Discussion
At a party there are 3 large pizzas of equal size. Each pizza has been cut into 9 equal pieces. \(\frac{8}{9}\) of the first pizza has been eaten; \(\frac{2}{3}\) of the second pizza has been eaten; \(\frac{7}{9}\) of the third pizza has been eaten. What fraction of the 3 pizzas is left ?
Answer: A
The fraction of the three pizzas left is \(\frac{2}{9}\).
Work in ninths of a pizza, since each pizza has 9 pieces. The second pizza's \(\frac{2}{3}\) is \(\frac{6}{9}\).
\[ \begin{aligned} \text{eaten} &= \tfrac{8}{9} + \tfrac{6}{9} + \tfrac{7}{9} \\ &= \tfrac{21}{9} \\ \text{left} &= \tfrac{27}{9} - \tfrac{21}{9} = \tfrac{6}{9} \end{aligned} \]
So 6 of the 27 pieces are left, and as a fraction of the three pizzas that is \(\frac{6}{27} = \frac{2}{9}\).
The left-over amount, 6 pieces, is \(\frac{2}{3}\) of one pizza; the question asks for a fraction of all three, so it must be divided by 3. \(\frac{1}{3}\), \(\frac{2}{7}\) and \(\frac{1}{6}\) do not come from the counts.
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