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Mathematics

What should be added to −34\dfrac{-3}{4} to get 76\dfrac{7}{6}?

  1. 1124\dfrac{11}{24}

  2. 924\dfrac{9}{24}

  3. 1025\dfrac{10}{25}

  4. 2312\dfrac{23}{12}

Rational Numbers

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Answer

Let the required number be xx.

According to the given condition,

⇒−34+x=76⇒x=76−(−34)⇒x=76+34[ LCM of 6 and 4=12]⇒x=7×2+3×312⇒x=14+912=2312\Rightarrow \dfrac{-3}{4} + x = \dfrac{7}{6} \\[1em] \Rightarrow x = \dfrac{7}{6} - \left(\dfrac{-3}{4}\right) \\[1em] \Rightarrow x = \dfrac{7}{6} + \dfrac{3}{4} \\[1em] [\text{ LCM of } 6 \text{ and } 4 = 12] \\[1em] \Rightarrow x = \dfrac{7 \times 2 + 3 \times 3}{12} \\[1em] \Rightarrow x = \dfrac{14 + 9}{12} = \dfrac{23}{12}

Hence, Option 4 is the correct option.

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