To solve the expression \( \frac{4}{15} + \frac{1}{3} \), we start by finding a common denominator. The least common multiple (LCM) of 15 and 3 is 15.
Now we'll rewrite \( \frac{1}{3} \) with a denominator of 15:
\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \]
Now we can add the two fractions:
\[ \frac{4}{15} + \frac{5}{15} = \frac{4 + 5}{15} = \frac{9}{15} \]
Next, we can simplify \( \frac{9}{15} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
\[ \frac{9 \div 3}{15 \div 3} = \frac{3}{5} \]
Thus, the final result of \( \frac{4}{15} + \frac{1}{3} \) is \( \frac{3}{5} \).
If you meant to compare this result to options A through D, it is clear that:
- A: \( \frac{5}{18} \)
- B: \( \frac{5}{3} \)
- C: \( \frac{4}{5} \)
- D: \( \frac{3}{5} \)
The correct answer is D: \( \frac{3}{5} \).