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.
10/16, 8/16, 9/16: The cheese quiche was eaten the most.
9/16, 5/8, 2/4: The spinach quiche was eaten the most.
16, 8, 4: The cheese quiche was eaten the most.
5/8, 9/16, 2/4: The cheese quiche was eaten the most.
To compare which quiche was eaten the most, we should first express the consumed amounts in terms of the same denominator so that we can easily compare the fractions.
For the cheese quiche, 5 out of 8 pieces were eaten. This fraction is:
5/8
For the spinach quiche, 9 out of 16 pieces were eaten. This fraction is already in sixteenths, so we leave it as:
9/16
For the mushroom quiche, 2 out of 4 pieces were eaten. To convert this to sixteenths, we multiply both the numerator and the denominator by 4:
(2 * 4) / (4 * 4) = 8/16
Now that the fractions are on a common basis, we can compare them:
- Cheese: 5/8 --> To express in sixteenths, multiply by 2: (5 * 2)/(8 * 2) = 10/16
- Spinach: 9/16
- Mushroom: 8/16
In order from greatest to least, we see:
- Cheese: 10/16
- Spinach: 9/16
- Mushroom: 8/16
Thus, the correct answer is:
10/16, 9/16, 8/16: The cheese quiche was eaten the most.