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

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UpStudy AI · Accepted Answer

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:**

$$
\left( \frac{1}{2} \pm \frac{3}{20} \right) - \frac{2}{20} = 
\begin{cases}
\frac{11}{20} & \text{if } + \text{ is used}, \
\frac{1}{4} & \text{if } - \text{ is used}.
\end{cases}
$$
The expression evaluates to $$\frac{11}{20}$$ when using the "+" sign and $$\frac{1}{4}$$ when using the "-" sign.

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