1. (a) Evaluate each expression exactly. (i) Evaluate $$\left(\frac{3}{2}\right)^2 - 1 + 6$$. Step 1: Square the fraction: $$\left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2} = \frac{9}{4}$$ Step 2: Substitute back: $$\frac{9}{4} - 1 + 6$$ Step 3: Convert 1 and 6 to fractions with denominator 4: $$1 = \frac{4}{4}, \quad 6 = \frac{24}{4}$$ Step 4: Combine all terms: $$\frac{9}{4} - \frac{4}{4} + \frac{24}{4} = \frac{9 - 4 + 24}{4} = \frac{29}{4}$$ Final answer for (i): $$\frac{29}{4}$$ (ii) Evaluate $$\left( 2.1 \times \frac{10}{7} \right) + 12 \div 1 \frac{3}{5}$$. Step 1: Convert mixed number to improper fraction: $$1 \frac{3}{5} = \frac{5 \times 1 + 3}{5} = \frac{8}{5}$$ Step 2: Calculate multiplication: $$2.1 \times \frac{10}{7} = \frac{21}{10} \times \frac{10}{7}$$ (since 2.1 = \frac{21}{10}) Step 3: Simplify multiplication: $$\frac{21}{10} \times \frac{10}{7} = \frac{\cancel{21}}{\cancel{10}} \times \frac{\cancel{10}}{7} = \frac{21}{7} = 3$$ Step 4: Calculate division: $$12 \div \frac{8}{5} = 12 \times \frac{5}{8} = \frac{12 \times 5}{8} = \frac{60}{8} = \frac{15}{2}$$ Step 5: Add results: $$3 + \frac{15}{2} = \frac{6}{2} + \frac{15}{2} = \frac{21}{2}$$ Final answer for (ii): $$\frac{21}{2}$$