Adding and Subtracting Mixed Fractions

13/4

Quick Definition: A Mixed Fraction is a
whole number and a fraction combined,
such as  1 3 4

1 3/4
(one and three-quarters)

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

4/43/4

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

such as  7 4  or  4 3

(It is "top-heavy")

7/4
(seven-fourths or seven-quarters)

 

Adding Mixed Fractions

I find this is the best way to add mixed fractions:

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: 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

 

  Hard Question