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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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,

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

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

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

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

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

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

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