Question

Kim made three quiches for a party cheese spinach and mushroom the cheese quinche 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 cheese 9 pieces of spinach and two pieces of the mushroom which quinche did people eat the most of identify the fraction in numerical order from greatest to least

Answer 1

To compare how much of each quiche was eaten, we first need to figure out how many pieces were consumed of each type relative to the total pieces available.

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 compare the fractions \( \frac{5}{8} \), \( \frac{9}{16} \), and \( \frac{1}{2} \).

To do this, we can convert all fractions to have a common denominator. The least common multiple (LCM) of 8, 16, and 2 is 16.

Here are the fractions:

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

- For \( \frac{9}{16} \):
\[
\frac{9}{16} = \frac{9}{16}
\]

- For \( \frac{1}{2} \):
\[
\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}
\]

Now we can compare the fractions:

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

Now we can order them from greatest to least:

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

So, people ate the most of the **cheese quiche**. The order of quiches eaten from greatest to least fraction of pieces consumed is:

1. Cheese Quiche: \( \frac{5}{8} \)
2. Spinach Quiche: \( \frac{9}{16} \)
3. Mushroom Quiche: \( \frac{1}{2} \)