Question

find four rational number between 1/5 and 1/4?

Answer 1

1/5    and 1/4
1/4 =  5  / 20  = 25 /100  nultiply by 5 in numerator & denominator
1/5  = 4 / 20  = 20 / 100  multiply by 5  in Nr  and Dr
So now we want rational numbers between  20 /100  and 25 /100
They are easily
 21        22        23      24     
---- ,    ----    ,    ----,     ----    
100      100      100     100

Answer 2

$\frac{1}{5} < x <\frac{1}{4}\\\\\frac{1}{5}\to the\ denominator\ is\ 5\\\\\frac{1}{4}\to the\ denominator\ is\ 4\\\\LCD(\frac{1}{5};\ \frac{1}{4})=4\times5=20\\\\\frac{1}{5}=\frac{1\times4}{5\times4}=\frac{4}{20}\\\\\frac{1}{4}=\frac{1\times5}{4\times5}=\frac{5}{20}\\\\\frac{4}{20} < x < \frac{5}{20}\\\\multiply\ numerators\ and\ denominators\ by\ 5$

$\frac{4}{20}=\frac{4\times5}{20\times5}=\frac{20}{100}\\\\\frac{5}{20}=\frac{5\times5}{20\times5}=\frac{25}{100}\\\\\frac{20}{100} < x < \frac{25}{100}\ then\ x\in\left\{\frac{21}{100};\ \frac{22}{100};\ \frac{23}{100};\ \frac{24}{100}\right\}.$

$other\ method:\\\\\frac{1}{5}=\frac{2}{10}=0.20\\\\\frac{1}{4}=\frac{25}{100}=0.25\\\\0.20 < x < 0.25\ then\ x\in\left\{0.21;\ 0.22;\ 0.23;\ 0.24\right\}\\\\or\\\\0.200 < x < 0.250\ then\ x\in\{0.201;\ 0.202;\ 0.203;...;0.249\}\\\vdots$

Answer 3

to find out the rational nos. between them we have to find it's Average of these 2 nos.-1/5+1/4= 4+5 = 9
           2        20    40  
                      2 
1/5,9/20,1/4
Now to find the other nos. we have to find the average of 1/5 and 9/20
the LCM of 5 and 20 is 20= 5+13 =18/40
                                         20   
                                        2               
1/518/40,9/20,1/4
Now to find the other nos. we have to find the average of 9/20 and 1/4
the LCM of 40 and 20 is 40=18+18 =36/80
                                          40   
                                             2           
1/5,18/40,9/20,36/80,1/4
Now to find the other nos. we have to find the average of 9/20 and 36/80
the LCM of 20 and 80 is 80=360+36=420/160=21/8
                                            80   
                                            2
Now to find the other nos. we have to find the average of 9/20 and 18/40
the LCM of 40 and 20 is 40=18+18 =36/80
                                            40   
                                           2
Therefore thefour rational nos. are-1/5,18/40,9/20,36/80,36/80,1/4 which can be simplified...