BECE Mathematics 2023 Paper

Concept:Simplify the mixed fraction inside the bracket first, then subtract, and finally multiply by the remaining fraction.Explanation:Convert the mixed number $1\frac{1}{2}$ into an improper fraction.$1\frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}$Now rewrite the whole expression:$\left(1\frac{1}{2} - \frac{5}{6}\right) \times \frac{9}{10} = \left(\frac{3}{2} - \frac{5}{6}\right) \times \frac{9}{10}$To subtract, use the common denominator $6$.$\frac{3}{2} - \frac{5}{6} = \frac{9 - 5}{6} = \frac{4}{6}$Simplify $\frac{4}{6}$ by dividing numerator and denominator by $2$.$\frac{4}{6} = \frac{2}{3}$Multiply: $\frac{2}{3} \times \frac{9}{10}$Cancel common factors: $3$ divides both $3$ and $9$, and $2$ divides both $2$ and $10$.$\frac{2}{3} \times \frac{9}{10} = \frac{1}{1} \times \frac{3}{5} = \frac{3}{5}$The fraction $\frac{3}{5}$ is already in its simplest form because $3$ and $5$ have no common factor other than $1$.Answer:$\frac{3}{5}$, which is option D.