Answer :

To add the fractions
$$
\frac{16}{15} \quad \text{and} \quad \frac{12}{25},
$$
we first need a common denominator. The least common multiple (LCM) of 15 and 25 is 75.

1. Write each fraction with the denominator 75:

 - For $\frac{16}{15}$, multiply the numerator and denominator by 5 since $15 \times 5 = 75$. This gives:
$$
\frac{16 \times 5}{15 \times 5} = \frac{80}{75}.
$$

 - For $\frac{12}{25}$, multiply the numerator and denominator by 3 since $25 \times 3 = 75$. This gives:
$$
\frac{12 \times 3}{25 \times 3} = \frac{36}{75}.
$$

2. Now, add the two fractions:
$$
\frac{80}{75} + \frac{36}{75} = \frac{80 + 36}{75} = \frac{116}{75}.
$$

3. The final result of the sum is:
$$
\frac{116}{75} \quad \text{or approximately } 1.5467.
$$

Thus, the sum of $\frac{16}{15}$ and $\frac{12}{25}$ is
$$
\frac{116}{75}.
$$