13.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?

Let the number be x
As per given, we have

\(x× \frac{5}2 +\frac{2}3 = \frac{-7}{12}\)

\(\Rightarrow \frac{5x}2 = \frac{-7}{12}-\frac{2}3 \quad\)[ subtracting \(\frac{2}3\) from both the sides]

\(\Rightarrow \frac{5x}2 = \frac{-7-8}{12}\)

\(\Rightarrow \frac{5x}2 = \frac{-15}{12}\)

\(\Rightarrow x = \frac{-15}{12}÷\frac{5}2\quad \)[transposing \(\frac{5}2\) to RHS]

\(\Rightarrow X= \frac{-30}{60}=\frac{-1}2\)

Hence, the required rational number is \(\frac{-1}2\)