Basics of multiplication and Division (fractions)

Hello,

I have a few questions regarding multiplication of and division of fractions of size less than 1.

I understand how to multiply straight across:

ex. -

1/2 x 3/8 = (1*3)/(2*8) = 3/16

But, if I was to explain to say, a third grader, how and why we can multiply across, and why when we multiply these fractions the resultant value gets smaller than its original multiplicants, what would I say?

Similarly, why when we divide, can we flip the second term and multiply across? And why does the division of two fractions of the like produce a value greater than its two original fractions?

How could I explain this in a discrete manner?

Thanks a lot!