Assertion: `(-63)/(147) and (-21)/(-49)` are equivalent rational numbers.
Reason : If the numerator and denominator of a rational number are multiplied or divide by a same non-zero integer, we get a rational number which is said to be equivalent to the given rational number.

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 determine whether the assertion that \((-63)/(147)\) and \((-21)/(-49)\) are equivalent rational numbers is true, we will simplify both fractions step by step.

### Step 1: Simplify the first fraction \((-63)/(147)\)

1. **Factor the numerator and denominator**:
\[ -63 = -1 \times 63 = -1 \times 9 \times 7 \]
\[ 147 = 21 \times 7 = 3 \times 7 \times 7 \]

2. **Rewrite the fraction**:
\[ \frac{-63}{147} = \frac{-1 \times 9 \times 7}{3 \times 7 \times 7} \]

3. **Cancel the common factor (7)**:
\[ = \frac{-1 \times 9}{3 \times 7} = \frac{-9}{21} \]

4. **Further simplify \(-9/21\)**:
\[ = \frac{-3 \times 3}{3 \times 7} = \frac{-3}{7} \]

### Step 2: Simplify the second fraction \((-21)/(-49)\)

1. **Factor the numerator and denominator**:
\[ -21 = -1 \times 21 = -1 \times 3 \times 7 \]
\[ -49 = -1 \times 49 = -1 \times 7 \times 7 \]

2. **Rewrite the fraction**:
\[ \frac{-21}{-49} = \frac{-1 \times 3 \times 7}{-1 \times 7 \times 7} \]

3. **Cancel the common factor (-1)**:
\[ = \frac{3 \times 7}{7 \times 7} \]

4. **Cancel the common factor (7)**:
\[ = \frac{3}{7} \]

### Step 3: Compare the simplified fractions

Now we have:
- \(\frac{-63}{147} = \frac{-3}{7}\)
- \(\frac{-21}{-49} = \frac{3}{7}\)

Since \(\frac{-3}{7}\) is not equal to \(\frac{3}{7}\), we conclude that the two fractions are not equivalent.

### Conclusion

The assertion that \((-63)/(147)\) and \((-21)/(-49)\) are equivalent rational numbers is **false**. However, the reason provided is **true** because it correctly states that multiplying or dividing the numerator and denominator of a rational number by the same non-zero integer results in an equivalent rational number.

### Final Answer

- **Assertion**: False
- **Reason**: True