Adding Like and Unlike Fractions

Practice Unlimited Questions

What are like fractions?

Fractions with same denominators are called like fractions.

What are unlike fractions?

Fractions with different denominators are called unlike fractions.

How to add like fractions?

Step 1: Add all the numerators. (Denominator will remain the same.)
Step 2: Simplify if required.

See the example below

How to add unlike fractions?

Step 1: Change unlike fractions to like fractions. i.e. find a common denominator.
Step 2: Add all the numerators.
Step 3: Simplify if required.

See the example below

1. The video below explains how to add proper fractions.

A proper fraction is a fraction in which the numerator is smaller than the denominator.

2. Jen and Fred each had   
1
4
of a pie.
What fraction of the pie did they have together?

Jen  =>  
1
4

Fred  =>  
1
4

Jen  +  Fred  =>  
1
4
 + 
1
4

square metre or square meter
   
1
4
 + 
1
4

= 
1 + 1
4

= 
2
4

= 
2 / 2
4 / 2
(simplify)
= 
1
2

Jen and Fred had
1
2
a pie together.

3. Charlie gives   
1
2
of a pizza to Alfred and   
1
3
of a pizza to Beatrice.
How much of the pizza does Charlie give to Alfred and Beatrice together?

Alfred  =>  
1
2

Beatrice  =>  
1
3

Alfred  +  Beatrice  =>  
1
2
 + 
1
3


square metre or square meter
   
1
2
 + 
1
3

= 
1 x 3
2 x 3
 + 
1 x 2
3 x 2

= 
3
6
 + 
2
6
  (changed the denominator to 6)
= 
5
6


Charlie gives
5
6
of the pizza to Alfred and Beatrice together.
Since the two fractions,
1
2
and
1
3
, are unlike fractions (as the denominators are different), we must first change them to like fractions before we can add them (that is, find a common denominator).

In other words, at first, the pizzas are cut into different number of slices. To add them, we must cut them into same number of slices.