Question

product of two rational numbers is
-18/75
If one of the rational number is -9/20 then find the other​

Answer 1

Answer:

$\boxed{Other \: number = \frac{8}{15}}$

Given:

Product of two rational numbers = $-\frac{18}{75}$

One rational number = $-\frac{9}{20}$

Step-by-step explanation:

Let the other rational number be 'x'

So,

$\implies -\frac{9}{20} x=-\frac{18}{75}$

$\sf Solve \: for \: x: \\ \sf \implies -\frac{9}{20}x =-\frac{18}{75} \\\\ \sf \frac{-18}{75}=\frac{3 \times(-6)}{3 \times 25} = \frac{\cancel{3}}{\cancel{3}}\times (-\frac{6}{25} )=-\frac{6}{25} :\\ \sf \implies -\frac{9}{20}x = \boxed{-\frac{6}{25}} \\\\ \sf Divide \: both \: sides \: of \: -\frac{9}{20}x = -\frac{6}{25} \: by \: -\frac{9}{20}:\\ \sf \implies \frac{-9x}{20(\frac{-9}{20}) } =-6(\frac{\frac{1}{25} }{\frac{-9}{20} } )$

$\sf \frac{\frac{-9}{20} }{\frac{-9}{20} } =1: \\ \sf \implies x=-6(\frac{\frac{1}{25} }{\frac{-9}{20} } )\\\\ \sf \frac{\frac{1}{25} }{\frac{-9}{20} } = \frac{1}{25} \times (\frac{20}{-9} ): \\ \sf \implies x = -6 \boxed{\frac{1}{25} \times (\frac{20}{-9} )}\\\\ \sf \implies x = \frac{(-6) \times 20}{(-9) \times 25} \\\\ \sf \implies x = \frac{\cancel{-}120}{\cancel{-}225} \\\\ \sf \implies x = \frac{120}{225} \\\\ \sf \implies x = \frac{15 \times 8}{15 \times 15}$

$\sf \implies x = \frac{\cancel{15}}{\cancel{15}} \times \frac{8}{15} \\\\ \sf \implies x = \frac{8}{15}$

Other number = $\frac{8}{15}$

Answer 2

$\underline{\bigstar{\sf\ Solution:-}}$

Let the other number be y

So ,

$\longmapsto\sf \dfrac{-9}{20}\times y= \dfrac{-18}{75}\\ \\ \\ \longmapsto\sf y = \dfrac{\cancel{-18}}{\cancel{75}}\times \dfrac{\cancel{20}}{\cancel{-9}}\\ \\ \\ \longmapsto\sf y= \dfrac{2\times 4}{15\times 1}\\ \\ \\ \longmapsto\sf y= \dfrac{8}{15}$

Now we have the value of y = 8/15

$\boxed{\sf {y=\dfrac{8}{15}}}$

$\underline{\boxed{\sf{\red{Verification:-}}}}$

$\longmapsto\sf \dfrac{-18}{75}\times y= \dfrac{-9}{20}\\ \\ \\ \bullet\sf \ y= \dfrac{8}{15}\\ \\ \\ \longmapsto\sf \dfrac{-9}{\cancel{20}}\times \dfrac{\cancel{8}}{15}= \dfrac{-18}{75}\\ \\ \\ \longmapsto\sf \dfrac{-9\times 4}{15\times 10}=\dfrac{-18}{75}\\ \\ \\ \longmapsto\sf \cancel{\dfrac{-36}{150}}= \dfrac{-18}{75}\\ \\ \\ \longmapsto\sf \dfrac{-18}{75}= \dfrac{-18}{75}\\ \\ \\ \sf\ L.H.S = R.H.S \ \ (\ Hence \ verified\ !)$

$\underline{\bigstar{\sf\ So \ other\ number \ is \ \ {\boxed{\sf \dfrac{8}{15}}}}}$