\( ( \frac { 1 } { 2 } \pm \frac { 3 } { 20 } ) - \frac { 2 } { 20 } \)

Let's evaluate the expression: \[ \left( \frac{1}{2} \pm \frac{3}{20} \right) - \frac{2}{20} \] This expression has two cases due to the "±" sign. --- ### **Case 1: Using the "+" sign** \[ \left( \frac{1}{2} + \frac{3}{20} \right) - \frac{2}{20} \] 1. **Combine the fractions inside the parentheses:** \[ \frac{1}{2} + \frac{3}{20} = \frac{10}{20} + \frac{3}{20} = \frac{13}{20} \] 2. **Subtract the remaining fraction:** \[ \frac{13}{20} - \frac{2}{20} = \frac{11}{20} \] --- ### **Case 2: Using the "−" sign** \[ \left( \frac{1}{2} - \frac{3}{20} \right) - \frac{2}{20} \] 1. **Combine the fractions inside the parentheses:** \[ \frac{1}{2} - \frac{3}{20} = \frac{10}{20} - \frac{3}{20} = \frac{7}{20} \] 2. **Subtract the remaining fraction:** \[ \frac{7}{20} - \frac{2}{20} = \frac{5}{20} = \frac{1}{4} \] --- ### **Final Result** The expression \( \left( \frac{1}{2} \pm \frac{3}{20} \right) - \frac{2}{20} \) evaluates to: - **\(\frac{11}{20}\)** when using the **"+"** sign. - **\(\frac{1}{4}\)** when using the **"−"** sign. --- **Summary:** \[ \left( \frac{1}{2} \pm \frac{3}{20} \right) - \frac{2}{20} = \begin{cases} \frac{11}{20} & \text{if } + \text{ is used}, \\ \frac{1}{4} & \text{if } - \text{ is used}. \end{cases} \]