Sharing a Fraction

Four fifths of a chocolate bar is left, and 8 friends share it equally. How much of the whole bar does each friend get? Sharing equally is dividing, so use p for portion: $p = \frac{\frac{4}{5}}{8}$.

Dividing by 8 is the same as multiplying by its reciprocal, $\frac{1}{8}$: each friend gets one eighth of the four fifths. So the next line is $p = \frac{4}{5}\cdot \frac{1}{8}$, then $p = \frac{4}{40}$, which simplifies to $p = \frac{1}{10}$. Each friend gets one tenth of the bar.

Notice what the answer measures: a fraction of the whole bar, not of the piece that was shared. That is why it is smaller than the 4/5 you started with. Check it by multiplying back: 8 friends times 1/10 each is 8/10, which is 4/5.