BECE Mathematics 2018 Paper

Concept:Simplify the bracket first using the LCM of the denominators, then divide the fractions by multiplying with the reciprocal.Explanation:First, simplify the bracket: $\frac{2}{3} - \frac{1}{4}$.The LCM of $3$ and $4$ is $12$.Convert each fraction to an equivalent fraction with denominator $12$:$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$Now subtract the numerators:$\frac{8}{12} - \frac{3}{12} = \frac{5}{12}$The bracket simplifies to $\frac{5}{12}$.Now perform the division: $\frac{5}{12} \div \frac{5}{6}$.Apply the fraction division rule, which means multiply by the reciprocal of the second fraction:$\frac{5}{12} \div \frac{5}{6} = \frac{5}{12} \times \frac{6}{5}$Cancel the common factor $5$ from the numerator and denominator.Also, $6$ divides $12$ to give $2$ in the denominator.This leaves $\frac{1}{2}$.Therefore, the value of the expression is $\frac{1}{2}$.Answer:Option A: $\frac{1}{2}$