in short, if the denominator is a decimal or a fraction and you have an integer in the numerator, the numerator gets blown up.
so if you divide by 1/2, the numerator blows up to twice as large, if you divide by 1/5, to five times as large, if you divide by 1/3... well, let's see,
[tex]\bf 2\div \cfrac{1}{3}\implies \cfrac{2}{1}\div \cfrac{1}{3}\implies \cfrac{2}{1}\cdot \cfrac{3}{1}\implies \cfrac{6}{1}\implies 6[/tex]
why is that? well, you're dividing, and so is saying "how many times 1/3 goes into 2"?
well, 1/3 + 1/3 + 1/3 = 3/3 or 1, so in 1 whole, the fraction goes there 3 times, so in 2 wholes, it'll be 6 times.
