Question

Product of two rational no is
15/22. if one of the no -5/6
find the other one​

Answer 1

Solution

Given,

Product of two rational number is = $\dfrac{15}{22}$

One of the number is = $-\dfrac{5}{6}$

and other number = ?

                                                                     

Let the other number be 'x'

According to the question

$\implies x\times-\dfrac{5}{6}=\dfrac{15}{22}\\\\\\\implies x=\dfrac{15}{22}\div\dfrac{-5}{6}\\\\\\\implies x=\dfrac{15}{22}\times\dfrac{-6}{5}\:\because reciprocal\\\\\\\implies x=\boxed{\bold{\dfrac{-9}{11}}}$

Therefore other number is $\dfrac{-9}{11}$

Let us verify that,

When we put the value of 'x' which is  $\dfrac{-9}{11}$

then we get

$\implies-\dfrac{5}{6} \times-\dfrac{9}{11}=\dfrac{15}{22}\\\\\\\implies-\dfrac{5}{2}\times-\dfrac{3}{11}=\dfrac{15}{22}\\\\\\\implies\dfrac{15}{22} =\dfrac{15}{22}$

We observed that LHS = RHS,

Hence it is verified.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

Required number is - 9/11

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :- Product of two rational number = $\sf{ \dfrac{15}{22} }$

One of the number = $\sf{- \dfrac{5}{6} }$

To find :- Another number

Solution :-

Product of two rational number = $\sf{ \dfrac{15}{22} }$

Let one of the number be = x

Another number = $\sf{- \dfrac{5}{6} }$

According to the question :-

Equation formed :-

$\tt{ - \dfrac{5}{6} \times x =\dfrac{15}{22} }$

$\tt{ - \dfrac{5}{6} \times x = \dfrac{15}{22} }$

$\tt{ - \dfrac{5x}{6} = \dfrac{15}{22} }$

$\tt{ - 5x = \dfrac{15 \times 6}{22} }$

$\tt{ - 5x = \dfrac{90}{22} }$

$\tt{ - 5x = \dfrac{90}{22} }$

$\tt{ x = \dfrac{90}{22(-5)} }$

$\tt{ x = \dfrac{90}{-110} }$

$\tt{ x = - \dfrac{90 \div 10}{110 \div 10} }$

$\tt{ x = - \dfrac{9}{11} }$

$\mathfrak{\large{\underline{\underline{Verification:-}}}}$

$\tt{ - \dfrac{5}{6} \times - \dfrac{9}{11} =\dfrac{15}{22} }$

$\tt{ - \dfrac{5}{2} \times - \dfrac{3}{11} =\dfrac{15}{22} }$

$\tt{\dfrac{15}{22} =\dfrac{15}{22} }$

Therefore required number is - 9/11