Adding and Subtracting Mixed Fractions
  |
Quick Definition: A Mixed Fraction is a |
| 1 3/4 | |
| (one and three-quarters) |
To make it easy to add and subtract them, just convert to Improper Fractions first:
 |
Quick Definition: An Improper fraction has a |
| 7/4 | |
| (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".
Adding Mixed Fractions
I find this is the best way to add mixed fractions:
- convert them to Improper Fractions
- then add them (using Addition of Fractions)
- then convert back to Mixed Fractions
(You may like to read how to Convert from or to 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:
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