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Mathematics

By what rational number must 126\dfrac{1}{26} be divided to get −839\dfrac{-8}{39}?

Rational Numbers

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Answer

Let the required rational number be xx.

According to the given condition,

⇒126÷x=−839⇒x=126÷−839⇒x=126×39−8⇒x=1×3926×(−8)⇒x=39−208=−316\Rightarrow \dfrac{1}{26} \div x = \dfrac{-8}{39} \\[1em] \Rightarrow x = \dfrac{1}{26} \div \dfrac{-8}{39} \\[1em] \Rightarrow x = \dfrac{1}{26} \times \dfrac{39}{-8} \\[1em] \Rightarrow x = \dfrac{1 \times 39}{26 \times (-8)} \\[1em] \Rightarrow x = \dfrac{39}{-208} = \dfrac{-3}{16}

Hence, the required rational number is −316\mathbf{\dfrac{-3}{16}}.

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