# Addition of Mixed Fractions – Definition, Examples | How to Add Mixed Fractions with Like and Unlike Denominators?

Looking for ways on How to Add Mixed Fractions? If so, halt your search as we have listed all about Mixed Fractions Addition and different methods of it clearly in the later modules. Mixed Fractions are one of the types of fractions. These are also called Mixed Numbers. Go through the entire article to be well versed with the details like Adding Mixed Fractions Definition, How to Add Mixed Fractions with Same and Different Denominators, Examples, etc.

## Mixed Fraction – Definition

A Mixed Fraction is a form of a fraction that has a whole number next to a fraction.

Example: 3 $$\frac { 1 }{ 5 }$$ where 3 is a whole number and $$\frac { 1 }{ 5 }$$ is a fraction.

### How to Add Mixed Numbers?

When it comes to Adding Mixed Fractions we can have either the same or different denominators for both the fractions to be added. There are two different methods for Adding Mixed Numbers with Like, Unlike Denominators. Here is a Step by Step Procedure on How to Add Mixed Fractions. They are as such

#### Method 1: Adding the Whole Numbers and Fractions Separately

• In the first step add the whole numbers separately.
• In order to add fractions with the same denominator, simply add the numerators and keep the denominator unaltered. However, if you have different or unlike denominators take the LCM of them and change to Like Fractions.
• Once, you have a Common Denominator adding fractions is much simpler.
• Find the Sum of Whole Numbers and Fractions in Simplest Form.

#### Method 2: Convert Mixed Numbers to Improper Fractions and then Add them

• Initially, change the given Mixed Fractions to Improper Fractions.
• If Denominators of the Improper Fractions are the same simply add the numerators. If the Denominators of Improper Fractions are Unlike or Different take the LCM of Denominators and change them to like fractions.
• Add Like Fractions and express the sum to its Simplest Form.

Also, Check:

### Examples on Adding Mixed Fractions using Method 1

1. Add 3 $$\frac { 1 }{ 3 }$$, 2 $$\frac { 1 }{ 4}$$?

Solution:

3 $$\frac { 1 }{ 3 }$$+ 2 $$\frac { 1 }{ 4}$$

Let us add the whole numbers and fraction parts separately i.e.

Whole Numbers Part 3+2 = 5

Fractions Part = $$\frac { 1 }{ 3 }$$+ $$\frac { 1 }{ 4}$$

Since the denominators of the fractions are not same find the LCM of the Denominators to make them like fractions

LCM(3,4) = 12

$$\frac { 1*4 }{ 3*4 }$$ + $$\frac { 1*3 }{ 4*3}$$

= $$\frac { 4 }{ 12 }$$ + $$\frac { 3 }{ 12 }$$

= $$\frac { (4+3) }{ 12 }$$

= $$\frac { 7 }{ 12 }$$

Now add the like fractions and express the sum to its simplest form

= 5 $$\frac { 7 }{ 12 }$$

Therefore, 3 $$\frac { 1 }{ 3 }$$, 2 $$\frac { 1 }{ 4}$$ when added gives 5 $$\frac { 7 }{ 12 }$$

2. Add 5 $$\frac { 1 }{ 4}$$, 2 $$\frac { 1 }{ 5}$$, $$\frac { 1 }{ 6 }$$?

Solution:

5 $$\frac { 1 }{ 4}$$ + 2 $$\frac { 1 }{ 5}$$ + $$\frac { 1 }{ 6 }$$

Firstly, let us add the whole numbers and fraction parts separately i.e.

Whole Numbers Part (5+2+0) = 7

Fractions Part = $$\frac { 1 }{ 4}$$ + $$\frac { 1 }{ 5}$$ + $$\frac { 1 }{ 6 }$$

Since the Denominators of Fractions aren’t the same find the LCM of Denominators and express them as like fractions

LCM(4, 5, 6) = 60

= $$\frac { (1*15) }{ (4*15) }$$ + $$\frac { (1*12) }{ (5*12)}$$ + $$\frac { (1*10) }{ (6*10) }$$

= $$\frac { 15 }{ (60) }$$ + $$\frac { 12 }{ 60}$$ + $$\frac { 10 }{ 60 }$$

= $$\frac { (15+12+10) }{ 60 }$$

= $$\frac { 37 }{ 60 }$$

Now add the like fractions and express the sum to its simplest form

= 7 $$\frac { 37 }{ 60 }$$

Therefore, 5 $$\frac { 1 }{ 4}$$, 2 $$\frac { 1 }{ 5}$$, $$\frac { 1 }{ 6 }$$ when added gives 7 $$\frac { 37 }{ 60 }$$

### Adding Mixed Fractions Examples using Method 2

1. Add 5 $$\frac { 1 }{ 4 }$$, 3 $$\frac { 1 }{ 2 }$$?

Solution:

5 $$\frac { 1 }{ 4 }$$ + 3 $$\frac { 1 }{ 2 }$$

Change the given Mixed Numbers to Improper Fractions

= $$\frac { (5*4+1) }{ 4 }$$ +  $$\frac { (3*2+1) }{ 2 }$$

= $$\frac { 21 }{ 4 }$$ +  $$\frac { 7 }{ 2 }$$

Since the Denominators aren’t same find the LCM and express them as Like Fractions

LCM(4,2) = 2

= $$\frac { (21*1) }{ 4*1 }$$ +  $$\frac { (7*2) }{ (2*2) }$$

= $$\frac { 21 }{ 4 }$$ +  $$\frac { 14 }{ 4 }$$

= $$\frac { (21+14) }{ 4 }$$

= $$\frac { 35 }{ 4 }$$

Thus, 5 $$\frac { 1 }{ 4 }$$, 3 $$\frac { 1 }{ 2 }$$ added results in $$\frac { 35 }{ 4 }$$

2. Add 6 $$\frac { 1 }{ 4 }$$, 7 $$\frac { 1 }{ 4 }$$, 3 $$\frac { 1 }{ 4 }$$?

Solution:

6 $$\frac { 1 }{ 4 }$$ + 7 $$\frac { 1 }{ 4 }$$ + 3 $$\frac { 1 }{ 4 }$$

Change the given Mixed Fractions to Improper Fractions

= $$\frac { (6*4+1) }{ 4 }$$ +  $$\frac { (7*4+1) }{ 4 }$$ + $$\frac { (3*4+1) }{ 4 }$$

= $$\frac { 25 }{ 4 }$$ + $$\frac {29 }{ 4 }$$ + $$\frac { 13 }{ 4 }$$

= $$\frac { (25+29+13) }{ 4 }$$

= $$\frac { 67 }{ 4 }$$

Thus, 6 $$\frac { 1 }{ 4 }$$, 7 $$\frac { 1 }{ 4 }$$, 3 $$\frac { 1 }{ 4 }$$ results in $$\frac { 67 }{ 4 }$$

### FAQs on Adding Mixed Fractions

1. What is a Mixed Fraction with Example?

A Mixed Fraction is a form of a fraction that has a whole number next to a fraction. For Example 6 $$\frac { 1 }{ 4 }$$ is a Mixed Fraction where 6 is a whole number and $$\frac { 1 }{ 4 }$$ is the fraction part.

2. What does a Mixed Fraction look like?

Mixed Fraction is simply an improper fraction written as the sum of a whole number and a proper fraction. For instance, improper fraction $$\frac { 5 }{ 2 }$$ can be written as Mixed Fraction 2 $$\frac { 1 }{ 2 }$$.

3. How to add Mixed Fractions Step by Step?

Follow the simple and easy steps listed below to add Mixed Fractions and they are as such

• Convert the given Mixed Fractions to Improper Fractions
• Find the LCM of Denominators and then make them like fractions.
• Add the Like Fractions and Express the Sum to its Simplest Form.