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A rational number is such that when you multiply it by $$\frac{{5}}{{2}}{\quad\text{and}\quad}\frac{{2}}{{3}}$$ add to the product, you get $$-\frac{{7}}{{{12}}}.$$ What is the number ?
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## QuestionMathsClass 8

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

Let the rational number is $${x}$$. Then,

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

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

$$\Rightarrow\frac{{5}}{{2}}{x}=-\frac{{15}}{{12}}\Rightarrow{x}=-\frac{{1}}{{2}}$$