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Question

Find five rational numbers between $$\dfrac {2}{3}$$ and $$\dfrac {3}{5}$$


Solution

The $$LCM$$ of the denominators of the given rational numbers $$\dfrac { 2 }{ 3 }$$ and $$\dfrac {3 }{ 5 }$$ is $$LCM(3,5)=15$$.

Therefore, with denominator $$15$$, the rational numbers becomes $$\dfrac { 10 }{ 15 }$$ and $$\dfrac {9 }{ 15 }$$

The difference between the numerators $$9$$ and $$10$$ is very less, so we multiply both the numerators and denominators of the rational numbers $$\dfrac { 10 }{ 15 }$$ and $$\dfrac {9 }{ 15 }$$ by $$10$$ to obtain the five rational numbers between them.

Now, the rational numbers becomes $$\dfrac { 100 }{ 150 }$$ and $$\dfrac {90 }{ 150 }$$
 
Hence, the $$5$$ rational numbers between $$\dfrac {90 }{ 150 }$$ and $$\dfrac { 100 }{ 150 }$$ are as follows:

$$\dfrac { 91 }{ 150 } ,\dfrac { 93 }{ 150 },\dfrac { 94 }{ 150 } ,\dfrac { 97 }{ 150 } ,\dfrac { 99 }{ 150 }$$

Mathematics

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