b) \( \frac{4}{12}+\frac{5}{9} \times \frac{3}{15} \)

First, let's solve the multiplication part of the expression: \( \frac{5}{9} \times \frac{3}{15} \). When you multiply fractions, you multiply the numerators together and the denominators together. So, \( 5 \times 3 = 15 \) and \( 9 \times 15 = 135 \). This gives us \( \frac{15}{135} \), which simplifies to \( \frac{1}{9} \) (dividing by 15). Now, we can add this to \( \frac{4}{12} \). First, simplify \( \frac{4}{12} \) to \( \frac{1}{3} \). To add \( \frac{1}{3} \) and \( \frac{1}{9} \), convert \( \frac{1}{3} \) to ninths: \( \frac{1}{3} = \frac{3}{9} \). Now, adding \( \frac{3}{9} + \frac{1}{9} \) gives \( \frac{4}{9} \). Therefore, the final answer is \( \frac{4}{9} \).