To determine which quiche was eaten the most, we first need to represent the number of pieces eaten as fractions of each quiche.
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Cheese Quiche: 5 pieces out of 8 \[ \text{Fraction of cheese quiche eaten} = \frac{5}{8} \]
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Spinach Quiche: 9 pieces out of 16 \[ \text{Fraction of spinach quiche eaten} = \frac{9}{16} \]
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Mushroom Quiche: 2 pieces out of 4 \[ \text{Fraction of mushroom quiche eaten} = \frac{2}{4} = \frac{1}{2} \]
Now we need to compare these fractions:
- \(\frac{5}{8}\)
- \(\frac{9}{16}\)
- \(\frac{1}{2} = \frac{8}{16}\)
To compare \(\frac{5}{8}\) and \(\frac{9}{16}\), we can convert \(\frac{5}{8}\) to sixteenths: \[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \]
Now we have:
- \(\frac{10}{16}\)
- \(\frac{9}{16}\)
- \(\frac{8}{16}\)
Next, we order these fractions from greatest to least:
- \(\frac{10}{16}\) (cheese quiche)
- \(\frac{9}{16}\) (spinach quiche)
- \(\frac{8}{16}\) (mushroom quiche)
So the order is: \(\frac{10}{16}, \frac{9}{16}, \frac{8}{16}\).
Thus, the conclusion is that the cheese quiche was eaten the most.
Answer: \(\frac{10}{16}, \frac{9}{16}, \frac{8}{16}\): The cheese quiche was eaten the most.