The product of two rational numbers is -1 if one number is -17/8 find other.​

2 thoughts on “The product of two rational numbers is -1 if one number is -17/8 find other.​”

1. Answer :–

   • The other rational number is 8/17.

   To find :–

   • The other rational number.

   Solution :–

   • It is given that the product of two rational numbers is -1 and one of the numbers is -17/8. We have to find the other number.

   Let the other rational number be “x”.

   It has been given that :–

   • Their product is -1.

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   Therefore :–

   [tex] \longmapsto\sf \left(\dfrac{ – 17}{ \: \: \: \: \: 8} \right) \times x = – 1[/tex]

   [tex] \longmapsto\sf x = – 1 \div \left(\dfrac{ – 17}{ \: \: \: \: \: 8} \right)[/tex]

   [tex] \longmapsto\sf x = – 1 \times \left(\dfrac{ \: \: \: \: \: 8}{ – 17} \right) [/tex]

   [tex] \longmapsto\sf x = \left(\dfrac{ – 8}{ – 17} \right)[/tex]

   [tex] \longmapsto\sf x = \left(\dfrac{ \: \: \not\!\!- 8}{ \not\!\!- 17} \right)[/tex]

   [tex] \longmapsto\sf x = \left(\dfrac{8}{17} \right)[/tex]

   • Hence, the other rational number is 8/17.

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   Know more :-

   What is a rational number?

   • A number that can be expressed in the form of p/q, where p, q are integers and q ≠ 0, is called a rational number.

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2. [tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{Given} :}}}} \end{gathered}[/tex]

   • Product of two rational numbers is -1
   • One number is [tex] \sf \dfrac{-17}{8}[/tex]

   [tex] \\ [/tex]

   [tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{To \: Find} :}}}} \end{gathered}[/tex]

   • Other number = ?

   [tex] \\ [/tex]

   [tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{Solution} :}}}} \end{gathered}[/tex]

   Let other number be “x”.

   [tex] \\ [/tex]

   As, we are given that the product of two rational numbers is -1 and one number is [tex] \sf \dfrac{-17}{8}[/tex].

   [tex] \\ [/tex]

   So to find another number, we have equation :

   [tex] \\ [/tex]

   [tex] \sf : \implies x \times \dfrac{-17}{8} = -1[/tex]

   [tex] \sf : \implies x \times -17 = -1\times 8[/tex]

   [tex] \sf : \implies x \times -17 = -8[/tex]

   [tex] \sf : \implies x = \dfrac{-8}{-17}[/tex]

   [tex] \sf : \implies x = \dfrac{8}{17}[/tex]

   [tex] \\ [/tex]

   [tex] \underline{\boxed{\bf x = \dfrac{8}{17}}}[/tex]

   [tex] \\ [/tex]

   [tex] \pink{\underline{\sf Hence, \: another\: rational\: number\: is\: \dfrac{8}{17}}.}[/tex]

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