Question

Insert 10 rational numbers between 3/5 and 1/5

Answer 1

$\frac{3}{5} > \frac{1}{5}$


As we have to find 10 rational numbers, multiply by 11 on both numerator and Denominator,


$\frac{3(11)}{5(11)} > \frac{1(11)}{5(11)} \\ \\ \\ \\ \frac{33}{55} > \frac{11}{55}$


Hence, 10 rational numbers are,

$\frac{32}{55} \\ \\ \frac{31}{55} \\ \\ \frac{30}{55} \\ \\ \\ \frac{29}{55} \\ \\ \\ \frac{28}{55} \\ \\ \\ \frac{27}{55} \\ \\ \\ \frac{26}{55} \\ \\ \\ \frac{25}{55} \\ \\ \\ \frac{24}{55} \\ \\ \\ \frac{23}{55}$



I hope this will help you


(-:

Answer 2

Let n=11
Thus,1/5*11/11=11/55 ; 3/5*11/11=33/55

Clearly, we have
11/55< 12/55 <13/55 < 14/55 < 15/55 < 16/55 < 17/55 < 18/55< 19/55 < 33/55