If 2 + 2 6, then 1 + 3
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.
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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.
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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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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