Ncert solutions

# Question 13

Q13) 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?

Solution:

Let the rational number be x.

According to the question, \frac{5}{2}x+\frac{2}{3}=-\frac{7}{12}

\Rightarrow\ \frac{5}{2}x+\frac{2}{3}-\frac{2}{3}=-\frac{7}{12}-\frac{2}{3}

[Subtracting \frac{2}{3} from both sides]

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

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

\Rightarrow\ 5x\times12=-15\times2

\Rightarrow60x=-30

\Rightarrow\ \frac{60x}{60}=\frac{-30}{60}

[Dividing both sides by 60]

\Rightarrow\ x=\ \frac{-1}{2}

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

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