Lesson 11: Add and Subtract Mixed Numbers

Property

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD.
Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

Examples

• Add $3\frac{1}{3} + 4\frac{1}{2}$. The LCD of 3 and 2 is 6. The problem becomes $3\frac{2}{6} + 4\frac{4}{6}$. Add the wholes $3+4=7$ and fractions $\frac{2}{6}+\frac{4}{6}=\frac{6}{6}=1$. The sum is $7+1=8$.

• Subtract $8\frac{1}{4} - 3\frac{5}{6}$. The LCD of 4 and 6 is 12. This is $8\frac{3}{12} - 3\frac{10}{12}$. Borrow 1 from 8 to get $7\frac{15}{12}$. Now, $7\frac{15}{12} - 3\frac{10}{12} = 4\frac{5}{12}$.