Multiplying and Dividing Fractions

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:

$\displaystyle x\div y = \frac{x}{y} = x\cdot \frac{1}{y}$

Here's what it looks like with fractions:

$\displaystyle\frac{A}{B}\div\frac{C}{D} = \frac{A}{B}\cdot\frac{D}{C} = \frac{AD}{BC}$

EXAMPLES:

$\displaystyle \frac{1}{3}\cdot\frac{2}{5} =\frac{2}{15}$

$\displaystyle\frac{1}{6}\cdot\frac{3}{7} = \frac{3}{42} = \frac{1}{14}$

(You may input your answer in either form, simplified or not.)

$\displaystyle\frac{1}{3}\div\frac{2}{5} =\frac{1}{3}\cdot\frac{5}{2} = \frac{5}{6}$

Master the ideas from this section
by practicing the exercise at the bottom of this page.

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.

(10 different problem types; request any # of problems)