Division II - Dividing Fractions

The Experiment

Let's do an experiment. You will need:

  • a kitchen scale
  • a teapot
  • some small glasses
  • 750g of water

Place the teapot on the kitchen scale and fill it with water until the scale shows 750g. The 750g is equal to 3/4 litres of water.

Now place a small glass on the scales and fill in 150g of water from the teapot. The 150g corresponds to 3/20 litres of water.

How many small glasses do you need?

There are two ways to calculate the result:

  1. Divide 750g by 150g
  2. Divide 3/4 litres by 3/20 litres

Since we are talking about fractions, we will choose the second option... :-)

Formula: Dividing Fractions

Two fractions are divided by multiplying by the reciprocal:

Example: 24/14 ÷ 8/21

We already can multiply fractions - Again, remember to simplify BEFORE multiplying:

Trick 1: Simplify BEFORE dividing fractions!

First check if you can simplify one or the other fraction. This reduces the numbers and makes it easier to calculate.

And of course, cross simplification is also possible:

Trick 2: Cross Simplification

The fraction can be multiplied by the reciprocal even more easily - before multiplying, it is also possible to simplify "crosswise". That means, the first numerator can be simplified with the second denominator and the first denominator can be simplified with the second numerator.

If you have simplified as much as possible before multiplying, the result cannot be simplified further. Of course, a short review doesn't hurt either :-)

Online Practice: Dividing Fractions

Here you can practice dividing fractions online: Dividing Fractions.

If you have any problems with the exercise, please have a look at the hint and the sample solution first.

Back to our experiment:

So you should have needed 5 small glasses. Right?

Formula: Dividing Mixed Numbers

Mixed numbers cannot be divided directly. First you have to convert the mixed numbers into improper fractions.

If the numerator is greater than the denominator, the result can be converted back to a mixed number.

Example: 7 1/3 ÷ 2 6/7

Congratulations! Step 5 is done!

Great! On the last pages you have learned, to calculate with fractions: Multiplication und Division.

It's essential that you know:

  • a fraction is multiplied by a whole number by multiplying the numerator by the whole number and remaining the denominator unchanged
  • a fraction is divided by a whole number by multiplying the denominator by the whole number and remaining the numerator unchanged
  • two fractions are multiplied by calculating "numerator times numerator" and "denominator times denominator"
  • two fractions are divided by multiplying the reciprocal
  • mixed numbers have to be converted into improper fractions before multiplying/dividing

Always check, whether fractions can be simplified/reduced, especially the result! Also check, whether you can "cross simplify".
If the result is an improper fraction (the numerator is greater than the denominator): convert into a mixed number.

To complete Step 5, please take a minute to answer the comprehension questions:

Let's continue with:
Once again the most important - Test your knowledge!