HSPT 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 comparing fractions, you need to either convert them to the same denominator or calculate their decimal values. In this case, since one quantity involves multiplication, let's first simplify $\frac{3}{4} \times \frac{8}{9}$. To multiply fractions, multiply the numerators together and the denominators together: $\frac{3}{4} \times \frac{8}{9} = \frac{3 \times 8}{4 \times 9} = \frac{24}{36}$. Now simplify by finding the greatest common factor of 24 and 36, which is 12: $\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$. So quantity (a) equals $\frac{2}{3}$, and quantity (b) is $\frac{2}{3}$. Therefore, the quantities are equal. Looking at the wrong answers: Choice A claims (a) is greater than (b), but since both equal $\frac{2}{3}$, this is incorrect. Choice B claims (b) is greater than (a), which is also wrong for the same reason. Choice D suggests the relationship cannot be determined, but we can clearly calculate and compare these definite values. The key strategy here is recognizing that fraction multiplication problems often simplify to common fractions that appear elsewhere in the question. Always reduce your fractions to lowest terms before comparing, and look for patterns—the HSPT frequently creates problems where different expressions yield the same simplified result. This tests whether you can perform operations accurately rather than just recognize obvious relationships.