1. **Problem Statement:** Multiply the fractions given in Part 4. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Important Rule:** Always simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). 4. **Work each problem:** **a.** $$\frac{21}{4} \times \frac{8}{3} \div 14 = \frac{21 \times 8}{4 \times 3} \times \frac{1}{14}$$ Calculate numerator and denominator: $$= \frac{168}{12} \times \frac{1}{14}$$ Simplify $$\frac{168}{12}$$: $$= \frac{\cancel{168}^{14}}{\cancel{12}^{1}} \times \frac{1}{14} = 14 \times \frac{1}{14}$$ Multiply: $$= \frac{14}{1} \times \frac{1}{14} = \frac{14 \times 1}{1 \times 14} = \frac{14}{14}$$ Simplify: $$= 1$$ **b.** $$\frac{3}{15} \times \frac{2}{20} \div \frac{1}{50} = \frac{3 \times 2}{15 \times 20} \times \frac{50}{1}$$ Calculate numerator and denominator: $$= \frac{6}{300} \times 50$$ Simplify $$\frac{6}{300}$$: $$= \frac{\cancel{6}^{1}}{\cancel{300}^{50}} \times 50 = \frac{1}{50} \times 50$$ Multiply: $$= \frac{1 \times 50}{50 \times 1} = \frac{50}{50}$$ Simplify: $$= 1$$ **c.** $$\frac{7}{9} \times \frac{27}{28} \div \frac{3}{4} = \frac{7 \times 27}{9 \times 28} \times \frac{4}{3}$$ Calculate numerator and denominator: $$= \frac{189}{252} \times \frac{4}{3}$$ Simplify $$\frac{189}{252}$$: $$= \frac{\cancel{189}^{63}}{\cancel{252}^{84}} \times \frac{4}{3}$$ Multiply: $$= \frac{63 \times 4}{84 \times 3} = \frac{252}{252}$$ Simplify: $$= 1$$ **d.** $$\frac{1}{10} \times \frac{70}{11} = \frac{1 \times 70}{10 \times 11} = \frac{70}{110}$$ Simplify $$\frac{70}{110}$$: $$= \frac{\cancel{70}^{7}}{\cancel{110}^{11}}$$ Final answer: $$= \frac{7}{11}$$ **e.** $$45 \times \frac{3}{5} = \frac{45 \times 3}{5} = \frac{135}{5}$$ Simplify $$\frac{135}{5}$$: $$= \frac{\cancel{135}^{27}}{\cancel{5}^{1}} = 27$$ **f.** $$\frac{2}{7} \times \frac{49}{10} = \frac{2 \times 49}{7 \times 10} = \frac{98}{70}$$ Simplify $$\frac{98}{70}$$: $$= \frac{\cancel{98}^{14}}{\cancel{70}^{10}}$$ Final answer: $$= \frac{14}{10} = \frac{7}{5}$$