b) \( \frac{2}{5}+\frac{1}{2} \) e) \( \frac{2}{4}+\frac{2}{3} \)

### b) \( \frac{2}{5}+\frac{1}{2} \) 1. Find the least common denominator (LCD) of \(5\) and \(2\). The LCD is \(10\). 2. Rewrite each fraction with the denominator \(10\): \[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}, \quad \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \] 3. Add the fractions: \[ \frac{4}{10} + \frac{5}{10} = \frac{4+5}{10} = \frac{9}{10} \] ### e) \( \frac{2}{4}+\frac{2}{3} \) 1. Notice that \( \frac{2}{4} \) can be simplified: \[ \frac{2}{4} = \frac{1}{2} \] Now, the expression becomes \( \frac{1}{2}+\frac{2}{3} \). 2. Find the least common denominator (LCD) of \(2\) and \(3\). The LCD is \(6\). 3. Rewrite each fraction with the denominator \(6\): \[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}, \quad \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \] 4. Add the fractions: \[ \frac{3}{6} + \frac{4}{6} = \frac{3+4}{6} = \frac{7}{6} \]