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.