What should come in place of the question mark (?) in the following questions ?
`(5)/(6) + (8)/(9) xx (3)/(5) = ?`

Options

A. `(5)/(9)`
B. `(7)/(16)`
C. `(9)/(16)`
D. `(7)/(9)`

Answer

To solve the equation \( \frac{5}{6} + \frac{8}{9} \times \frac{3}{5} = ? \), we will follow the order of operations (BODMAS/BIDMAS rules), which dictate that we perform multiplication before addition.

### Step-by-step Solution:

1. **Identify the operations**: We have addition and multiplication in the expression. According to BODMAS, we will perform multiplication first.

2. **Perform the multiplication**:
\[ \frac{8}{9} \times \frac{3}{5} \]
To multiply fractions, we multiply the numerators together and the denominators together:
\[ = \frac{8 \times 3}{9 \times 5} = \frac{24}{45} \]

3. **Simplify the multiplication result**:
We can simplify \( \frac{24}{45} \) by finding the greatest common divisor (GCD) of 24 and 45, which is 3:
\[ = \frac{24 \div 3}{45 \div 3} = \frac{8}{15} \]

4. **Add the result to \( \frac{5}{6} \)**:
Now we need to add \( \frac{5}{6} \) and \( \frac{8}{15} \). To do this, we need a common denominator. The least common multiple (LCM) of 6 and 15 is 30.

5. **Convert fractions to have a common denominator**:
- For \( \frac{5}{6} \):
\[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \]
- For \( \frac{8}{15} \):
\[ \frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30} \]

6. **Add the two fractions**:
\[ \frac{25}{30} + \frac{16}{30} = \frac{25 + 16}{30} = \frac{41}{30} \]

7. **Final result**:
The final answer is:
\[ \frac{41}{30} \]

### Conclusion:
Thus, the value that should come in place of the question mark (?) is \( \frac{41}{30} \).