Question

# Find four rational numbers between $$\dfrac{3}{5}$$ and $$\dfrac{4}{5}$$

Solution

## Since, We want five rational numbers, we write $$\dfrac{3}{5}$$ and $$\dfrac{4}{5}$$ . So multiply in numerator and denominator by $$5+1=6$$ and we get, $$\dfrac{3\times 6}{5\times 6}=\dfrac{18}{30}$$        and        $$\dfrac{4}{5}=\dfrac{4\times 6}{5\times 6}=\dfrac{24}{30}$$ We know that, $$19<20<21<22<23$$ $$\Rightarrow \dfrac{18}{30}<\dfrac{19}{30}<\dfrac{20}{30}<\dfrac{21}{30}<\dfrac{22}{30}<\dfrac{23}{30}<\dfrac{24}{30}$$ Hence, $$5$$ rational numbers between $$\dfrac{3}{5}$$ and $$\dfrac{4}{5}$$ are: $$\Rightarrow \dfrac{19}{30},\dfrac{20}{30},\dfrac{21}{30},\dfrac{22}{30},\dfrac{23}{30}$$  ans.Mathematics

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