# How to Divide Fractions: Step by Step

By William Springer

Dividing fractions is actually quite simple, if you already understand how to multiply them. We cover how to use the reciprocal to quickly divide fractions.

## Dividing Fractions

Early on in mathematics, dividing by fractions doesn't come up very often; we're more accustomed to dividing things into a discrete number of parts. A pizza, for example, might be divided into eight slices.

As it turns out, we never actually have to learn a new technique; because dividing is the same as multiplying by the reciprocal, there are two simple steps to dividing fractions. (If you're not familiar with some of the words used in this article, you should take a minute to read the rules for fractions).

Step one: Take the reciprocal of the fraction you want to divide by. This means to swap the numerator and the denominator, at the reciprocal of a number is the number it multiplies by to get a product of one. Thus, the reciprocal of 4/5 is 5/4, and the reciprocal of 3, which is the same as 3/1, is 1/3.

Step two: Take the number that was originally going to be divided and multiply it by your new number.

## Example

Suppose, for example, that we want to divide 4/5 by 2/3. Unlike with adding, subtracting, or comparing fractions, there's no need to find a common denominator. Simply reverse 2/3 to get 3/2 and then multiply. We now have:

4/5 * 3/2 = (4 * 3) / (5 * 2) = 12/10 = 6/5 = 1.2.

This works with improper fractions as well. Want to divide three by nine-sixth?

3 / (9/6) = 3/1 * 6/9 = (3 * 6) / (1 * 9) = 18/9 = 2

## Practice Problems

Follow the above steps to dividing fractions to answer the problems below; the solutions are in the following section.

1) What is 2/3 divided by 4/5?

2) If you have three small chocolate cakes and divided them into pieces such that each piece is 1/8 of a cake, how many pieces do you have?

3) A taxi ride costs \$3 for the first quarter mile and 25 cents for each additional quarter mile. If the fare is \$5.25, how long was the ride?