JAMB Mathematics 2012 Paper

Concept:Simplify the complex fraction by converting mixed numbers to improper fractions first.Then carry out the multiplication and division step by step.Explanation:Convert each mixed number into an improper fraction.$2\frac{2}{3} = \frac{8}{3}$$1\frac{1}{2} = \frac{3}{2}$$4\frac{4}{5} = \frac{24}{5}$The given expression becomes $\frac{\frac{8}{3} \times \frac{3}{2}}{\frac{24}{5}}$.First, multiply the numerators: $\frac{8}{3} \times \frac{3}{2} = \frac{24}{6} = 4$.Now divide $4$ by $\frac{24}{5}$.Dividing by a fraction is the same as multiplying by its reciprocal.So, $4 \div \frac{24}{5} = 4 \times \frac{5}{24} = \frac{20}{24}$.Simplify $\frac{20}{24}$ by dividing the numerator and denominator by $4$.This gives $\frac{5}{6}$.Answer:The simplified result is $\frac{5}{6}$, which matches option C.