Write five rational number between -1'3 and 1/3
Answers
Step-by-step explanation:
Given:-
-1/3 and 1/3
To find:-
Write five rational number between -1/3 and 1/3?
Solution:-
Given two numbers are -1/3 and 1/3
Required rational numbers = 5
On writing the denominator as (5+1)=6
then
-1/3 can be written as
= (-1/3)×(6/6)
= (-1×6)/(3×6)
=> -6/18
and
1/3 can be written as
= (1/3)×(6/6)
= (1×6)/(3×6)
=> 6/18
The rational numbers between them are
-5/18;-4/18;-3/18;-2/18;-1/18;0;1/18;2/18;3/18;4/18;5/18
Alternative Method:-
Given two numbers are -1/3 and 1/3
We know that
The rational number between a and b = (a+b)/2
First rational number
= [(-1/3)+(1/3)]/2
= [(-1+1)/3]/2
=> (0/3)/2
=> 0
Second rational number between -1/3 and 0
=> [(-1/3)+0]/2
=> [(-1/3)/2]
=> -1/6
Third rational number between 0 and 1/3
=> [0+(1/3)]/2
=> (1/3)/2
=> 1/6
Fourth rational number between 1/6 and 1/3
=> [(1/6)+(1/3)]/2
=> [(1+2)/6]/2
=> (3/6)/2
=> (1/2)/2
=>1/4
Fifth rational number between 1/4 and 1/3
=> [(1/4)+(1/3)]/2
=> [(3+4)/12]/2
=> (7/12)/2
=> 7/24
Answer:-
The required rational numbers are -1/6,0,1/6,1/4,7/24
Used formulae:-
Mean Method:-
The rational number between a and b = (a+b)/2
Dense Property:-
There are infinitely number of many rational numbers between two numbers