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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 $\frac{49}{80}, \frac{50}{80}, ........,\frac{57}{80}, \frac{58}{80}$.