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Mathematics

Find a rational number between 35\dfrac{3}{5} and 79\dfrac{7}{9}.

Rational Irrational Nos

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Answer

Let x be a rational number between 35\dfrac{3}{5} and 79\dfrac{7}{9}.

x=12(35+79)x=12(27+3545)x=12(6245)x=3145\Rightarrow x = \dfrac{1}{2}\Big(\dfrac{3}{5} + \dfrac{7}{9}\Big) \\[1em] \Rightarrow x = \dfrac{1}{2}\Big(\dfrac{27 + 35}{45} \Big) \\[1em] \Rightarrow x = \dfrac{1}{2}\Big(\dfrac{62}{45} \Big) \\[1em] \Rightarrow x = \dfrac{31}{45} \\[1em]

Hence, a rational number between 35 and 79 is 3145\dfrac{3}{5} \text{ and } \dfrac{7}{9} \text{ is } \dfrac{31}{45}.

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