1. **State the problem:** We need to calculate the sum and difference of the fractions $\frac{4}{5} + \frac{3}{20} - \frac{1}{10}$ and simplify the result. 2. **Find a common denominator:** The denominators are 5, 20, and 10. The least common denominator (LCD) is 20. 3. **Convert each fraction to have denominator 20:** $$\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}$$ $$\frac{3}{20} = \frac{3}{20}$$ $$\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}$$ 4. **Perform the addition and subtraction:** $$\frac{16}{20} + \frac{3}{20} - \frac{2}{20} = \frac{16 + 3 - 2}{20} = \frac{17}{20}$$ 5. **Simplify the fraction:** $\frac{17}{20}$ is already in simplest form because 17 is a prime number and does not share any common factors with 20. **Final answer:** $$\boxed{\frac{17}{20}}$$