Kim made three quiches for a party: cheese, spinach, and mushroom. The cheese quiche was cut into 8 equal pieces, the spinach quiche was cut into 16 equal pieces, and the mushroom quiche was cut into 4 equal pieces. At the party, people ate 5 pieces of the cheese, 9 pieces of the spinach, and 2 pieces of the mushroom.
Which quiche did people eat the most of? Identify the fractions in numerical order from greatest to least.
A 10/16, 8/16, 9/16: The cheese quiche was eaten the most.
B 9/16, 5/8, 2/4: The spinach quiche was eaten the most.
C 16, 8, 4: The cheese quiche was eaten the most.
D 5/8, 9/16, 2/4: The cheese quiche was eaten the most.
To determine which quiche people ate the most of, we need to look at the fraction of each quiche that was eaten and compare them.
- For the cheese quiche, 5 out of 8 pieces were eaten, so the fraction eaten was 5/8.
- For the spinach quiche, 9 out of 16 pieces were eaten, so the fraction eaten was 9/16.
- For the mushroom quiche, 2 out of 4 pieces were eaten, so the fraction eaten was 2/4.
Now, let's compare the fractions:
The cheese quiche: 5/8 can also be represented as 10/16 (by multiplying both numerator and denominator by 2) to compare it directly with 9/16 (the fraction of the spinach quiche that was eaten).
The spinach quiche: 9/16 remains as it is.
The mushroom quiche: 2/4 simplifies to 1/2, which is equal to 8/16 (by multiplying both numerator and denominator by 4) for comparison.
The numerical order from greatest to least for these eaten fractions (after converting to have a common denominator of 16) is:
- Cheese quiche: 10/16
- Spinach quiche: 9/16
- Mushroom quiche: 8/16
Therefore, people ate the most of the cheese quiche. The correct fraction order is A: 10/16 for the cheese quiche, followed by 9/16 for the spinach quiche, and then 8/16 (equivalent to 2/4) for the mushroom quiche. However, the conclusion to which quiche was eaten the most is correct but the options are not correctly correlating with their respective fractions. The correct fractions corresponding to each quiche should be:
5/8 (Cheese quiche) = 10/16
9/16 (Spinach quiche) = 9/16
2/4 (Mushroom quiche) = 8/16
So in order from greatest to least we have:
- 10/16 (Cheese)
- 9/16 (Spinach)
- 8/16 (Mushroom)
The correct answer is therefore closest to option A, with the fractions in the right order, though the statement regarding which was eaten the most is incorrectly ascribed to cheese in option A; it should state that the cheese quiche was eaten the most, not spinach. The fractions should be corrected as described above.