nber of terms, if possible. (b) \( \left(\frac{2}{3} y+\frac{5}{8} x+\frac{1}{4}\right)+\left(\frac{1}{4} x+\frac{1}{2}\right) \)

Sure, let's simplify the given expression and determine the number of terms. **Given Expression:** \[ \left(\frac{2}{3} y + \frac{5}{8} x + \frac{1}{4}\right) + \left(\frac{1}{4} x + \frac{1}{2}\right) \] **Step 1: Remove the Parentheses** \[ \frac{2}{3} y + \frac{5}{8} x + \frac{1}{4} + \frac{1}{4} x + \frac{1}{2} \] **Step 2: Combine Like Terms** 1. **Combine the \(x\) terms:** \[ \frac{5}{8} x + \frac{1}{4} x = \frac{5}{8} x + \frac{2}{8} x = \frac{7}{8} x \] 2. **Combine the constant terms:** \[ \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \] 3. **The \(y\) term remains unchanged:** \[ \frac{2}{3} y \] **Step 3: Write the Simplified Expression** \[ \frac{2}{3} y + \frac{7}{8} x + \frac{3}{4} \] **Number of Terms:** There are **3 terms** in the simplified expression: 1. \(\frac{2}{3} y\) 2. \(\frac{7}{8} x\) 3. \(\frac{3}{4}\)