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

Answers (1)

Finding rational numbers between \frac{3}{5} and \frac{3}{4} is equivalent to find rational numbers between rational numbers between  \frac{12}{20} and  \frac{15}{20} ,since these numbers are obtained by just making their denomenators equal. 

Further it is equivalent to find rational number between \frac{96}{160} and \frac{120}{160}

(We obtained above numbers by multiplying and dividing numbers by 8 to create differnce of atleast 10 numbers).

Thus required numbers are \frac{97}{160},\frac{98}{160},\frac{99}{160},........,\frac{106}{160}


Alternate:- Rational numbers can also be found by taking mean of the given numbers and the newly obtained number.