What Is Left

A pie is cut up at lunch. Tom eats 1/2 of the pie and Sara eats 1/6 of the whole pie. What fraction is left? The whole pie is 1, so start from 1 and take both pieces away. Use r for the rest: $r = 1-\frac{1}{2}-\frac{1}{6}$.

Now work it as any subtraction of fractions: write 1 as $\frac{6}{6}$ and use the common denominator 6, which gives $r = \frac{6}{6}-\frac{3}{6}-\frac{1}{6}$, then $r = \frac{2}{6}$, and in lowest terms $r = \frac{1}{3}$. One third of the pie is left.

Read the story closely. Here both pieces are fractions of the whole pie, so both come off the 1. If a story says someone eats 1/6 of what is left, that piece is a fraction of a smaller amount, and the calculation is different.