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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 four equal pieces. At the party, people ate five pieces of the cheese, nine pieces of the spinach, and two pieces of the mushroom. Which quiche did people eat the most of? Identify the fractions in numerical order from greatest to least. (1 point)

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To determine which quiche people ate the most of, we need to look at the pieces of each quiche and how many were eaten.

  1. Cheese Quiche:

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

  2. Spinach Quiche:

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

  3. Mushroom Quiche:

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

Next, we need to compare the fractions: \( \frac{5}{8} \), \( \frac{9}{16} \), and \( \frac{1}{2} \).

To compare these fractions, we can convert them to have a common denominator:

  • The least common multiple of 8, 16, and 2 is 16.

Converting the fractions:

  • \( \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \)
  • \( \frac{9}{16} \) remains the same.
  • \( \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \)

Now we have:

  • \( \frac{10}{16} \) for cheese
  • \( \frac{9}{16} \) for spinach
  • \( \frac{8}{16} \) for mushroom

Now, let's order these fractions from greatest to least:

  1. \( \frac{10}{16} \) (cheese)
  2. \( \frac{9}{16} \) (spinach)
  3. \( \frac{8}{16} \) (mushroom)

Therefore, people ate the most of the cheese quiche.

The fractions in numerical order from greatest to least are:

  1. \( \frac{5}{8} \) (cheese)
  2. \( \frac{9}{16} \) (spinach)
  3. \( \frac{1}{2} \) (mushroom)