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Mathematics

The product of two rational numbers is -1, if one of them is 25\dfrac{2}{5}, then the other is :

  1. −25-\dfrac{2}{5}

  2. 52\dfrac{5}{2}

  3. −52-\dfrac{5}{2}

  4. none of these

Rational Numbers

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Answer

Let the number be xx.

25×x=−1⇒25×x=−11⇒x=−11÷25⇒x=−11×52⇒x=−1×51×2⇒x=−52\dfrac{2}{5} \times x = -1\\[1em] ⇒ \dfrac{2}{5} \times x = -\dfrac{1}{1}\\[1em] ⇒ x = -\dfrac{1}{1} ÷ \dfrac{2}{5}\\[1em] ⇒ x = -\dfrac{1}{1} \times \dfrac{5}{2}\\[1em] ⇒ x = -\dfrac{1 \times 5}{1 \times 2}\\[1em] ⇒ x = -\dfrac{5}{2}

Hence, option 3 is the correct option.

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