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Mathematics

The product of two rational numbers is -7. If one of the numbers is −811\dfrac{-8}{11}, find the other.

Rational Numbers

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Answer

Let the other rational number be xx.

As the product of the two rational numbers is -7,

⇒−811×x=−7⇒x=−7÷−811⇒x=−71×11−8⇒x=(−7)×111×(−8)⇒x=−77−8=778⇒x=958\Rightarrow \dfrac{-8}{11} \times x = -7 \\[1em] \Rightarrow x = -7 \div \dfrac{-8}{11} \\[1em] \Rightarrow x = \dfrac{-7}{1} \times \dfrac{11}{-8} \\[1em] \Rightarrow x = \dfrac{(-7) \times 11}{1 \times (-8)} \\[1em] \Rightarrow x = \dfrac{-77}{-8} = \dfrac{77}{8} \\[1em] \Rightarrow x = 9\dfrac{5}{8}

Hence, the other rational number is 778\mathbf{\dfrac{77}{8}}.

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