Adding Mixed Numbers or Mixed Fractions

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

A mixed number or mixed fraction has two parts: a whole number and a proper fraction.

Mixed number  =  whole number  +  proper fraction

2. How many pizzas do I have altogether if I have   
1 2
3
pepperoni pizzas and   
2 1
2
cheese pizzas?

Pepperoni pizza  =>  
1 2
3

Cheese pizza  =>  
2 1
2

Total  =>  
1 2
3
 + 
2 1
2


square metre or square meter

     
1 2
3
 + 
2 1
2

(1 x 3) + 2
3
 + 
(2 x 2) + 1
2
   (First, change both mixed numbers to improper fractions)
5
3
 + 
5
2

5 x 2
3 x 2
 + 
5 x 3
2 x 3
   (Second, change the fractions to like fractions)
10
6
 + 
15
6

25
6
   (Next, add the two fractions)
=  4  + 
1
6
   (Finally, change the improper fraction to a mixed number)
4 1
6

I have  
4 1
6
  pizzas altogether.

3. What is   
3 1
4
 + 
1
2
?

     
3 1
4
 + 
1
2

(3 x 4) + 1
4
 + 
1
2
   (First, change both mixed numbers to improper fractions)
13
4
 + 
1
2

13
4
 + 
1 x 2
2 x 2
   (Second, change the fractions to like fractions)
13
4
 + 
2
4

13 + 2
4
   (Next, add the two fractions)
15
4

=  3  + 
3
4
   (Finally, change the improper fraction to a mixed number)
3 3
4