Question

What products are greater than 2 5/6

1/8 x 2 5/6
6/5 x 2 5/6
5/6 x2 5/6
2 5/6x2/3

Answer 1

To determine which products are greater than \( 2 \frac{5}{6} \), we need to calculate each of the products:

1. **Calculate \( \frac{1}{8} \times 2 \frac{5}{6} \)**:
- First, convert \( 2 \frac{5}{6} \) to an improper fraction:
\( 2 \frac{5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \)
- Now calculate:
\( \frac{1}{8} \times \frac{17}{6} = \frac{17}{48} \)
- \( \frac{17}{48} \) is less than \( 2 \frac{5}{6} \).

2. **Calculate \( \frac{6}{5} \times 2 \frac{5}{6} \)**:
- Using the improper fraction again:
\( \frac{6}{5} \times \frac{17}{6} = \frac{6 \times 17}{5 \times 6} = \frac{17}{5} \)
- Convert \( \frac{17}{5} \) to a mixed number:
\( \frac{17}{5} = 3 \frac{2}{5} \) (which is greater than \( 2 \frac{5}{6} \)).

3. **Calculate \( \frac{5}{6} \times 2 \frac{5}{6} \)**:
- Again using the improper fraction:
\( \frac{5}{6} \times \frac{17}{6} = \frac{5 \times 17}{6 \times 6} = \frac{85}{36} \)
- Convert \( \frac{85}{36} \) to a mixed number:
\( \frac{85}{36} = 2 \frac{13}{36} \) (which is also less than \( 2 \frac{5}{6} \)).

4. **Calculate \( 2 \frac{5}{6} \times \frac{2}{3} \)**:
- Using the improper fraction again:
\( \frac{17}{6} \times \frac{2}{3} = \frac{17 \times 2}{6 \times 3} = \frac{34}{18} = \frac{17}{9} \)
- Convert \( \frac{17}{9} \) to a mixed number:
\( \frac{17}{9} = 1 \frac{8}{9} \) (which is less than \( 2 \frac{5}{6} \)).

**Summary**:
- **Products Greater than \( 2 \frac{5}{6} \)**:
- \( \frac{6}{5} \times 2 \frac{5}{6} = \frac{17}{5} \) or \( 3 \frac{2}{5} \).

- **Products Not Greater**:
- \( \frac{1}{8} \times 2 \frac{5}{6} \)
- \( \frac{5}{6} \times 2 \frac{5}{6} \)
- \( 2 \frac{5}{6} \times \frac{2}{3} \)

Thus, only **\( \frac{6}{5} \times 2 \frac{5}{6} \)** is greater than \( 2 \frac{5}{6} \).