Question

The product of two rational numbers is -28/81 if one of them is -2/3 then find the other.

Answer 1

The other rational number is 14/27

Explanation:

Given the product of two rational numbers is -28/81 and one of the rational number is -2/3 so let the other rational number be x then atq,

-2/3 × x = -28/81

x = -28/81 × 3/-2

cancelling both the - symbols and then cancelling 28 by 2 as (2 × 14 = 28) and 81 by 3 as (3 × 27 = 81) we get,

x = 14/27

thus the other number is 14/27

verification :-

product of -2/3 and 14/27 = -28/81

-2/3 × 14/27 = -28/81

-2×14/3×27 = -28/81

-28/81 = -28/81

as LHS = RHS

hence Verified

Answer 2

`\begin{gathered} \; \sf{\color{pink}{Let \; the \; other \; number \; be \; (x)::}} \\ \\ \end{gathered}`

Atq,,

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{( - 2)/(3) * x = ( - 28)/(81)} \\ \\ \end{gathered}`

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{\frac{\cancel{-}2x}{3} = \frac{\cancel{-}28}{81}} \\ \\ \end{gathered}`

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{(2x)/(3) = (28)/(81)} \\ \\ \end{gathered}`

Cross Multiplying,,

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{2x * 81 = 28 * 3} \\ \\ \end{gathered}`

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{162x = 84} \\ \\ \end{gathered}`

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \frac{\cancel{84}}{\cancel{162}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 2} \bigg \rgroup \\ \\ \end{gathered}`

`\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \frac{\cancel{42}}{\cancel{81}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 3} \bigg \rgroup \\ \\ \end{gathered}`

`\begin{gathered} \; \color{pink} :\dashrightarrow \underline{\boxed{\tt{x = (14)/(27)}}} \: \pmb{\bigstar} \\ \\ \end{gathered}`

`\begin{gathered} \\ \\ {\underline{\pmb{\rule{170pt}{10pt}}}} \end{gathered}`