Adding and Subtracting Mixed Fractions
Quick Definition: A Mixed Fraction is a 

1 ^{3}/_{4}  
(one and threequarters) 
To make it easy to add and subtract them, just convert to Improper Fractions first:
Quick Definition: An Improper fraction has a 

^{7}/_{4}  
(sevenfourths or sevenquarters) 
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:
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}