1. **State the problem:** Simplify the expression $\frac{1}{5} \times 3 + \frac{7}{10} - \frac{1}{2}$. 2. **Recall the order of operations:** Multiplication and division come before addition and subtraction. 3. **Calculate the multiplication first:** $$\frac{1}{5} \times 3 = \frac{3}{5}$$ 4. **Rewrite the expression:** $$\frac{3}{5} + \frac{7}{10} - \frac{1}{2}$$ 5. **Find a common denominator for the fractions:** The denominators are 5, 10, and 2. The least common denominator (LCD) is 10. 6. **Convert each fraction to have denominator 10:** $$\frac{3}{5} = \frac{6}{10}, \quad \frac{7}{10} = \frac{7}{10}, \quad \frac{1}{2} = \frac{5}{10}$$ 7. **Perform the addition and subtraction:** $$\frac{6}{10} + \frac{7}{10} - \frac{5}{10} = \frac{6 + 7 - 5}{10} = \frac{8}{10}$$ 8. **Simplify the fraction:** $$\frac{8}{10} = \frac{4}{5}$$ **Final answer:** $\frac{4}{5}$