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

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.

16, 8, 4: The cheese quiche was eaten the most.
16, 8, 4: 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 first need to represent the number of pieces eaten as fractions of each quiche.

  1. Cheese Quiche: 5 pieces out of 8 \[ \text{Fraction of cheese quiche eaten} = \frac{5}{8} \]

  2. Spinach Quiche: 9 pieces out of 16 \[ \text{Fraction of spinach quiche eaten} = \frac{9}{16} \]

  3. Mushroom Quiche: 2 pieces out of 4 \[ \text{Fraction of mushroom quiche eaten} = \frac{2}{4} = \frac{1}{2} \]

Now we need to compare these fractions:

  • \(\frac{5}{8}\)
  • \(\frac{9}{16}\)
  • \(\frac{1}{2} = \frac{8}{16}\)

To compare \(\frac{5}{8}\) and \(\frac{9}{16}\), we can convert \(\frac{5}{8}\) to sixteenths: \[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \]

Now we have:

  • \(\frac{10}{16}\)
  • \(\frac{9}{16}\)
  • \(\frac{8}{16}\)

Next, we order these fractions from greatest to least:

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

So the order is: \(\frac{10}{16}, \frac{9}{16}, \frac{8}{16}\).

Thus, the conclusion is that the cheese quiche was eaten the most.

Answer: \(\frac{10}{16}, \frac{9}{16}, \frac{8}{16}\): The cheese quiche was eaten the most.