Simpilfy:
`8(5)/(6)-3(3)/(8)+2(7)/(12)`

Answer

To simplify the expression \( 8 \times \frac{5}{6} - 3 \times \frac{3}{8} + 2 \times \frac{7}{12} \), we will follow these steps:

### Step 1: Calculate each term separately
1. **First Term**: \( 8 \times \frac{5}{6} = \frac{8 \times 5}{6} = \frac{40}{6} \)
2. **Second Term**: \( 3 \times \frac{3}{8} = \frac{3 \times 3}{8} = \frac{9}{8} \)
3. **Third Term**: \( 2 \times \frac{7}{12} = \frac{2 \times 7}{12} = \frac{14}{12} \)

### Step 2: Simplify the fractions
- The first term \( \frac{40}{6} \) can be simplified to \( \frac{20}{3} \) (by dividing both the numerator and denominator by 2).
- The second term \( \frac{9}{8} \) is already in simplest form.
- The third term \( \frac{14}{12} \) can be simplified to \( \frac{7}{6} \) (by dividing both the numerator and denominator by 2).

### Step 3: Find a common denominator
The denominators we have are 3, 8, and 6. The least common multiple (LCM) of these numbers is 24.

### Step 4: Convert each fraction to have the common denominator
1. **Convert \( \frac{20}{3} \)**:
\[ \frac{20}{3} = \frac{20 \times 8}{3 \times 8} = \frac{160}{24} \]
2. **Convert \( \frac{9}{8} \)**:
\[ \frac{9}{8} = \frac{9 \times 3}{8 \times 3} = \frac{27}{24} \]
3. **Convert \( \frac{7}{6} \)**:
\[ \frac{7}{6} = \frac{7 \times 4}{6 \times 4} = \frac{28}{24} \]

### Step 5: Combine the fractions
Now we can combine the fractions:
\[ \frac{160}{24} - \frac{27}{24} + \frac{28}{24} = \frac{160 - 27 + 28}{24} = \frac{161}{24} \]

### Step 6: Final Result
The simplified expression is:
\[ \frac{161}{24} \]

### Step 7: Convert to Mixed Number (if needed)
To convert \( \frac{161}{24} \) to a mixed number:
- Divide 161 by 24, which gives 6 with a remainder of 17.
- Therefore, \( \frac{161}{24} = 6 \frac{17}{24} \).

### Final Answer:
\[ 6 \frac{17}{24} \]