Adding Proper Fractions

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.