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Mathematics

A rational number between 15 and 12\dfrac{1}{5} \text{ and } \dfrac{1}{2} is

  1. 110\dfrac{1}{10}

  2. 120\dfrac{1}{20}

  3. 710\dfrac{7}{10}

  4. 720\dfrac{7}{20}

Rational Numbers

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Answer

Finding the average of the two given rational numbers,

⇒12×(15+12)[ LCM of 5 and 2=10]⇒12×2+510⇒12×710=720\Rightarrow \dfrac{1}{2} \times \left(\dfrac{1}{5} + \dfrac{1}{2}\right) \\[1em] [\text{ LCM of } 5 \text{ and } 2 = 10] \\[1em] \Rightarrow \dfrac{1}{2} \times \dfrac{2 + 5}{10} \\[1em] \Rightarrow \dfrac{1}{2} \times \dfrac{7}{10} = \dfrac{7}{20}

As 15=420 and 12=1020\dfrac{1}{5} = \dfrac{4}{20} \text{ and } \dfrac{1}{2} = \dfrac{10}{20}, we see that 420<720<1020\dfrac{4}{20} \lt \dfrac{7}{20} \lt \dfrac{10}{20}

Hence, Option 4 is the correct option.

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