JAMB Mathematics 2011 Paper

Concept:Simplify the compound fraction by converting mixed numbers to improper fractions, then multiplying by the reciprocal of the denominator.Explanation:Rewrite $3\frac{2}{3}$ as an improper fraction:$$3\frac{2}{3} = \frac{11}{3}$$Substitute into the original expression:$$\frac{\frac{11}{3}\times\frac{5}{6}\times\frac{2}{3}}{\frac{11}{15}\times\frac{3}{4}\times\frac{2}{27}}$$Multiply the numerator fractions:$$\frac{11}{3}\times\frac{5}{6}\times\frac{2}{3} = \frac{110}{54} = \frac{55}{27}$$Multiply the denominator fractions:$$\frac{11}{15}\times\frac{3}{4}\times\frac{2}{27} = \frac{66}{1620} = \frac{11}{270}$$Now divide the numerator by the denominator:$$\frac{55}{27}\div\frac{11}{270} = \frac{55}{27}\times\frac{270}{11}$$Cancel the common factors:$$\frac{55}{27}\times\frac{270}{11} = 5 \times 10 = 50$$Answer:D. $50$