Let's solve this step by step! 🎉 **Step 1:** Multiply $0.4$ by $\frac{3}{5}$. Imagine you have 4 🍎 out of 10 (that's 0.4), and you want to take 3 parts out of 5 parts of them. $$0.4 \times \frac{3}{5} = \frac{4}{10} \times \frac{3}{5}$$ Multiply the top numbers: $4 \times 3 = 12$ Multiply the bottom numbers: $10 \times 5 = 50$ So, $$\frac{12}{50}$$ Simplify the fraction: divide top and bottom by 2 $$\frac{12 \div 2}{50 \div 2} = \frac{6}{25}$$ **Step 2:** Add $\frac{6}{25}$ to $\frac{2}{3}$. We need the same bottom number to add fractions. Let's find the common bottom number. The bottom numbers are 25 and 3. The smallest number both divide into is 75. Change both fractions: $$\frac{6}{25} = \frac{6 \times 3}{25 \times 3} = \frac{18}{75}$$ $$\frac{2}{3} = \frac{2 \times 25}{3 \times 25} = \frac{50}{75}$$ **Step 3:** Add the fractions: $$\frac{18}{75} + \frac{50}{75} = \frac{18 + 50}{75} = \frac{68}{75}$$ **Final answer:** $$\frac{68}{75}$$ Great job! 🎯 You multiplied and added fractions step by step!