## Division II - Dividing Fractions

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:

- Divide 750g by 150g
- 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:*

^{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.

^{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: