I'll solve each exercise step-by-step.

1) $3 \cdot \frac{1}{9} + 0.3$

• $3 \cdot \frac{1}{9} = \frac{3}{9} = \frac{1}{3}$.
• Convert $0.3$ to a fraction: $0.3 = \frac{3}{10}$.
• Adding: $\frac{1}{3} + \frac{3}{10} = \frac{10 + 9}{30} = \frac{19}{30}$.

2) $\frac{2}{5} \cdot 2 - 0.5$

• $\frac{2}{5} \cdot 2 = \frac{4}{5}$.
• $0.5 = \frac{1}{2}$.
• Subtracting: $\frac{4}{5} - \frac{1}{2} = \frac{8 - 5}{10} = \frac{3}{10}$.

3) $1.5 - 3 \cdot \frac{5}{12}$

• $1.5 = \frac{3}{2}$.
• $3 \cdot \frac{5}{12} = \frac{15}{12} = \frac{5}{4}$.
• Subtracting: $\frac{3}{2} - \frac{5}{4} = \frac{6 - 5}{4} = \frac{1}{4}$.

4) $2 \cdot \frac{7}{15} \cdot 3 - \frac{1}{5}$

• $2 \cdot \frac{7}{15} = \frac{14}{15}$.
• $\frac{14}{15} \cdot 3 = \frac{42}{15} = \frac{14}{5}$.
• Subtracting: $\frac{14}{5} - \frac{1}{5} = \frac{13}{5}$.

5) $\frac{1}{6} + 6 \cdot \frac{1}{12}$

• $6 \cdot \frac{1}{12} = \frac{6}{12} = \frac{1}{2}$.
• Adding: $\frac{1}{6} + \frac{1}{2} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3}$.

6) $\frac{5}{2} \cdot \frac{2}{3} \cdot 15 - 3 \cdot \frac{2}{5}$

• $\frac{5}{2} \cdot \frac{2}{3} = \frac{5 \cdot 2}{2 \cdot 3} = \frac{5}{3}$.
• $\frac{5}{3} \cdot 15 = 25$.
• $3 \cdot \frac{2}{5} = \frac{6}{5}$.
• Subtracting: $25 - \frac{6}{5} = \frac{125 - 6}{5} = \frac{119}{5}$.

Let me know if you need further details or clarification on any of these steps.

Here are five related questions:

1. How do you convert a decimal to a fraction?
2. What is the process for adding fractions with different denominators?
3. How do you simplify fractions in multiplication problems?
4. How can you handle mixed numbers in similar problems?
5. What steps can you take to convert a fraction to a decimal?

Tip: When adding or subtracting fractions, always find a common denominator for easier calculation.