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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 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)

Responses

16, 8, 4: The cheese quiche was eaten the most.
16, 8, 4: The cheese quiche was eaten the most.

1016, 816, 916: The cheese quiche was eaten the most.
Start Fraction 10 over 16 End Fraction ,  Start Fraction 8 over 16 End Fraction ,  Start Fraction 9 over 16 End Fraction : The cheese quiche was eaten the most.

58, 916, 24: The cheese quiche was eaten the most.
Start Fraction 5 over 8 End Fraction ,  Start Fraction 9 over 16 End Fraction ,  Start Fraction 2 over 4 End Fraction : The cheese quiche was eaten the most.

916, 58, 24: The spinach quiche was eaten the most.

1 answer

To determine which quiche was eaten the most, we should compare the portions consumed as fractions of each quiche.

  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: \( \frac{2}{4} = \frac{1}{2} \)

Now let's convert all fractions to a common denominator to easily compare them. The least common multiple of 8, 16, and 4 is 16.

  • Cheese Quiche:

    • Convert \( \frac{5}{8} \) to sixteenths: \( \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \)

  • Spinach Quiche:

    • Already in sixteenths: \( \frac{9}{16} \)

  • Mushroom Quiche:

    • Convert \( \frac{1}{2} = \frac{2}{4} \) to sixteenths: \( \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \)

Now we have:

  • Cheese: \( \frac{10}{16} \)
  • Spinach: \( \frac{9}{16} \)
  • Mushroom: \( \frac{8}{16} \)

In numerical order from greatest to least:

  1. \( \frac{10}{16} \) (Cheese)
  2. \( \frac{9}{16} \) (Spinach)
  3. \( \frac{8}{16} \) (Mushroom)

Thus, people ate the most of the cheese quiche. The correct response is: Start Fraction 10 over 16 End Fraction, Start Fraction 9 over 16 End Fraction, Start Fraction 8 over 16 End Fraction: The cheese quiche was eaten the most.