Question

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

Answer 1

Find rational numbers between the given numbers

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

As these numbers don't have common denominator we cannot directly find the numbers between them.

So, we need to convert the numbers by multiplying both numerator and denominator of $\frac{3}{5}$ by $16$ , we will get $\frac{3}{5}\times \frac{16}{16}=\frac{48}{80}$.

Similarly, multiply both numerator and denominator of $\frac{3}{4}$ by $20$, we get $\frac{3}{4}\times \frac{20}{20}=\frac{60}{80}$

Now, we can find ten numbers between $\frac{48}{80}$ and $\frac{60}{80}$. which are $\frac{49}{80},\frac{50}{80},\frac{51}{80},\frac{52}{80},\frac{53}{80},\frac{54}{80},\frac{55}{80},\frac{56}{80},\frac{57}{80},\frac{58}{80}$

Hence, the required numbers are $\frac{49}{80},\frac{50}{80},\frac{51}{80},\frac{52}{80},\frac{53}{80},\frac{54}{80},\frac{55}{80},\frac{56}{80},\frac{57}{80},\frac{58}{80}$.