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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)


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

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