Parts of a Whole

A pizza is cut into 8 equal slices and you eat 3. You ate three eighths of it, written $\frac{3}{8}$. The number under the bar, the denominator, says how many equal parts the whole is cut into. The number on top, the numerator, says how many of those parts you have.

The parts must be equal. Cut a pizza into one huge slice and seven thin ones, and 'one slice of eight' no longer means one eighth. The bar is the same division bar as in Section 1: $\frac{3}{8}$ is 3 divided by 8, three wholes shared into 8 equal parts.

A fraction is also a number with its own place on the number line. Cut the stretch from 0 to 1 into 3 equal parts, and each part is $\frac{1}{3}$. Count two parts from 0 and you reach $\frac{2}{3}$.

Cut 0 to 1 into 3 equal parts and count from 0.