = 5 815

## Addition of Fractions with Whole Numbers

When we have to add a fraction with a whole number first  write the given whole number in the form of a fraction. If the denominators are different then make it the same and then add. Further, simplify the fraction

Solution: Here, 89  is a fraction, and 3 is a whole number.
We can write 3 as 31.

Now making the denominators the same, we get;

=8*1 + 3*39 =8 + 99 = 179

Hence, the sum of  89 + 3 is  179

= 2735

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