Question

Which products are greater than 2 5/6 A 1/8 * 2 5/6 B 6/5 * 2 5/6 C 5/6 * 2 5/6 2 D 5/6 * 2/3

Answer 1

To compare the products, we first need to convert \( 2 \frac{5}{6} \) to an improper fraction.

### Step 1: Convert \( 2 \frac{5}{6} \)

\[
2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
\]

### Step 2: Calculate each product

#### A: \( \frac{17}{6} \times \frac{1}{8} \)

\[
A = \frac{17}{6} \times \frac{1}{8} = \frac{17 \times 1}{6 \times 8} = \frac{17}{48}
\]

#### B: \( \frac{17}{6} \times \frac{6}{5} \)

\[
B = \frac{17}{6} \times \frac{6}{5} = \frac{17 \times 6}{6 \times 5} = \frac{17}{5}
\]

#### C: \( \frac{17}{6} \times \frac{5}{6} \)

\[
C = \frac{17}{6} \times \frac{5}{6} = \frac{17 \times 5}{6 \times 6} = \frac{85}{36}
\]

#### D: \( \frac{5}{6} \times \frac{2}{3} \)

\[
D = \frac{5}{6} \times \frac{2}{3} = \frac{5 \times 2}{6 \times 3} = \frac{10}{18} = \frac{5}{9}
\]

### Step 3: Compare each product with \( 2 \frac{5}{6} \) or \( \frac{17}{6} \)

1. **Product A: \( \frac{17}{48} \)**
- \( \frac{17}{48} < \frac{17}{6} \)

2. **Product B: \( \frac{17}{5} \)**
- Converting to a common denominator (30):
\[
\frac{17}{5} = \frac{17 \times 6}{5 \times 6} = \frac{102}{30}
\]
\[
\frac{17}{6} = \frac{17 \times 5}{6 \times 5} = \frac{85}{30}
\]
- Since \( 102 > 85 \), \( \frac{17}{5} > \frac{17}{6} \)

3. **Product C: \( \frac{85}{36} \)**
- Converting to a common denominator (108):
\[
\frac{85}{36} = \frac{85 \times 3}{36 \times 3} = \frac{255}{108}
\]
\[
\frac{17}{6} = \frac{17 \times 18}{6 \times 18} = \frac{306}{108}
\]
- Since \( 255 < 306 \), \( \frac{85}{36} < \frac{17}{6} \)

4. **Product D: \( \frac{5}{9} \)**
- Converting to a common denominator (18):
\[
\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}
\]
\[
\frac{17}{6} = \frac{17 \times 3}{6 \times 3} = \frac{51}{18}
\]
- Since \( 10 < 51 \), \( \frac{5}{9} < \frac{17}{6} \)

### Conclusion

The only product that is greater than \( 2 \frac{5}{6} \) is:

- **B: \( \frac{17}{5} \)**

So the final answer is:

**B \( 6/5 * 2 5/6 \)** is greater than \( 2 \frac{5}{6} \).