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Why you can't divide fractions! How do we convert a division of two fractions into a multiplication problem

Updated on August 13, 2013

How to Divide Fractions

The truth a math teacher rarely tells you is that you never really divide fractions. Instead students are taught to multiply by the reciprocal. The division problem is then changed into a multiplication problem.

Think about a simple non - fraction problem. 10 divided by 2 is 5. It can be evaluated that the answer is 5. So instead of dividing the problem this time, I will turn it into a multiplication problem. 10 multiplied by 1/2 is equal to 5. Why does this work? It is because 2 and 1/2 are called reciprocals.

What is a reciprocal? It is an inversely related number. What exactly does that mean? Good question! It means that when you multiply a number by its reciprocal you get the number 1. 2 times 1/2 is equal to 1 making 2 & 1/2 reciprocals. In fractions, typically the fraction is flipped over in order to create the reciprocal. Don't forget in mixed numbers the number must be turned into an improper fraction because flipping it over.

We will take a look at a division problem that incorporates two fractions.

Here we have the original division of fractions problem
Here we have the original division of fractions problem
We need to find the reciprocal of 5/2
We need to find the reciprocal of 5/2
We then set up the new problem as a multiplication problem by the reciprocal
We then set up the new problem as a multiplication problem by the reciprocal
We then multiplication fractions as normal, including any cross canceling.
We then multiplication fractions as normal, including any cross canceling.
Don't forget to reduce and create proper answers!
Don't forget to reduce and create proper answers!

Once you know how to convert the division problem into a multiplication problem we are simply repeating the steps that we already know how to do. don't forget to put your answers in the correct format at the end. It is a shame to do all the hard work and then forget about proper fractions and reducing to lowest terms.


Division Quiz!


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