Dividing by a Whole Number

A whole number is a fraction over 1, so its reciprocal is 1 over it: 2 is $\frac{2}{1}$, and its reciprocal is $\frac{1}{2}$. That makes $\frac{4}{7} \div 2$ the same as $\frac{4}{7}\cdot \frac{1}{2}$, which is $\frac{4}{14}$, or $\frac{2}{7}$ in lowest terms.

It matches what dividing by 2 means: sharing between two, taking half. And half of $\frac{4}{7}$ is $\frac{1}{2}\cdot \frac{4}{7}$, the same multiplication you met in the last chapter, since of means multiply.

When the top divides evenly by the whole number, there is a shortcut: divide the top. 4 sevenths shared between 2 is 2 sevenths. Either way, never divide the bottom: that makes the pieces bigger, so the fraction would grow instead of shrinking.