Question

find fifteen rational number between 1/3 and1/2 also represent on the number line

Answer 1

In order to find a number of rational numbers between two numbers, we need to make the given numbers broader and then find the rational numbers between them.

So according to question, 
We need to first find their LCM and make their denominators equal. Thus, we get :-
1/3 can be written as 2/6 and 1/2 an be written as 3/6.

Next, we broaden the numbers by multiplying 16/16 to both the numbers :-
(2x16)/(6x16) = 32/96 and
(3x16)/(6x16) = 48/96.

So, we get the rational numbers between 30/90 and 45/90 as :-
33/96, 34/96, 35/96, 36/96, 37/96, 38/96, 39/96, 40/96, 41/96, 42/96, 43/96, 44/96, 45/96, 46/96 and 47/96.

For plotting these on the number line, draw a 96 unit line and make 95 divisions in it. Now, mark the 33rd division as 33/96, 34th division as 34/96 and so on till 47/96.
 
Hope that helps !!