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

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