1. The problem is to simplify the expression $0.4 \times 3 \frac{a}{b}$. 2. First, rewrite the mixed expression clearly: $0.4 \times 3 \times \frac{a}{b}$. 3. Multiply the constants: $0.4 \times 3 = 1.2$. 4. So the expression becomes $1.2 \times \frac{a}{b} = \frac{1.2a}{b}$. 5. This is the simplified form of the expression.