1. **State the problem:** Simplify the expression $$\frac{7}{10} - \frac{3}{5} \times \frac{1}{2} + \frac{3}{4}$$. 2. **Recall order of operations:** Multiplication comes before addition and subtraction. 3. **Multiply the fractions:** $$\frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10}$$. 4. **Rewrite the expression:** $$\frac{7}{10} - \frac{3}{10} + \frac{3}{4}$$. 5. **Find a common denominator for all fractions:** The denominators are 10 and 4. The least common denominator (LCD) is 20. 6. **Convert each fraction to have denominator 20:** $$\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20}$$ $$\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}$$ $$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$$ 7. **Substitute back:** $$\frac{14}{20} - \frac{6}{20} + \frac{15}{20}$$. 8. **Combine the fractions:** $$\frac{14 - 6 + 15}{20} = \frac{23}{20}$$. 9. **Final answer:** $$\frac{23}{20}$$ or as a mixed number $$1 \frac{3}{20}$$. This is the simplified result of the original expression.