Discussion
The product of two rational numbers is \(-\frac{40}{3}\). If one of them is \(-\frac{5}{2}\), and the reciprocal of the other is x, then what is the value of \(\left(8x + 2\frac{1}{4}\right)\) ?
Answer: B
The value is \(3\frac{3}{4}\).
The other number is the product divided by the known number.
\[ \begin{aligned} -\frac{40}{3} \div \left(-\frac{5}{2}\right) &= \frac{40}{3} \times \frac{2}{5} \\ &= \frac{16}{3} \end{aligned} \]
Its reciprocal is \(x = \frac{3}{16}\).
\[ \begin{aligned} 8x + 2\tfrac{1}{4} &= \frac{3}{2} + \frac{9}{4} \\ &= \frac{15}{4} = 3\tfrac{3}{4} \end{aligned} \]
Using the other number itself instead of its reciprocal would give \(8 \times \frac{16}{3}\), far larger than any option.
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