HSPT Quantitative Question of the Day

1. (A) is greater than (B)
2. (B) is greater than (A)
3. (A) and (B) are equal (correct answer)
4. The relationship cannot be determined

Explanation: When you encounter division of fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal. This transforms each expression into a more manageable multiplication problem. For expression (A): $\frac{8}{15} \div \frac{2}{5} = \frac{8}{15} \times \frac{5}{2} = \frac{40}{30} = \frac{4}{3}$ For expression (B): $\frac{6}{7} \div \frac{9}{14} = \frac{6}{7} \times \frac{14}{9} = \frac{84}{63} = \frac{4}{3}$ Both expressions equal $\frac{4}{3}$, so they are equal. Looking at the answer choices: Choice (A) suggests that $\frac{8}{15} \div \frac{2}{5}$ is greater than $\frac{6}{7} \div \frac{9}{14}$, but since both equal $\frac{4}{3}$, this is incorrect. Choice (B) makes the opposite incorrect claim that the second expression is larger. Choice (C) correctly identifies that the expressions are equal. Choice (D) suggests we can't determine the relationship, but we clearly can through direct calculation. The key insight here is that even though the original fractions look quite different, the division operations transform them into identical values. Always simplify your final answers when comparing fractions—it makes relationships much clearer. Study tip: When comparing complex fraction expressions, calculate each one completely and reduce to lowest terms before making your comparison. Don't try to estimate or compare the original fractions visually, as the operations can dramatically change the relative values.