1. **Problem statement:** Calculate and simplify the following expressions. 2. **Part a:** $\frac{2}{8} + \frac{2}{8}$ - Since denominators are the same, add numerators: $\frac{2+2}{8} = \frac{4}{8}$ - Simplify $\frac{4}{8}$ by dividing numerator and denominator by 4: $$\frac{\cancel{4}}{\cancel{8}} = \frac{1}{2}$$ 3. **Part b:** $\frac{2}{3} \cdot \frac{3}{8}$ - Multiply numerators and denominators: $$\frac{2 \cdot 3}{3 \cdot 8} = \frac{6}{24}$$ - Simplify $\frac{6}{24}$ by dividing numerator and denominator by 6: $$\frac{\cancel{6}}{\cancel{24}} = \frac{1}{4}$$ 4. **Part c:** $\frac{1}{3} + \frac{2}{6} - \frac{5}{12}$ - Find common denominator: 12 - Convert fractions: $$\frac{1}{3} = \frac{4}{12}, \quad \frac{2}{6} = \frac{4}{12}$$ - Add and subtract: $$\frac{4}{12} + \frac{4}{12} - \frac{5}{12} = \frac{4+4-5}{12} = \frac{3}{12}$$ - Simplify $\frac{3}{12}$ by dividing numerator and denominator by 3: $$\frac{\cancel{3}}{\cancel{12}} = \frac{1}{4}$$ 5. **Part d:** $\frac{1}{4} : \frac{1}{4}$ - Division of fractions means multiply by reciprocal: $$\frac{1}{4} \cdot \frac{4}{1} = \frac{1 \cdot 4}{4 \cdot 1} = \frac{4}{4} = 1$$ --- **Final answers:** - a) $\frac{1}{2}$ - b) $\frac{1}{4}$ - c) $\frac{1}{4}$ - d) $1$