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.(1 point)

To determine which quiche was eaten the most and identify the fractions in numerical order from greatest to least, let's analyze the amounts eaten from each quiche.

1. Cheese Quiche:

   • Total pieces: 8
   • Pieces eaten: 5
   • Fraction: \( \frac{5}{8} \)

2. Spinach Quiche:

   • Total pieces: 16
   • Pieces eaten: 9
   • Fraction: \( \frac{9}{16} \)

3. Mushroom Quiche:

   • Total pieces: 4
   • Pieces eaten: 2
   • Fraction: \( \frac{2}{4} = \frac{1}{2} \)

Now, let's convert these fractions to have a common denominator to easily compare them:

• The least common multiple (LCM) of the denominators (8, 16, and 4) is 16.
• Convert each fraction:

1. \( \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \)
2. \( \frac{9}{16} = \frac{9}{16} \)
3. \( \frac{2}{4} = \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{16} \)

Now we have:

• Cheese: \( \frac{10}{16} \)
• Spinach: \( \frac{9}{16} \)
• Mushroom: \( \frac{4}{16} \)

Now, ordering the fractions from greatest to least:

1. \( \frac{10}{16} \) (Cheese Quiche)
2. \( \frac{9}{16} \) (Spinach Quiche)
3. \( \frac{4}{16} \) (Mushroom Quiche)

Thus, people ate the most of the cheese quiche.

Final answer:

Fractions in order: \( \frac{10}{16}, \frac{9}{16}, \frac{4}{16} \); The cheese quiche was eaten the most.

Apologies for the confusion earlier. Let's go through the options you provided again step by step and determine which quiche was eaten the most based on the choices available.

We already determined:

• Cheese quiche: \( \frac{5}{8} \)
• Spinach quiche: \( \frac{9}{16} \)
• Mushroom quiche: \( \frac{2}{4} \) (which we converted to \( \frac{1}{2} \))

Now, we want to compare these fractions:

1. Convert them to have the same denominator for easier comparison. Let's use 16 as a common denominator:
   • Cheese: \[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \]
   • Spinach: \[ \frac{9}{16} = \frac{9}{16} \quad (\text{already has denominator 16}) \]
   • Mushroom: \[ \frac{2}{4} = \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{16} \]

Thus, we have:

• Cheese: \( \frac{10}{16} \)
• Spinach: \( \frac{9}{16} \)
• Mushroom: \( \frac{4}{16} \)

Now, ranking these fractions from greatest to least:

1. \( \frac{10}{16} \) (Cheese)
2. \( \frac{9}{16} \) (Spinach)
3. \( \frac{4}{16} \) (Mushroom)

From this analysis, the cheese quiche was eaten the most.

Now, looking back at your options:

1. \( \frac{5}{8} , \frac{9}{16} , \frac{2}{4} \) : The cheese quiche was eaten the most.
2. \( \frac{9}{16} , \frac{5}{8} , \frac{2}{4} \) : The spinach quiche was eaten the most.
3. \( 16, 8, 4 \) : The cheese quiche was eaten the most.
4. \( \frac{10}{16} , \frac{8}{16} , \frac{9}{16} \) : The cheese quiche was eaten the most.

The correct response matching "The cheese quiche was eaten the most" and the order of fractions is from the first option, "Start Fraction 5 over 8 End Fraction , Start Fraction 9 over 16 End Fraction , Start Fraction 2 over 4 End Fraction".

I appreciate your patience! If you have any more questions or need further clarification, feel free to ask.