Question

A rational number is such that when you multiply it by $\frac{5}{2}$ and add $\frac{2}{3}$to the product, you get $\frac{-7}{12}$. What is the number?

Answer 1

Let the required rational number be $n$

According to the given details, the equation becomes

$$\begin{gathered} n\times \left(\frac{5}{2}\right)+\frac{2}{3}=\left(-\frac{7}{12}\right) \\ \Rightarrow \frac{5n}{2}+\frac{2}{3}=-\frac{7}{12} \\ \Rightarrow \frac{5n}{2}=\left(-\frac{7}{12}-\frac{2}{3}\right) \\ \Rightarrow \frac{5n}{2}=\left(\frac{-7-8}{12}\right) \\ \Rightarrow \frac{5n}{2}=\frac{-15}{12} \\ \Rightarrow n=\left(\frac{-15}{12}\right)\times \frac{2}{5} \\ =\frac{-3}{6}=\frac{-1}{2} \end{gathered}$$

Thus, $n=\frac{-1}{2}$

Therefore, the rational number will be $\frac{-1}{2}$