Question

if a and b are two positive integers where b > a , then which of the following rational numbers can never fall b/w a and b on the number line.?
a) a+b/2
b) a+b/3
c) a-b/ 2
d) a+b/4

explain the ryt answer​

Answer 1

Given :  a and b are two positive integers where b > a

To find : which of the given rational numbers can never fall b/w a and b on the number line.

Solution:

a and b are two positive integers where b > a

Let say b = a + x    x > 0

(a + b) / 2

= ( a + a + x)/2

= a  + x/2  

a  + x/2   > a

a + x/2 <  a + x  

=> a + x/2  < b

=> (a + b) / 2 lies between   a & b

(a + b) / 3

= ( a + a + x)/3

= a  + x/3  

a  + x/3   > a

a + x/3 <  a + x  

=> a + x/3  < b

=> (a + b) /3 lies between   a & b

(a - b) / 2

= ( a - a - x)/2

=  - x/2  

= - ve

while a & b are positive

hence (a - b) / 2 can never fall b/w a and b on the number line

(a + b) / 4

= ( a + a + x)/4

= a  + x/4  

a  + x/4   > a

a + x/4 <  a + x  

=> a + x/4  < b

=> (a + b) /4 lies between   a & b

(a - b) / 2 can never fall b/w a and b on the number line

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Answer 2

Answer:

a and b are two positive rational numbers, where a < b, then