Assertion : Multiplication of `(-7)/(8) and (2)/(3) is (-7)/(12)`
Reason : To multiply two reaction numbers, we multiply their numerators and denominators separately, and write the product as
`("Product of numerators")/("Product of denominators")`

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the assertion and reason provided, we need to evaluate the multiplication of the rational numbers \(-\frac{7}{8}\) and \(\frac{2}{3}\) and check if the assertion is true.

### Step-by-Step Solution:

1. **Identify the Rational Numbers**:
We have two rational numbers:
\[ A = -\frac{7}{8}, \quad B = \frac{2}{3} \]

2. **Multiply the Rational Numbers**:
To multiply two rational numbers, we multiply their numerators and their denominators separately.
\[ A \times B = \left(-\frac{7}{8}\right) \times \left(\frac{2}{3}\right) = \frac{-7 \times 2}{8 \times 3} \]

3. **Calculate the Numerators and Denominators**:
- Numerator:
\[ -7 \times 2 = -14 \]
- Denominator:
\[ 8 \times 3 = 24 \]

4. **Combine the Results**:
Now, we can write the result of the multiplication:
\[ A \times B = \frac{-14}{24} \]

5. **Simplify the Fraction**:
To simplify \(\frac{-14}{24}\), we find the greatest common divisor (GCD) of 14 and 24, which is 2.
\[ \frac{-14 \div 2}{24 \div 2} = \frac{-7}{12} \]

6. **Conclusion**:
The result of the multiplication is:
\[ -\frac{7}{12} \]
Therefore, the assertion that the multiplication of \(-\frac{7}{8}\) and \(\frac{2}{3}\) is \(-\frac{7}{12}\) is **true**.

### Verification of Reason:
The reason states that to multiply two rational numbers, we multiply their numerators and denominators separately and write the product as:
\[ \frac{\text{Product of numerators}}{\text{Product of denominators}} \]
This is indeed the correct method for multiplying rational numbers.

### Final Conclusion:
Both the assertion and the reason are true, and the reason correctly explains the assertion.