Discussion
The product of two rational numbers is \(-\frac{40}{3}\). If one of the two numbers is \(-\frac{5}{2}\), then the reciprocal of the other number lies between :
Answer: B
The reciprocal lies between \(\frac{9}{50}\) and \(\frac{1}{5}\).
The other number is the product divided by the known number, and its reciprocal follows:
\[ \begin{aligned} \text{other} &= -\tfrac{40}{3} \div \left(-\tfrac{5}{2}\right) = \tfrac{40}{3} \times \tfrac{2}{5} = \tfrac{16}{3} \\ \text{reciprocal} &= \tfrac{3}{16} = 0.1875 \end{aligned} \]
Since 9/50 = 0.18 and 1/5 = 0.2, 0.1875 lies between them. 3/20 = 0.15 to 0.18 stops just short, and 1/5 to 1/4 and 1/4 to 1/3 are above it.
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