Addition of Fractions (original) (raw)

Last Updated : 11 Feb, 2026

Addition of Fractions is a simple process in which we add two fractions together to get a single fraction. A fraction represents the division of one number by another, written with a numerator (top number) and a denominator (bottom number) separated by a horizontal line.

Illustration of How To Add Fractions

Adding Fractions with Same Denominators

Fractions with the same denominator are also called **like fractions.

We can easily add these fractions using the following formula,

**a/b + c/b = (a+c)/b

To add fractions with the same denominators we simply add the numerators specified in the fraction and use the same denominator to obtain the result.

Let’s consider an example of 1/4 + 2/4, which is a like fraction. We will represent both fractions in the form of a circle as follows:

Adition-of-fraction-1

The denominator is the same for both i.e., both circles are divided in equal parts which can be easily added. So there is no need to modify the denominator , As a result, our answer is (1+2)/4 = 3/4, as indicated in the image below.

Example: Add 2/5 and 3/5. These fractions have the same denominator.

**Solution:

**Given fractions : 2/5 and 3/5

Here 5 and 5 are the denominator of the given fractions****,** As both denominators are the same.
Since, the Denominators are the same we can simply add the numerators.

2/5 + 3/5= (2 + 3) /5 = 5/5 = 1

Our numerators are 2 and 3 add it (2+3 = 5) and hence we got 5/5. Simplify it and the result will be 1.

Adding Fractions with Different Denominators

Fractions with different denominators are also called **unlike fractions.

We add unlike fractions using the following formula:

**a/b + c/d = (a/b) × (d/d) (c/d) × (b/b) = ad/bd + cb/bd = (ad + bc)/bd

Addition-of-fraction

**Steps to Add Fractions with Different Denominators:

**Step 1: Find the different denominators of the fractions you wish to add .
**Step 2: Determine lowest common multiples (LCM) of the denominators of the fractions.
**Step 3: Multiply the numerator and denominator by the same number to make the denominator equal to the LCM.
**Step 4: Add the fractions' numerators while maintaining the LCM as the denominator.

Let's try to understand this with the help of examples.

**Example 1:Add 1/4 and 3/8. These fractions have different denominators, so we need to find a common denominator.

**Step 1: The denominators, 4, and 8, are dissimilar.

**Step 2: Determine the denominators' least common multiple (LCM).

8 is the LCM of 4 and 8.

**Step 3: To make the denominator equal, multiply the numerator and denominator by the LCM factor.

1/4 = (1 × 2)/(4 × 2) = 2/8

3/8 = (3 × 1)/(8 × 1) = 3/8

**Step 4: Add the fractions' numerators while maintaining the LCM as the denominator.

2/8 + 3/8 = 5/8

5/8 is the final answer.

**Learn more about, **Adding Fractions with Unlike Denominators

How To Add Mixed Fractions?

Mixed fractions are numbers that combine a whole number and a fraction, such as 2 \frac{1}{3}. Adding mixed fractions involves a few extra steps compared to regular fractions.

**Steps to Add Mixed Fractions:

**Step 1: Convert the mixed fractions into improper fractions.

**Step 2: Determine the denominators' least common multiples (LCM), or the lowest integer that can be divided equally by each denominator.

**Step 3: To make the denominator equal, multiply the numerator and denominator by the LCM factor.

**Step 4: Add the fractions' numerators while maintaining the LCM as the denominator.

Here is an example to illustrate how to add mixed fractions.

**Example: Consider two numbers 2(3/4) and 1(1/2). Add the given mixed fractions.

Convert the mixed fractions into improper fractions.
2(3/4) = (2 × 4 + 3) / 4 = 11/4
1(1/2) = (1 × 2 + 1) / 2 = 3/2

Find a common denominator.
The denominators are 4 and 2, so the LCM of 4 and 2 is 4.

To make the denominator equal, multiply the numerator and denominator by the LCM factor.
11/4 remains the same.
3/2 = (3 × 2) / (2 × 2) = 6/4

Add the fractions' numerators while maintaining the LCM as the denominator.
11/4 + 6/4 = 17/4

How to Add Fractions with Whole Numbers

To add fractions with whole numbers, first we convert the whole number into a fraction. Take the denominator of the whole number as one. Then add the fraction as you would when adding fractions with different denominators.

**Steps to add fractions with whole numbers:

**Step 1: Convert the whole number into an Improper Fraction.

**Step 2: Add the improper fraction and the given fraction just like adding with same denominators.

**Step 3: Simplify the resulting fraction, if possible.

**Example: Suppose we want to add 2/3 and 1. To add a fraction and a whole number, simply express the whole number as a fraction with the same denominator as the other fraction.

**Solution :

**Step 1: Convert the whole number to an improper fraction: Multiply 1 by the denominator of the given fraction which is 3. So,1 can be written by 3/3 .

**Step 2: Now , we have to add 2/3 + 3/3 which is equal to 5/3 .(just like adding fractions with same denominators)

**Step 3: We can write 5/3 in mixed fraction 1\frac{2}{3}

Solved Examples on Addition of Fractions

Here are some solved examples on addition of fractions:

**Example 1: Add 2/3 and 1/3

**Solution:

3 is the denominator in the both given fractions. (Like Fractions)
Given Fractions : 2/3, 1/3
So, 2/3 + 1/3
= (2+1) / 3
= 3/3
= 1

**Example 2: Add 1/4 and 2/3

**Solution:

Given Fraction: 1/4, 2/3

LCM of denominators ( 4 & 3) is 12.
First Fractional Number: (1×3)/(4×3) = 3/12
Second Fractional Number: (2×4)/(3×4) = 8/12
So, 3/12 + 8/12 = (3+8) / 12
= 11/12

**Example 3: Add 3/2 and 1

**Solution:

1 can be represented as, (1 /1) = ( 1 × 2) / ( 1 × 2) = 2/2

= 3/2 + 1
= 3/2 + 2/2
= (3+2)/2
= 5/2
5/2 in mixed fraction is 2\frac{1}{2}

**Example 4: Add 1(2/5) and 2(1/5)

**Solution:

Change mixed fraction to improper fraction
= 1(2/5) = ((1 × 5)+2)/5 = 7/5
= 2(1/5) = ((2 × 5)+1)/5 = 11/5
= 7/5 + 11/5
= 18/5
= 3\frac{3}{5}

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