What is the result of dividing 4/13 by 5/4?

To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. In this case, to divide ( \frac{4}{13} ) by ( \frac{5}{4} ), we multiply ( \frac{4}{13} ) by the reciprocal of ( \frac{5}{4} ), which is ( \frac{4}{5} ).

The calculation can be seen as follows:

[

\frac{4}{13} \div \frac{5}{4} = \frac{4}{13} \times \frac{4}{5}

]

Now we multiply the numerators together and the denominators together:

[

\frac{4 \times 4}{13 \times 5} = \frac{16}{65}

]

As a result of this operation, the correct answer is ( \frac{16}{65} ).

This answer is correct as it correctly follows the mathematical procedure of dividing fractions by multiplying by the reciprocal. The resulting fraction is also simplified properly because neither the numerator nor denominator shares any common factors apart from 1.