Divide Mixed Numbers

Dividing Mixed Numbers

A mixed number has a whole number part and a fraction part, such as (2\tfrac{1}{3}). To divide mixed numbers, first rewrite each mixed number as an improper fraction. Then divide by multiplying by the reciprocal of the second fraction.

Method

1. Convert to improper fractions.
   • Multiply the whole number by the denominator.
   • Add the numerator.
   • Keep the same denominator.
2. Change division to multiplication.
   • Keep the first fraction.
   • Flip the second fraction to its reciprocal.
3. Multiply and simplify.
   • Multiply numerators together and denominators together.
   • Reduce the answer to lowest terms.
4. If needed, convert back to a mixed number.

Example structure

If you have (a\tfrac{b}{c} \div d\tfrac{e}{f}), rewrite it as (\frac{ac+b}{c} \times \frac{f}{df+e}).

Check

To check your work, multiply the quotient by the divisor. You should get back the original dividend. Also make sure the final answer is simplified exactly.

Watch for common mistakes: forgetting to convert mixed numbers first, or only flipping the top fraction instead of the entire second mixed number.