Adding and Subtracting Mixed Fractions

A Mixed Fraction is a
whole number and a fraction combined:

1 whole pizza3/4
1 34
(one and three-quarters)

To make it easy to add and subtract them, just convert to Improper Fractions first:

An Improper fraction has a
top number larger than or equal to
the bottom number:

4/43/4
74
(seven-fourths or seven-quarters)

Can you see that 134 is the same as 74 ?

In other words "one and three quarters" is the same as "seven quarters".

(You may like to read how to Convert from or to Mixed Fractions)

Adding Mixed Fractions

To add mixed fractions:

Like this:

Example: What is  2 3 4  +  3 1 2   ?

Convert to Improper Fractions:

2 3 4  =  11 4

3 1 2  =  7 2

Common denominator of 4:

11 4  stays as  11 4

7 2  becomes  14 4
(by multiplying top and bottom by 2)

Now Add:

11 4  +  14 4  =  25 4

Convert back to Mixed Fractions:

25 4  =  6 1 4

When you get more experience you can do it faster like this example:

Example: What is  3 5 8  +  1 3 4

Convert them to improper fractions:

3 5 8  =  29 8
1 3 4  =  7 4

Make same denominator:  7 4  becomes  14 8  (by multiplying top and bottom by 2)

And add:

29 8  +  14 8  =  43 8  =  5 3 8

 

Subtracting Mixed Fractions

Just follow the same method, but subtract instead of add:

Example: What is  15 3 4  −  8 5 6  ?

Convert to Improper Fractions:

15 3 4  =  63 4

8 5 6  =  53 6

Common denominator of 12:

63 4  becomes  189 12

53 6  becomes  106 12

Now Subtract:

189 12  −  106 12  =  83 12

Convert back to Mixed Fractions:

83 12  =  6 11 12

 

935, 1414, 1415, 1416, 936, 1417, 3585, 3586, 3587