Reciprocals

The reciprocal of a fraction is that fraction to the negative first power. Which is, for the most part, a fancy way of saying the fraction flipped upside down, switching the numerator with the denominator.

For example, the reciprocal of 1/2 is 2/1, or 2. The reciprocal of 3/4 is 4/3 or reduced down to 1 1/3.

Uses of Reciprocals

If you are dividing fractions and we set those fractions up in a fraction such as:

                       2/3

                       3/4 

Then how would you get rid of the bottom fraction in order to divide? 

You would multiply it by the reciprocal 4/3, so that it's now equal to one, and then because you multiplied the bottom by 4/3, you must also multiply the top by 4/3.

Now you have:

2/3 * 4/3      = 8/9       = 8/9

3/4 * 4/3          1/1

What did you learn from this section?

When dividing fractions: find the reciprocal of the bottom fraction and multiply both the original numerator and denominator by the reciprocal to find the original answer to the problem you are solving.