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) 
Can you see that 1\frac{3}{4} is the same as \frac{7}{4} ?
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 \frac{3}{4} + 3 \frac{1}{2} ?
Convert to Improper Fractions:
2 \frac{3}{4} = \frac{11}{4}
3 \frac{1}{2} = \frac{7}{2}
Common denominator of 4:
\frac{11}{4} stays as \frac{11}{4}
\frac{7}{2} becomes \frac{14}{4}
(by multiplying top and bottom by 2)
Now Add:
\frac{11}{4} + \frac{14}{4} = \frac{25}{4}
Convert back to Mixed Fractions:
\frac{25}{4} = 6 \frac{1}{4}
When you get more experience you can do it faster like this example:
Example: What is 3 \frac{5}{8} + 1 \frac{3}{4}
Convert them to improper fractions:
3 \frac{5}{8} = \frac{29}{8}
1 \frac{3}{4} = \frac{7}{4}
Make same denominator: \frac{7}{4} becomes \frac{14}{8} (by multiplying top and bottom by 2)
And add:
\frac{29}{8} + \frac{14}{8} = \frac{43}{8} = 5 \frac{3}{8}
Subtracting Mixed Fractions
Just follow the same method, but subtract instead of add:
Example: What is 15 \frac{3}{4} − 8 \frac{5}{6} ?
Convert to Improper Fractions:
15 \frac{3}{4} = \frac{63}{4}
8 \frac{5}{6} = \frac{53}{6}
Common denominator of 12:
\frac{63}{4} becomes \frac{189}{12}
\frac{53}{6} becomes \frac{106}{12}
Now Subtract:
\frac{189}{12} − \frac{106}{12} = \frac{83}{12}
Convert back to Mixed Fractions:
\frac{83}{12} = 6 \frac{11}{12}