Find ten rational numbers between $\frac{1}{4}$ and $\frac{1}{2}$.

Given: 

Given rational numbers are $\frac{1}{4}$ and $\frac{1}{2}$.

To do:  

We have to find ten rational numbers between $\frac{1}{4}$ and $\frac{1}{2}$.

Solution:

LCM of 4 and 2 is 4.

$\frac{1}{2}=\frac{1\times2}{2\times2}$

$=\frac{2}{4}$

As we need 10 rational numbers between $\frac{1}{4}$ and $\frac{2}{4}$, multiply both the fractions by $\frac{20}{20}$.

This implies,

$\frac{1}{4}=\frac{1}{4}\times\frac{20}{20}$

$=\frac{20}{80}$

$\frac{2}{4}=\frac{2}{4}\times\frac{20}{20}$

$=\frac{40}{80}$

This implies,

$\frac{21}{80}, \frac{22}{80}, ........,\frac{38}{80}, \frac{39}{80}$ lie between $\frac{20}{80}$ and $\frac{40}{80}$

Therefore,

Ten rational numbers between $\frac{1}{4}$ and $\frac{1}{2}$ are $\frac{21}{80}, \frac{22}{80}, ........,\frac{38}{80}, \frac{39}{80}$. 

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Updated on: 10-Oct-2022

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