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Mathematics

Two rational numbers between −37 and −17-\dfrac{3}{7} \text{ and } -\dfrac{1}{7} is :

  1. 414,314\dfrac{4}{14}, \dfrac{3}{14}

  2. −414,314-\dfrac{4}{14}, \dfrac{3}{14}

  3. 414,−314\dfrac{4}{14}, -\dfrac{3}{14}

  4. −414,−314-\dfrac{4}{14}, -\dfrac{3}{14}

Rational Irrational Nos

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Answer

Let the first rational number between −37 and −17-\dfrac{3}{7} \text{ and } -\dfrac{1}{7} be x.

⇒x=12[−37+(−17)]⇒x=12(−47)⇒x=−414\Rightarrow x = \dfrac{1}{2}\Big[-\dfrac{3}{7} + \Big(-\dfrac{1}{7}\Big)\Big] \\[1em] \Rightarrow x = \dfrac{1}{2}\Big(-\dfrac{4}{7}\Big)\\[1em] \Rightarrow x = -\dfrac{4}{14}

Let the second rational number be y.

⇒y=12[−414+(−17)]⇒y=12(−4−214)⇒y=12(−614)⇒y=−628=−314\Rightarrow y = \dfrac{1}{2}\Big[-\dfrac{4}{14} + \Big(-\dfrac{1}{7}\Big)\Big] \\[1em] \Rightarrow y = \dfrac{1}{2}\Big(\dfrac{-4 - 2}{14}\Big) \\[1em] \Rightarrow y = \dfrac{1}{2}\Big(-\dfrac{6}{14}\Big)\\[1em] \Rightarrow y = -\dfrac{6}{28} = -\dfrac{3}{14}

Hence, Option 4 is the correct option.

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