Question

${1. \quad \bullet \: \: {By \: what \: rational \: number \: should }} \\ \: \: \: {{\frac{ - 35}{6 } \: \: be \: \: divided \: \: to \: \: get \: \: \frac{ - 7}{2} \: ?}}$
​

Answer 1

$\frak{ \maltese \: \: Given} \: \begin{cases} \star \: \: \bf \underline{Dividend \: : \tt \dfrac{ - 35}{6} } \: \: \bigstar \\\\ \star \: \: \bf \underline{ Quotient \: : \tt \dfrac{ - 7}{2} } \: \: \: \: \bigstar\end{cases}$

❍ Need To Find : The Divisor .

Let's do it !!

✰$\:\; \large\: \: \large \underline \frak{Formula \: Used \: : }$

$\quad\bullet \: \: \: \: {\sf{Dividend \: \div \: \bf Divisor \: = \sf\: Quotient }}$

❍ Let,

• The required Rational number be x.

$\\ \large\maltese \: \: \Large \underline \frak{ Solution \: : }$

$\dag\: \: \frak{ \: \underline {Substituting \: the \: values \: according \: to \: the \:given \: info \: : }}$

${\large{\star }}\: \: \: \bf{ \frac{ - 35}{6} \div x = \frac{ - 7}{2} }$

$: \implies \sf {2\times \left(\frac{-35}{6}\right)=x\left(-7\right) }\\\\\ : \implies \sf {2\left(-\frac{35}{6}\right)=x\left(-7\right) }\\\\\ : \implies \sf {\frac{2\left(-35\right)}{6}=x\left(-7\right) }\\\\\ : \implies \sf {\frac{-70}{6}=x\left(-7\right) }\\\\\ : \implies \sf {-\frac{35}{3}=x\left(-7\right) }\\\\\ : \implies \sf {x\left(-7\right)=-\frac{35}{3} }\\\\\ : \implies \sf {x=\frac{-\frac{35}{3}}{-7} }\\\\\ : \implies \sf {x=\frac{-35}{3\left(-7\right)} }\\\\\ \qquad \underline { \boxed { : \longrightarrow \tt {x=\frac{5}{3} }}} \: \: \bigstar$

${\therefore \: \underline{\boldsymbol{ Hence, } {\rm\: the } {\bf\: required \: rational \:number}\: { \rm is } \bf\: \dfrac{5}{3} .}}$

Answer 2

$\begin{gathered}\\ \large\maltese \: \: \Large \underline \frak{ Solution \: : } \\ \\ \end{gathered} \\ \begin{gathered} \dag\: \: \frak{ \: \underline {Substituting \: the \: values \: according \: to \: the \:given \: info \: : }} \\ \\ \end{gathered} \\ \begin{gathered} {\large{\star }}\: \: \: \bf{ \frac{ - 35}{6} \div x = \frac{ - 7}{2} } \\ \\ \end{gathered} \\ \begin{gathered} : \implies \sf {2\times \left(\frac{-35}{6}\right)=x\left(-7\right) }\\\\\ : \implies \sf {2\left(-\frac{35}{6}\right)=x\left(-7\right) }\\\\\ : \implies \sf {\frac{2\left(-35\right)}{6}=x\left(-7\right) }\\\\\ : \implies \sf {\frac{-70}{6}=x\left(-7\right) }\\\\\ : \implies \sf {-\frac{35}{3}=x\left(-7\right) }\\\\\ : \implies \sf {x\left(-7\right)=-\frac{35}{3} }\\\\\ : \implies \sf {x=\frac{-\frac{35}{3}}{-7} }\\\\\ : \implies \sf {x=\frac{-35}{3\left(-7\right)} }\\\\\ \qquad \underline { \boxed { : \longrightarrow \tt {x=\frac{5}{3} }}} \: \: \bigstar \\ \\ \end{gathered}</p><p> \\ \\ </p><p>\begin{gathered} {\therefore \: \underline{\boldsymbol{ Hence, } {\rm\: the } {\bf\: required \: rational \:number}\: { \rm is } \bf\: \dfrac{5}{3} .}} \\ \\ \end{gathered}$