Question

Will the quotient of 2÷1/3 be smaller or bigger than each term? Explain in words.

Answer 1

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,

$\bf 2\div \cfrac{1}{3}\implies \cfrac{2}{1}\div \cfrac{1}{3}\implies \cfrac{2}{1}\cdot \cfrac{3}{1}\implies \cfrac{6}{1}\implies 6$

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.