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.

Question

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.

Answer 1

To determine which quiche people ate the most of, we first need to express the quantities eaten as fractions of the whole quiche and then compare these fractions.

For the cheese quiche, 5 out of 8 pieces were eaten, which is 5/8 of the quiche.
For the spinach quiche, 9 out of 16 pieces were eaten, which is 9/16 of the quiche.
For the mushroom quiche, 2 out of 4 pieces were eaten, which is 2/4 or simplified to 1/2 of the quiche.

Now we need to compare these fractions to determine which is the greatest. To compare fractions with different denominators, we can either find a common denominator, convert them to decimal form, or just compare them directly by understanding how fractions work. In this case, the denominators are 8, 16, and 4.

Let's look at each fraction's equivalent with a common denominator of 16:

- The cheese quiche part eaten is 5/8, which is equivalent to 10/16 (because 5 × 2 = 10 and 8 × 2 = 16).
- The spinach quiche part eaten is 9/16, which stays the same.
- The mushroom quiche part eaten is 1/2 (or 2/4), which is equivalent to 8/16 (because 1 × 8 = 8 and 2 × 8 = 16).

Now we can clearly see that:

- Cheese quiche = 10/16
- Spinach quiche = 9/16
- Mushroom quiche = 8/16

So, the cheese quiche was eaten the most.

When we order these fractions from greatest to least, we get 10/16 (cheese), 9/16 (spinach), and 8/16 (mushroom). Therefore, the correct answer in the format of the options provided is:

A) 10/16, 9/16, 8/16: The cheese quiche was eaten the most.

Note that option A had a typo in the fractions presented, but the correct answer mentioned that the cheese quiche was eaten the most. The correct numerical order from greatest to least is indeed 10/16 (cheese), 9/16 (spinach), and 8/16 (mushroom).