What's
Answer
Analysis
The basic equation for multiplication is:
Ok - so why does this work?
Let's look at the question and see why.
We can start with the
. If we think of a pizza, we're going to cut it in two and hold onto one piece. Now - if we multiply by a natural number, say like 5, what we're saying is that we're going to add 
to itself 5 times, so that looks like:
So what happens when we multiply by a fraction? We split the figure into more bits (the denominator says the number, so in our case, each of our 2 pieces is split into 3 more) and then we'll hold onto more bits as well (the numerator says the number, so in our case, for every 1 we're holding, we're going to hold 2).
Let's talk this out. In the denominator, we had 2 pieces. We multiply by 3, which now gives 6 pieces of pizza. In the numerator, we had 1 piece. We multiply by 2 and so now are holding 2 pieces. Holding 2 pieces of a pizza that is cut into 6 is the same as holding 1 piece when it's cut into 3 pieces:
~~~~~
Questions and comments always welcome!
