Question

I will mark you as brainlist if you give me the answers ​

Answer 1

GIVEN:

• A rational number when multiplied by 2/3 and subtract by 5/2 wiwill give the result = -7/12

TO FIND:

• The rational number.

SOLUTION:

Let, the rational number be p/q.

A.T.Q

$\implies \bf \: \bigg(\frac{2}{3} \times \frac{p}{q} \bigg) - \frac{5}{2} = \frac{ - 7}{12} \\ \\ \implies \bf \: \bigg(\frac{2}{3} \times \frac{p}{q} \ \bigg) = \bigg(\frac{ - 7}{12} + \frac{5}{2} \bigg) \\ \\ \implies \bf \: \bigg( \frac{2}{3} \times \frac{p}{q} \bigg) = \bigg( \frac{ - 7}{12} + \frac{5 \times 6}{2 \times 6} \bigg) \\ \\ \implies \bf \: \bigg( \frac{2}{3} \times \frac{p}{q} \bigg) = \bigg( \frac{ - 7 + 30}{12} \bigg) \\ \\ \implies \bf \bigg(\frac{2}{3} \times \frac{p}{q} \bigg)= \frac{23}{12} \\ \\ \implies \bf \: \frac{p}{q} = \frac{23}{12} \times \frac{3}{2} \\ \\ \implies \bf \: \frac{p}{q} = \frac{23}{8}$

Therefore, the rational number is 23/8.

Answer 2

Answer :

Let us assume that the rational number is p/q

$\sf\:(\:rational\:number\:\times\:\frac{2}{3}\:)\:-\:\frac{5}{2}\:=\:-\:\frac{7}{12}\\\\\implies\sf\:\frac{2}{3}\:\times\:\frac{p}{q}\:=\:-\:\frac{7}{12}\:+\:\frac{5}{2}\\\\\implies\sf\:\frac{2}{3}\:\times\:\frac{p}{q}\:=\:-\:\dfrac{7\:+\:30}{12}\:\:\:-\:-\:[\:Taking\:LCM\:]\\\\\implies\sf\:\frac{p}{q}\:=\:-\:\dfrac{7\:+\:30}{12}\:\div\:\frac{2}{3}\\\\\implies\sf\:\frac{p}{q}\:=\:\frac{23}{\cancel{12}}\:\times\:\frac{\cancel3}{2}\\\\\implies\sf\:\frac{p}{q}\:=\:\frac{23}{4}\:\times\:\frac{1}{2}\\\\\implies\boxed{\red{\sf\:\frac{p}{q}\:=\:\frac{23}{8}}}$