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Mathematics

What should be subtracted from −78-\dfrac{7}{8} so as to get 512\dfrac{5}{12}?

  1. 3124\dfrac{31}{24}

  2. 85\dfrac{8}{5}

  3. −3124\dfrac{-31}{24}

  4. −68\dfrac{-6}{8}

Rational Numbers

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Answer

Let the required number be xx.

According to the given condition,

⇒−78−x=512⇒x=−78−512[ LCM of 8 and 12=24]⇒x=(−7)×3−5×224⇒x=−21−1024=−3124\Rightarrow \dfrac{-7}{8} - x = \dfrac{5}{12} \\[1em] \Rightarrow x = \dfrac{-7}{8} - \dfrac{5}{12} \\[1em] [\text{ LCM of } 8 \text{ and } 12 = 24] \\[1em] \Rightarrow x = \dfrac{(-7) \times 3 - 5 \times 2}{24} \\[1em] \Rightarrow x = \dfrac{-21 - 10}{24} = \dfrac{-31}{24}

Hence, Option 3 is the correct option.

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