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Mathematics

The sum of two rational numbers is -6. If one of them is 4124\dfrac{1}{2}, the other number is:

  1. 2122\dfrac{1}{2}

  2. 1121\dfrac{1}{2}

  3. -1121\dfrac{1}{2}

  4. -101210\dfrac{1}{2}

Rational Numbers

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Answer

Let xx be the other number. 412+x=−6⇒92+x=−6⇒x=−6−92⇒x=−61−924\dfrac{1}{2} + x = -6 \\[1em] ⇒\dfrac{9}{2} + x = -6 \\[1em] ⇒ x = -6 - \dfrac{9}{2} \\[1em] ⇒ x = \dfrac{-6}{1} - \dfrac{9}{2}

LCM of 1 and 2 is 2

⇒x=−6×21×2−9×12×1⇒x=−122−92⇒x=−12−92⇒x=−212⇒x=−1012⇒ x = -\dfrac{6 \times 2}{1 \times 2} - \dfrac{9\times 1}{2 \times 1} \\[1em] ⇒ x = -\dfrac{12}{2} - \dfrac{9}{2} \\[1em] ⇒ x = \dfrac{-12 - 9}{2} \\[1em] ⇒ x = \dfrac{-21}{2} \\[1em] ⇒ x = -10\dfrac{1}{2}

The sum of two rational numbers is -6, if one of them is 4124\dfrac{1}{2}, the other number is -101210\dfrac{1}{2}.

Hence, option 4 is correct option.

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