1. Problem: Calculate the value of the expression $3 \times \frac{2}{5} + \frac{2}{3}$. 2. Formula and rules: To add fractions, they must have a common denominator. Multiplication of a whole number and a fraction is done by multiplying the whole number by the numerator. 3. Calculate $3 \times \frac{2}{5}$: $$3 \times \frac{2}{5} = \frac{3 \times 2}{5} = \frac{6}{5}$$ 4. Now add $\frac{6}{5} + \frac{2}{3}$: Find the least common denominator (LCD) of 5 and 3, which is 15. 5. Convert fractions to have denominator 15: $$\frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15}$$ $$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$$ 6. Add the fractions: $$\frac{18}{15} + \frac{10}{15} = \frac{18 + 10}{15} = \frac{28}{15}$$ 7. Final answer: $\frac{28}{15}$, which is not among the options given, so let's re-check the problem statement. Re-examining the original expression: $3 (2/5) + 2/3$ means $3 \times \frac{2}{5} + \frac{2}{3}$. Calculations are correct, so the answer is $\frac{28}{15}$. Since none of the options match $\frac{28}{15}$, the problem might have a typo or the options are for a different expression. Therefore, the correct result of the given expression is $\frac{28}{15}$.