Let's evaluate the assertion (A) and the reason (R) step-by-step.
### Assertion (A)
We are given:
[tex]\[ \left(\frac{1}{5}\right) + \left(\frac{5}{6}\right) = \left(\frac{1}{5}\right) \times \left(\frac{6}{5}\right) \][/tex]
Let's compute both sides.
#### Left Side:
[tex]\[ \frac{1}{5} + \frac{5}{6} \][/tex]
To add these fractions, we need a common denominator. The lowest common multiple of 5 and 6 is 30.
[tex]\[ \frac{1}{5} = \frac{6}{30} \][/tex]
[tex]\[ \frac{5}{6} = \frac{25}{30} \][/tex]
Adding these fractions:
[tex]\[ \frac{6}{30} + \frac{25}{30} = \frac{31}{30} \][/tex]
#### Right Side:
[tex]\[ \frac{1}{5} \times \frac{6}{5} \][/tex]
Multiplying these fractions:
[tex]\[ \frac{1 \times 6}{5 \times 5} = \frac{6}{25} \][/tex]
Thus, the left side is [tex]\(\frac{31}{30}\)[/tex] and the right side is [tex]\(\frac{6}{25}\)[/tex]. Clearly, these two values are not equal:
[tex]\[ \frac{31}{30} \neq \frac{6}{25} \][/tex]
Therefore, the assertion [tex]\(A\)[/tex] is false.
### Reason (R)
The reason states that when dividing one fraction by another, we multiply the first fraction by the reciprocal of the other fraction. This is indeed a true statement as it is a fundamental rule of dividing fractions.
### Conclusion
- [tex]\(A\)[/tex] is false.
- [tex]\(R\)[/tex] is true.
Therefore, the correct answer is:
[tex]\[ \boxed{(d) \text{A is false but R is true.}} \][/tex]
