1. The problem asks to add the fractions $\frac{1}{3}$ and $\frac{1}{2}$. To add fractions, we need a common denominator. 2. The least common denominator (LCD) of 3 and 2 is 6. 3. Convert each fraction to have denominator 6: $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$ $$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$ 4. Add the fractions: $$\frac{2}{6} + \frac{3}{6} = \frac{2+3}{6} = \frac{5}{6}$$ 5. The fraction $\frac{5}{6}$ is already in simplest form. --- 6. The next problem is to subtract $\frac{2}{5}$ from $\frac{7}{9}$. 7. Find the least common denominator of 9 and 5, which is 45. 8. Convert each fraction: $$\frac{7}{9} = \frac{7 \times 5}{9 \times 5} = \frac{35}{45}$$ $$\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}$$ 9. Subtract the fractions: $$\frac{35}{45} - \frac{18}{45} = \frac{35-18}{45} = \frac{17}{45}$$ 10. The fraction $\frac{17}{45}$ is in simplest form. --- 11. The last problem is to simplify an expression using BEDMAS (Brackets, Exponents, Division and Multiplication, Addition and Subtraction). However, the expression is not provided, so no simplification can be done. Final answers: - Addition: $\frac{5}{6}$ - Subtraction: $\frac{17}{45}$ - Simplification: No expression given to simplify.