﻿ Multiplying and Dividing Fractions
MULTIPLYING AND DIVIDING FRACTIONS
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)
Want more details, more exercises?

Multiplying fractions is easy:
just multiply the numerators, and multiply the denominators.
(Some people refer to this as multiplying across.)

That is:

$\displaystyle\frac{A}{B}\cdot\frac{C}{D} = \frac{AC}{BD}$

Every division problem is a multiplication problem in disguise:
to divide by a number means to multiply by its reciprocal.
That is, $\,x\,$ divided by $\,y\,$ is the same as $\,x\,$ times the reciprocal of $\,y\,$.
In symbols:

$\displaystyle \cssId{s16}{x\div y} \cssId{s17}{= \frac{x}{y}} \cssId{s18}{= x\cdot \frac{1}{y}}$

Here's what it looks like with fractions:

$\displaystyle \cssId{s20}{\frac{A}{B}\div\frac{C}{D}} \cssId{s21}{= \frac{A}{B}\cdot\frac{D}{C}} \cssId{s22}{= \frac{AD}{BC}}$

EXAMPLES:
$\displaystyle \frac{1}{3}\cdot\frac{2}{5} =\frac{2}{15}$
$\displaystyle\frac{1}{6}\cdot\frac{3}{7} = \frac{3}{42} = \frac{1}{14}$

$\displaystyle \cssId{s27}{\frac{1}{3}\div\frac{2}{5}} \cssId{s28}{=\frac{1}{3}\cdot\frac{5}{2}} \cssId{s29}{= \frac{5}{6}}$
Master the ideas from this section

When you're done practicing, move on to:
Practice with the Form $\,a\cdot\frac{b}{c}$

Where needed, input your answer as a diagonal fraction (like “2/5”), since you can't input horizontal fractions.
Answers do not need to be in simplest form.

Multiply/Divide:

 (10 different problem types)