Sharing a Fraction

Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 51 of 58.

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 = (4/5) / 8.

Dividing by 8 is the same as multiplying by its reciprocal, 1/8: each friend gets one eighth of the four fifths. So the next line is p = (4/5) × (1/8), then p = 4/40, which simplifies to p = 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.

Challenge

After a party, 2/3 of a pizza is left, and 4 friends share it equally. Find the fraction p of the whole pizza that each friend gets. Write p equal to the calculation, then work it down to one fraction in lowest terms.