Adding and Subtracting Mixed Fractions
A Mixed Fraction is a
whole number and a fraction combined:


1 \frac{3}{4}  
(one and threequarters) 
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:


\frac{7}{4}  
(sevenfourths or sevenquarters) 
Can you see that 1\frac{3}{4} is the same as \frac{7}{4} ?
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:
 convert them to Improper Fractions
 then add them (using Addition of Fractions)
 then convert back 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}