Addition of Fractions

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.

Let's learn the different kinds of addition in fractions, with the help of examples.

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:

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

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.

• Multiply the whole number with the denominator and add the numerator, the result will become our numerator and the denominator will be the same as given fractions.
• a(b/c) will be written as ((a × c) +b) / c.

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.

• Multiply the whole number by the denominator of the given fraction.
• The result becomes the new numerator, and the denominator will be the same as given 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}

Also Read,

• Subtraction of fractions
• Multiplication of Fractions