CCSS Math: 6.NS.A.1
Review the basics of dividing fractions, and try some practice problems.

Dividing fractions

Dividing fractions is the same as multiplying by the reciprocal (inverse).
For example:
Once we have a multiplication problem, we multiply the numerators then multiply the denominators.
Example 1: Fractions
32÷83=?\dfrac{3}{2} \div \dfrac{8}{3} = {?}
The reciprocal of 83\dfrac{8}{3} is 38\dfrac{3}{8}.
32÷83=32×38 \dfrac{3}{2} \div \dfrac{8}{3} = \dfrac{3}{2} \times \dfrac{3}{8}
32×38=3×32×8 \phantom{\dfrac{3}{2} \times \dfrac{3}{8}} = \dfrac{3 \times 3}{2 \times 8}
32×38=916 \phantom{\dfrac{3}{2} \times \dfrac{3}{8}} = \dfrac{9}{16}
Example 2: Mixed numbers
312÷114=3\dfrac{1}{2} \div 1\dfrac{1}{4} =
Let's start by converting the mixed numbers to fractions.
=312÷114\phantom{=}3\dfrac{1}{2} \div 1\dfrac{1}{4}
=72÷54= \dfrac{7}{2}\div\dfrac{5}{4}
=7245       Multiply by the reciprocal.=\dfrac{7}{2}\cdot\dfrac{4}{5} ~~~~~~~\text{Multiply by the reciprocal.}
=712245       Simplify.=\dfrac{7}{\blueD{1}\cancel{2}}\cdot \dfrac{\blueD{2}\cancel{4}}{5} ~~~~~~~\text{Simplify.}
=7125=\dfrac{7}{\blueD{1}}\cdot \dfrac{\blueD{2}}{5}
=145 or 245=\dfrac{14}{5}\text{ or }2\dfrac45
Want to learn more about dividing fractions? Check out this video.
Want to review multiplying fractions? Check out this article.


Problem 1
35÷19=?\dfrac{3}{5} \div \dfrac{1}{9} = {?}
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Want to try more problems like this? Check out this exercise.