# Multiplying and Dividing Fractions

## Examples with Solutions

Example 1:

Divide

and simplify the result.

solution: When we rewrite this problem using the divide symbol, you’ll see that it is very similar to the previous example:

That is, dividing by

is the same thing as multiplying by .

So, proceeding

Example 2:

Simplify .

solution: Suddenly addition symbols appear in a multiplication problem! This means we must apply the basic rules of multiplication a bit more carefully. The strategy is still to multiply numerator by numerator and denominator by denominator, and then simplify the result. So

as the final answer. In the second step here, we factored wherever possible. Then in the third step, we cancelled common factors between numerator and denominator. When multiplication involves factors with more than one term, very careful use of necessary brackets is mandatory.

Example 3:

Divide .

solution: This example brings together several operations illustrated in previous examples. Start by writing\par the problem completely in mathematical notation: