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Mathematics

The number which on multiplying with 5235\dfrac{2}{3} gives -1231\dfrac{2}{3} is:

  1. −57-\dfrac{5}{7}

  2. 57\dfrac{5}{7}

  3. −517-\dfrac{5}{17}

  4. 175\dfrac{17}{5}

Rational Numbers

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Answer

Let the number be xx. 523×x=−123⇒173×x=−53⇒x=−53÷173⇒x=−53×317⇒x=−5×33×17⇒x=−1551⇒x=−5175\dfrac{2}{3} × x = -1\dfrac{2}{3}\\[1em] ⇒ \dfrac{17}{3} × x = -\dfrac{5}{3}\\[1em] ⇒ x = -\dfrac{5}{3} ÷ \dfrac{17}{3}\\[1em] ⇒ x = -\dfrac{5}{3} × \dfrac{3}{17}\\[1em] ⇒ x = -\dfrac{5 \times 3}{3 \times 17}\\[1em] ⇒ x = -\dfrac{15}{51}\\[1em] ⇒ x = -\dfrac{5}{17}

Hence, option 3 is the correct option.

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