Question

Q1. Multiple choice questions:
a) For rational numbers 'a' and 'b', the number that always lies between 'a' and 'b' is
ii) 2b
iii) (a+b)/2
iv) (a-b)/2​

Answer 1

Answer:

b. a+b/2

Step-by-step explanation:

as if we take a =30,b=40

then a+b/2 = 30+40/2

=70/2

=35

Answer 2

Given  :  two rational number  a & b  and 4 options 2a   , 2 b  , (a + b)/2 , (a - b)/2

To find :  which of given option always lies between a and b is​

Solution:

Let check each case considering a  < b

a  <  2a    <  b

subtracting a from both sides

=> 0 <  a   < b - a

=> a has to be   greater than 0 for 2a to be between

a  < 2b  <  b

Subtracting b from both sides

=> a - b <  b  <  0

=> b has to be less than  0  for 2b to be between a  & b

a  <  (a - b)/2  < b

2a < a  - b  <  2b

subtracting a from both sides

a  <  - b  < 2b - a

a < b  , hence a < - b not possible

a <  (a + b)/2 < b

=> 2a < a + b  < 2b

2a < a + b   & subtracting a from both sides

=> a < b    

a + b  < 2b & subtracting b from both sides

=>    a  < b

Hence satisfied  

So (a + b)/2  always lies between rational number a & b

Learn More:

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