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Mathematics

The rational number by which should 12\dfrac{1}{2} be divided to get −23-\dfrac{2}{3} is:

  1. 34\dfrac{3}{4}

  2. −34-\dfrac{3}{4}

  3. 43\dfrac{4}{3}

  4. −43-\dfrac{4}{3}

Rational Numbers

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Answer

Let xx be the number.

12÷x=−23⇒12×1x=−23⇒12x=−23⇒2x=−32⇒x=12×−32⇒x=−1×32×2⇒x=−34\dfrac{1}{2} ÷ x = -\dfrac{2}{3}\\[1em] ⇒ \dfrac{1}{2} \times \dfrac{1}{x} = -\dfrac{2}{3} \\[1em] ⇒ \dfrac{1}{2x} = -\dfrac{2}{3} \\[1em] ⇒ 2x = -\dfrac{3}{2} \\[1em] ⇒ x = \dfrac{1}{2} \times -\dfrac{3}{2}\\[1em] ⇒ x = -\dfrac{1 \times 3}{2 \times 2}\\[1em] ⇒ x = -\dfrac{3}{4}

The rational number by which should 12\dfrac{1}{2} be divided to get −23-\dfrac{2}{3} is −34-\dfrac{3}{4}

Hence, Option 2 is the correct option.

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