**Dividing Fractions:**

Remember that given a fraction, such as _{}, the top number is the numerator (namely 1) and the bottom
number is the denominator (namely 2)

Recall that the reciprocal of a fraction is the
multiplicative inverse and is produced by inverting the fraction (placing the
original numerator as the denominator and the original denominator as the
numerator) For example, the reciprocal
of _{}is_{}

_{}

Example 1:

_{}

Whenever you divide fractions, first you find the
reciprocal of the second fraction (divisor) then you __multiply__ the **numerators**
to create the answer numerator, and __multiply__ the **denominators **to
create the answer denominator.

_{}

Example 2:

_{}

Whenever you divide fractions, first you find the
reciprocal of the second fraction (divisor) then you __multiply__ the **numerators**
to create the answer numerator, and __multiply__ the **denominators **to
create the answer denominator. Since we
are not doing cross-cancellation in this particular instance, you must also
reduce your final fraction.

_{}

Don’t forget to reduce your answer to lowest terms,
i.e. _{}

We will do an example that utilizes cross-cancellation.

Example 3:

_{}_{}

Lets first find the reciprocal of the second fraction (divisior)

_{}

Instead of multiplying first, we can combine the
factors of the numerator and denominator and make one fraction that is
equivalent to the original problem.
This is called cross-canceling:
(The 5 and the 10 in both the numerator and denominator respectively can
be reduced from _{} to _{} and the 3 and the 6
in numerator and denominator respectively can be reduced from _{} to _{}) You may cancel any common factors from the numerator and
denominator as shown in the following example:

_{}

The method shown in example 3 is the preferred method,
but if you are uncomfortable, use the method in example 2 for a while until you
get the hang of it, then try the method in example 3 and compare the answers
you get.

Try this problem using the method of your choice:

#### When you are
ready, click here to go to the division of fractions
with unlike denominators practice page. You may need some scratch paper to
do the practice.