Question

For what value of $x$ if <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{7}{x}$ not a rational number?

• A. -1
• B. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{-22}{19}$
• C. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{0}{14}$
• D. $\frac{\sqrt{8}}{\sqrt{2}}$
  <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->

Answer 1

The correct option is C <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{0}{14}$

Rational numbers are numbers of the form <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$

Let’s substitute the given options.

• Substituting $x=-1$, we get <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{7}{-1}$ which satisfies the conditions of rational numbers.
• Substituting $x$ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{-22}{19}$, we get <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{-133}{22}$ which satisfies the conditions of rational numbers.
• For the the given expression $\frac{7}{x}$ , the only constraint is that $x$ cannot be 0. Thus, substituting $x=\frac{0}{14}$, we get, $\frac{7}{0/14}$= <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{7\times 14}{0}$= <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{98}{0}$

Since,$\frac{98}{0}$ violates the definition of a rational number. The values of $x$ = $\frac{0}{14}$ does not make $\frac{7}{x}$ a rational number.

• For $x=\frac{\left(\sqrt{8}\right)}{\left(\sqrt{2}\right)}$ =$2\frac{\left(\sqrt{2}\right)}{\left(\sqrt{2}\right)}=2$

Substituting the value of $x=2$ in the given expression we get <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{7}{2}$, which makes $\frac{7}{2}$ a rational number.
Hence, the right answer is option (c).