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Mathematics

The product of two rational numbers is −169\dfrac{-16}{9}. If one of the numbers is −43\dfrac{-4}{3}, 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 −169\dfrac{-16}{9},

⇒−43×x=−169⇒x=−169÷−43⇒x=−169×3−4⇒x=(−16)×39×(−4)⇒x=−48−36=43⇒x=113\Rightarrow \dfrac{-4}{3} \times x = \dfrac{-16}{9} \\[1em] \Rightarrow x = \dfrac{-16}{9} \div \dfrac{-4}{3} \\[1em] \Rightarrow x = \dfrac{-16}{9} \times \dfrac{3}{-4} \\[1em] \Rightarrow x = \dfrac{(-16) \times 3}{9 \times (-4)} \\[1em] \Rightarrow x = \dfrac{-48}{-36} = \dfrac{4}{3} \\[1em] \Rightarrow x = 1\dfrac{1}{3}

Hence, the other rational number is 43\mathbf{\dfrac{4}{3}}.

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