Find ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$

Given: 

Given rational numbers are $\frac{3}{5}$ and $\frac{3}{4}$.

To do:  

We have to find ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$.

Solution:

LCM of 5 and 4 is 20.

$\frac{3}{5}=\frac{3\times4}{5\times4}$

$=\frac{12}{20}$

$\frac{3}{4}=\frac{3\times5}{4\times5}$

$=\frac{15}{20}$

As we need 10 rational numbers between $\frac{12}{20}$ and $\frac{15}{20}$, multiply both the fractions by $\frac{4}{4}$.

This implies,

$\frac{12}{20}=\frac{12}{20}\times\frac{4}{4}$

$=\frac{48}{80}$

$\frac{15}{20}=\frac{15}{20}\times\frac{4}{4}$

$=\frac{60}{80}$

Therefore,

Ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$ are $\frac{49}{80}, \frac{50}{80}, ........,\frac{57}{80}, \frac{58}{80}$.  

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Updated on: 10-Oct-2022

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