Dividing Fractions

Before we start to attempt to divide fractions, you must be able to multiply fractions. If you are not sure of your abilities, go to the entry about multiplying fractions and review that material.

To divide two fractions we write them in the following format:

The rule for dividing two fractions is to KEEP the first fraction, Change division sign to a multiplication sign, and then FLIP the second fraction, (many people call this process KCF the acronym for Keep, Change, Flip), so:

Now we follow the rules for multiplication of fractions:

This looks relatively easy, so let’s try a problem. If we had half a cake and had to evenly divide it among 4 children, how much of the original cake would each child receive? We need to convert this word problem into a mathematical relationship, so we want to take ½ the cake and divide it by 4 or:

Remember we can write any whole number as the number divided by one, so our equation can be written as:

Following the rules for division the problem works out as follows:

Again before we say the problem has been completed, we must be careful to make sure that when some of the terms have negative signs, we need to make sure our final answer has the correct sign. When multiplying or dividing terms with positive and negative signs, we count the number of negative signs and if the sum is even, then the final answer is a positive number. Then we count the number of negative signs and the sum is odd, then the final answer is a negative number.

If we had solve this problem:

We follow the rules for division:

Sometimes we may be presented with a fraction divided by a fraction, such as:

Following the rules we have:

So if we were asked to solve:


Our work would look as follows:

The key to sharpening your skills with division is to practice and check your work.

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