A mathematical expression involving fractions and division: 1 / (1/4 + 1/6) ÷ 2/5

Calculate the denominator sum first using $\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$. Here, $\frac{1}{4} + \frac{1}{6} = \frac{6+4}{24} = \frac{10}{24} = \frac{5}{12}$. Taking the reciprocal gives $12/5$, then multiply by the reciprocal of the divisor: $\frac{12}{5} \times \frac{5}{2} = 6$. Wait, the question implies $1 / (1/4 + 1/6)$ followed by division.

Students often misinterpret the order of operations by dividing $1/4$ by $2/5$ before performing the sum in the denominator, or forgetting to take the reciprocal after evaluating the bracket.

Always handle complex denominators by converting them to a single fraction before applying reciprocal operations, a technique frequently used in simplification and ratio-based algebra problems.