Division by fractions Why is it that to divide by a fraction you need to multiply by the reciprocal of that fraction? 
For instance:
$\eqalign{
  & 1 \div \frac{1}{3}  \cr 
  &  = 1 \times 3  \cr 
  &  = 3 \cr} $
Thank you.

Note that 
$$1 \div \frac{1}{3} = \frac{1}{\frac{1}{3}} = \frac{1}{\frac{1}{3}}\times 1 = \frac{1}{\frac{1}{3}}\times \frac{3}{3} = \frac{1\times 3}{\frac{1}{3}\times 3} = \frac{3}{1} = 3.$$
More generally, you can use the above manipulations to show $\dfrac{a}{b}\div\dfrac{c}{d} = \dfrac{ad}{bc}$.
