Question

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

Answer 1

1/5 =(1*4)/(5*4) =4/20= (4*4)/((20*4) =16/80
1/4 = (1*5)/(4*5)= 5/20=(5*4)/(20*4)=20/80

therefore
(1/5= 16/80),17/80,18/80,19/80,(1/4= 20/80)
17/80,18/80,19/80 are three rational numbers between 1/5 and 1/4

Answer 2

$\frac{17}{80}, \frac{18}{80}, \frac{19}{80}$ are three numbers between $\frac{1}{5} \text { and } \frac{1}{4}.$

Given:

$\frac{1}{5} \text { and } \frac{1}{4}$

To find:

Three rational numbers between $\frac{1}{5} \text { and } \frac{1}{4} = ?$  

Solution:

To find three rational numbers between $\frac{1}{5} \text { and } \frac{1}{4}$ we need to find the L.C.M of the denominators of both the fractions.

Accordingly, L.C.M of the denominators, 5 and 4 is $= 5 \times 4 = 20.$

Thus, $\frac{1}{5}=\frac{1 \times 4}{5 \times 4}=\frac{4}{20}$  

and $\frac{1}{4}=\frac{1 \times 5}{4 \times 5}=\frac{5}{20}$

Now to find 3 rational number between $\frac{1}{5} \text { and } \frac{1}{4}$ we need to multiply both the number and the denominator with 4.

$\frac{4 \times 4}{20 \times 4}=\frac{16}{80}$

and  

$\frac{5 \times 4}{20 \times 4}=\frac{20}{80}$

Hence, three rational number between $\bold{\frac{16}{80} \text { and } \frac{20}{80} are  \frac{17}{80}, \frac{18}{80}, \frac{19}{80}.}$