Question 996758
recall: 
Rational Numbers - any number that is either an integer "{{{a}}}" or is expressible as the ratio of two integers, {{{a/b}}}. The numerator, "{{{a}}}", may be any whole number, and the denominator, "{{{b}}}", may be any positive whole number greater than zero. If the denominator happens to be unity,{{{ b = 1}}}, the ratio is an integer. If "{{{b}}}" is other than {{{1}}},{{{ a/b }}}is a fraction.

to find {{{25}}} rational numbers between {{{1/2}}} and {{{5/1=5}}},solve inequality

{{{1/2<x<5}}} you can start with fractions, or you can pick numbers like  

{{{0.5<x<5}}} and write them all as fractions; it’s easier way to find them

start with first number greater than {{{0.5}}}

{{{0.6<x<5}}} =>{{{6/10<x<5}}} =>{{{3/5<x<5}}} 
{{{0.7<x<5}}}=>{{{7/10<x<5}}} 
{{{0.8<x<5}}}=>{{{8/10<x<5}}} =>{{{4/5<x<5 }}}
{{{0.9<x<5}}}=>{{{9/10<x<5}}} 
{{{1<x<5}}}=>{{{1/1<x<5}}}
{{{1.1<x<5}}}=>{{{11/10<x<5}}} 
{{{1.2<x<5}}}=>{{{12/10<x<5}}} =>{{{6/5<x<5}}} 
{{{1.3<x<5}}}=>{{{13/10<x<5}}} 
{{{1.4<x<5}}}=>{{{14/10<x<5}}} =>{{{7/5<x<5 }}}
{{{1.5<x<5}}}=>{{{15/10<x<5}}} =>{{{3/5<x<5 }}}
{{{1.6<x<5}}}=>{{{16/10<x<5}}} =>{{{8/5<x<5}}} 
{{{1.7<x<5}}}=>{{{17/10<x<5}}} 
{{{1.8<x<5}}}=>{{{18/10<x<5}}} =>{{{9/5<x<5 }}}
{{{1.9<x<5}}}=>{{{19/10<x<5}}} 
{{{2<x<5}}}=>{{{2/1<x<5}}}
{{{2.1<x<5}}}=>{{{21/10<x<5 }}}
{{{2.2<x<5}}}=>{{{22/10<x<5}}} =>{{{11/5<x<5}}} 
{{{2.3<x<5}}}=>{{{23/10<x<5}}} 
{{{2.4<x<5}}}=>{{{24/10<x<5}}} =>{{{12/5<x<5}}}
{{{2.5<x<5}}}=>{{{25/10<x<5}}} =>{{{5/2<x<5}}}
{{{2.6<x<5}}}=>{{{26/10<x<5}}} =>{{{13/5<x<5}}}
{{{2.7<x<5}}}=>{{{27/10<x<5}}}
{{{2.8<x<5}}}=>{{{28/10<x<5}}}=>{{{24/5<x<5}}}
{{{2.9<x<5}}}=>{{{29/10<x<5}}} 
{{{3<x<5}}}=>{{{3/1<x<5}}}

so, your numbers are:

{{{1/2}}} < {{{3/5}}},{{{7/10}}},{{{4/5}}},{{{9/10}}},{{{1/1}}},{{{11/10}}},{{{6/5}}},{{{13/10}}},{{{7/5}}},{{{3/5}}},{{{8/5}}},{{{17/10}}},{{{9/5}}},{{{19/10}}},{{{2/1}}},{{{21/10}}},{{{11/5}}},{{{23/10}}},{{{12/5}}},{{{5/2}}},{{{13/5}}},{{{27/10}}},{{{24/5}}},{{{29/10}}},{{{3/1}}}<{{{5/1}}}