identify the numeric order of these fractions and mixed numbers from smallest to largest 4/6 2 5/6 2 1/2 2 3/4 A 2/5, 4/11, 6/17, 4/6 B 4/6 2 1/2 2 3/4 2 5/6 C 5/2,11/4 17/6 4/5 D 2 5/6 2 3/4 2 1/2 4/6

Let's first convert all the fractions and mixed numbers into improper fractions or decimals to make visualization easier.

1. \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)
2. \( 2 = \frac{2}{1} = 2.0 \)
3. \( 2 \frac{1}{2} = \frac{5}{2} = 2.5 \)
4. \( 2 \frac{3}{4} = \frac{11}{4} = 2.75 \)
5. \( 2 \frac{5}{6} = \frac{17}{6} \approx 2.8333 \)

Now let's look at the set \( A \):

- \( \frac{2}{5} = 0.4 \)
- \( \frac{4}{11} \approx 0.3636 \)
- \( \frac{6}{17} \approx 0.3529 \)
- \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)

Now we convert the values in set \( B \):
- \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)
- \( 2 = 2.0 \)
- \( 2 \frac{1}{2} = 2.5 \)
- \( 2 \frac{3}{4} = 2.75 \)
- \( 2 \frac{5}{6} = 2.8333 \)

For set \( C \):
- \( \frac{5}{2} = 2.5 \)
- \( \frac{11}{4} = 2.75 \)
- \( \frac{17}{6} \approx 2.8333 \)
- \( \frac{4}{5} = 0.8 \)

For set \( D \):
- \( 2 \frac{5}{6} = 2.8333 \)
- \( 2 \frac{3}{4} = 2.75 \)
- \( 2 \frac{1}{2} = 2.5 \)
- \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)

Now, we can order each of the sets:

**Set A:**
- \( \frac{6}{17} \approx 0.3529\)
- \( \frac{4}{11} \approx 0.3636 \)
- \( \frac{2}{5} = 0.4 \)
- \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)

**Set B:**
- \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)
- \( 2 \frac{1}{2} = 2.5 \)
- \( 2 \frac{3}{4} = 2.75 \)
- \( 2 \frac{5}{6} \approx 2.8333 \)
- \( 2 = 2.0 \)

In order:
- \( \frac{4}{6} \)
- \( 2.0 \)
- \( 2.5 \)
- \( 2.75 \)
- \( 2.8333 \)

**Set C:**
- \( \frac{6}{17} \)
- \( \frac{5}{2} = 2.5 \)
- \( \frac{11}{4} = 2.75 \)
- \( \frac{4}{5} = 0.8 \)
- \( \frac{17}{6} \approx 2.8333 \)

In order:
- \( 0.8 \)
- \( 2.50 \)
- \( 2.75 \)
- \( 2.8333 \)

**Set D:**
- \( 2 \frac{5}{6} \approx 2.8333 \)
- \( 2 \frac{3}{4} = 2.75 \)
- \( 2 \frac{1}{2} = 2.5 \)
- \( \frac{4}{6} \approx 0.6667 \)

Final orders for each set:
- **A:** \( \frac{6}{17}, \frac{4}{11}, \frac{2}{5}, \frac{4}{6} \)
- **B:** \( \frac{4}{6}, 2, 2 \frac{1}{2}, 2 \frac{3}{4}, 2 \frac{5}{6} \)
- **C:** \( \frac{5}{2}, \frac{11}{4}, \frac{4}{5}, \frac{17}{6} \)
- **D:** \( \frac{4}{6}, 2 \frac{1}{2}, 2 \frac{3}{4}, 2 \frac{5}{6} \)

If we order all of them together, we get:
1. \( \frac{6}{17} \approx 0.3529 \)
2. \( \frac{4}{11} \approx 0.3636 \)
3. \( \frac{2}{5} = 0.4 \)
4. \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)
5. \( 2 = 2.0 \)
6. \( 2 \frac{1}{2} = 2.5 \)
7. \( 2 \frac{3}{4} = 2.75 \)
8. \( 2 \frac{5}{6} \approx 2.8333 \)