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Mathematics

The rational number between ab\dfrac{a}{b} and cd\dfrac{c}{d} is:

  1. 12(abcd)\dfrac{1}{2}\Big(\dfrac{a}{b} - \dfrac{c}{d}\Big)

  2. (acbd)\Big(\dfrac{a - c}{b - d}\Big)

  3. (a+cb+d)\Big(\dfrac{a + c}{b + d}\Big)

  4. (a+db+c)\Big(\dfrac{a + d}{b + c}\Big)

Rational Numbers

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Answer

For any two rational numbers ab\dfrac{a}{b} and cd\dfrac{c}{d}, (a+cb+d)\Big(\dfrac{a + c}{b + d}\Big) is also a rational number with its value lying between ab\dfrac{a}{b} and cd\dfrac{c}{d}.

Hence, Option 3 is the correct option.

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