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.(1 point) Responses 916 , 58 , 24 : The spinach quiche was eaten the most. Start Fraction 9 over 16 End Fraction , Start Fraction 5 over 8 End Fraction , Start Fraction 2 over 4 End Fraction : The spinach 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. 5/8 , 9/16 , 2/4 : 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. 1016 , 816 , 916 : The cheese quiche was eaten the most.

Answer 1

To determine which quiche was eaten the most, we need to compare the fractions of each quiche that 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: \( \frac{2}{4} = \frac{1}{2} \)

Now we will convert these fractions to a common denominator to compare them more easily:

• The denominators are 8, 16, and 4. The least common multiple (LCM) of these numbers is 16.

Now we convert each fraction:

• For \( \frac{5}{8} \): \[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \]

• For \( \frac{9}{16} \), it remains the same: \[ \frac{9}{16} \]

• For \( \frac{2}{4} \): \[ \frac{2}{4} = \frac{2 \times 4}{4 \times 4} = \frac{8}{16} \]

Now we compare the fractions:

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

Ordering them from greatest to least:

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

Thus, the fraction order from greatest to least is:

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

Therefore, the answer is that the cheese quiche was eaten the most.