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Answer :
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 \(\frac{-1}2\)