# Divide Fractions with Mixed Numbers

Just as you can't multiply with mixed numbers, you can't divide with mixed numbers either. **When dividing with mixed numbers, mixed numbers must be turned into improper fractions, and then the division process can continue as usual** (for more see lesson Convert Mixed Numbers to Improper Fractions and Multiply Fractions with Mixed Numbers/Whole Numbers)

*Example*:

$$\eqalign{1\dfrac{3}{5}\div 4\dfrac{3}{4}=&\\\dfrac{1\times5+3}{5}\times\dfrac{4\times4+3}{4}=&\qquad&&\text{Convert both mixed numbers to improper fractions}\\\dfrac{8}{5}\div\dfrac{19}{4}=&\\\dfrac{8}{5}\times\dfrac{4}{19}=& \quad&&\text{Find the reciprocal of the divisor and multiply}\\\dfrac{8}{5}\times\dfrac{4}{19}=&\dfrac{32}{95}&&\text{Now, you just multiply the fractions}}$$

Once the numbers are turned into improper fractions, you multiply just like you did in lesson Divide Fractions.

Bottom line, to divide fractions with mixed numbers: turm mixed numbers into improper fractions, find the reciprocal of the divisor, and then multiply the fractions.

#### Practice Problems:

## Fraction Division (With Mixed Numbers)

Find the quotient. Simplify all answers completely. Change improper fractions to mixed numbers.

1. $4\dfrac{4}{5}$ $\div$ $3\dfrac{1}{2}=$

2. $2\dfrac{4}{9}$ $\div$ $2\dfrac{1}{8}=$

3. $3\dfrac{1}{2}$ $\div$ $2\dfrac{1}{9}=$

4. $2\dfrac{1}{2}$ $\div$ $4\dfrac{4}{7}=$

5 .$4\dfrac{1}{5}$ $\div$ $2\dfrac{1}{3}=$

6. $4\dfrac{4}{5}$ $\div$ $2\dfrac{1}{2}=$

7. $3\dfrac{4}{7}$ $\div$ $3\dfrac{1}{3}=$

8. $4\dfrac{1}{4}$ $\div$ $3\dfrac{2}{7}=$

9. $4\dfrac{5}{9}$ $\div$ $3\dfrac{1}{4}=$

10. $2\dfrac{2}{9}$ $\div$ $2\dfrac{3}{5}=$

11. $2\dfrac{2}{3}$ $\div$ $2\dfrac{2}{7}=$

12. $2\dfrac{1}{7}$ $\div$ $3\dfrac{1}{3}=$

#### Answer Key: