## Multiplication II - Multiplying Fractions

The summer holidays are over! Finally Harry can escape the dull everyday life at the Dursleys and spend time with his friends in Hogwarts.

All he has to worry about is a letter he received last Thursday by owl mail:

Hopefully it's going to be all right, thinks Harry as he enters the big entrance door of the old station.

But at this moment his girlfriend Hermione is meeting him: "Harry, there you are! Hurry up, we have to get to **platform six and a half** today!"

## Formula: Multiplying Fractions

*Two fractions are multiplied by multiplying the two numerators and the two denominators.*

The result often can be simplified / reduced:

^{3}/

_{4}×

^{5}/

_{9}

For example, the fractions ^{3}/_{4} and ^{5}/_{9} should be multiplied:

## Trick 1: Simplify BEFORE multiplying fractions!

The rule for multiplying fractions is very simple. But before you apply it blindly, first check if you can simplify one or the other fraction. This reduces the numbers and makes it easier to multiply.

Then please check again whether the result can be simplified further.

## Trick 2: Cross Simplification!

Fractions can be multiplied 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 :-)

The numerator of the first fraction (**3**) can be simplified with the denominator of the second fractions (**3**):

## Online Practice: Multiplying Fractions

Here you can practice multiplying fractions online: Multiplying Fractions.

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

## Multiply Fractions and Mixed Numbers

Back to Harry and Hermione. The students of Hogwarts have to solve this problem:

This is done best by converting the mixed number
9 ^{3}/_{4} into an immproper fraction:

Now we apply the rule for multiplying two fractions. In addition we make a **cross simplification**:

The numerator of the first fraction (**2**) is simplified with the denominator of the second fraction (**4**) and
the denominator of the first fraction (**3**) is simplified with the numerator of the second fraction (**39**):

To convert the result back into a mixed number we have to divide 13 by 2: The result is **6 remainder 1**.

That's how Hermione came to the result as well: