# If 2 + 2 6, then 1 + 3

### Calculate fractions

Leonie needs a new bike. At the dealer she saw a used cross bike that costs $ 160 $. Her father says that if Leonie can collect $ 3/4 $ of the money himself, he'll add the rest. Now Leonie is wondering how much money she has to save herself.

So you determine the fraction $$ 3/4 $$ of the $$ 160 $$ €. The $$ 160 $$ € are the whole.

Divide the whole thing into 4 parts. You determine $$ 1/4 $$.

Mathematically: divide $$ 160 $$ € by the denominator.

$$160$$ € $$:$$ $$4 = 40$$ €.

Take 3 parts. You determine $$ 3/4 $$.

Mathematically: $$ 40 $$ € $$ * $$ $$ 3 = 120 $$ €

So Leonie has to save $ 120 $. Then she gets the rest of it.

Image: fotolia.com (Franz Pfluegl)

### The calculation method

So the fraction ($$ 3/4 $$) tells you how to do the math:

- Divide the whole thing.

$$160$$ € $$:$$ $$= 40 $$ € - You take the result with you.

$$40$$ € $$* $$ $$= 120$$ €

How to calculate the fraction:

- Divide the whole thing.
- Multiply the result by.

### That's how it works!

In some cases it is easier to reverse the two steps, so

- Take the whole thing with you.
- Share the result by.

**Example:**

Philipp likes to eat fish fingers. However, he has found that his father burns about $$ 2/6 $$ fish fingers in a pack of $$ 15 $$ pieces.

$$ 15 $$ (the whole) cannot be easily divided by. But if you take $$ 15 $$ with you first, you will get $$ 30 $$.

$$15$$ $$*$$ = $$30$$

Now sharing is easier.

$$30 :$$ $$= 5$$

So many fish fingers burned! Poor Philip!

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### Shorten, shorten

Take a close look at the fraction first: if you can shorten it, always do it. Then you can calculate with smaller numbers.

In the case of Philip's fish finger fiasco, it would have looked like this:

$$2/6 = (2:2)/(6:2) = 1/3$$

Here the counter is even $$ 1 $$. Then you just have to share the whole thing through, because you don't have to take it with me anymore.

$$15$$ $$ :$$ $$= 5$$

So you get the same result.

Don't forget: smaller numbers make arithmetic easier! :)

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