Question #e93f2

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Question #e93f2

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Answer 1 · 2017-04-14T12:46:12

I've assumed the question is "Why is $\frac{12}{9} = \frac{24}{18}$ $12/9=24/18$ ?"
(see below)

Explanation:

anything multiplied by $1$ $1$ is equal to itself.

$\frac{2}{2} = 1$ $2/2=1$

It follows that $\frac{12}{9} \times \frac{2}{2} = \frac{12}{9}$ $12/9 xx 2/2 = 12/9$

...but $\frac{12}{9} \times \frac{2}{2} = \frac{12 \times 2}{9 \times 2} = \frac{24}{18}$ $12/9 xx 2/2 =(12 xx 2)/(9 xx 2)=24/18$

...so $\frac{24}{18} = \frac{12}{9}$ $24/18 = 12/9$ (or stating it in reverse: $\frac{12}{9} = \frac{24}{18}$ $12/9=24/18$ )

Answer 2 · 2017-07-08T02:05:58

$\frac{12}{9} = \frac{24}{18}$ $12/9=24/18$ , that much is true.

The answer to "Why?" will take a bit more space, as below.

Explanation:

This weekend you are having $12$ $12$ friends over for your Birthday party. Everything is ready, but someone notices that the cake has already been sliced into $9$ $9$ equal pieces. Not enough!

Not being a mathematician or any type of magician, you decide to go back to the store and buy three more equal slices to add to the original nine, so now you have a total of:
$9 + 3 = 12$ $9+3=12$ slices, in a new cake that has grown to $\frac{12}{9}$ $12/9$ of the original, as below.

enter image source here

So getting back to the party, all is going well until your brother shows up with a gang of his friends, adding $12$ $12$ more people for a total of $12 + 12 = 24$ $12+12=24$ cake-eaters. Brothers just do that.

Now you have a problem again, and the cake store is closed.
Fortunately, your brother $i s$ $is$ a mathematician, and looking at the $12$ $12$ slices of cake he realizes that you will need to cut each one of them in half because $2 \times 12 = 24$ $2xx12=24$ slices. Just enough!

enter image source here

Everyone at the party had a great time, and all enjoyed the cake. There were enough equal size slices for all, although extras needed to be added in the beginning and then they had to be cut to half the size originally planned.

The original Cake was cut into $\frac{9}{9}$ $9/9$ slices, then three more equal slices were added:

$\frac{9}{9} + \frac{3}{9} = \frac{12}{9} \to$ $9/9+3/9=12/9to$ the top drawing.

The slices were then cut in half to make a total of $24$ $24$ slices.
But by doing that, each slice became smaller, or about $\frac{1}{18}$ $1/18$ of the original cake, as the bottom drawing shows.

Now we can see that: $\frac{1}{9} \times \frac{1}{2} = \frac{1}{18}$ $1/9xx1/2=1/18$

The total number of slices in the end was then: $24 \times \frac{1}{18} = \frac{24}{18}$ $24xx1/18=24/18$

And that is why $\frac{12}{9} = \frac{24}{18}$ $12/9=24/18$

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