Insert three rational nos between
2/3 and 3/5
Answers
Answer:
37/60, 38/60, 39/60.
Step-by-step explanation:
First, equal the denominator
2/3 × 20/20 = 40/60
3/5 × 12/12 = 36/60
therefore, 2/3 = 40/60 and 3/5 = 36/60
so, three rational no. b/w 2/3 and 3/5 ie,. 40/60 and 36/60 are :
37/60, 38/60, 39/60 .
Step-by-step explanation:
Given :-
2/3 and 3/5
To find :-
Three rational numbers between them
Solution :-
Method-1:-
Given numbers are 2/3 and 3/5
2/3 can be written as (2/3)×(5/5)
= (2×5)/(3×5)
= 10/15
and
3/5 can be written as (3/5)×(3/3)
= (3×3)/(5×3)
= 9/15
The two numbers are 10/15 and 9/15
Required rational numbers = 3
On writing the denominator as 3+1 = 4 multiple
Therefore, 9/15 = (9/15)×(4/4)
= (9×4)/(15×4)
= 36/60
and
10/15 = (10/15)×(4/4)
= (10×4)/(15×4)
= 40/60
The rational numbers between 36/60 and 40/60 are 37/60, 38/60 , 39/60
Method-2:-
Given numbers are 2/3 and 3/5
We know that
Mean Method :The rational number between the two numbers a and b is (a+b)/2
I) First rational number between 2/3 and 3/5
= [(2/3)+(3/5)]/2
LCM of 3 and 5 = 15
=>[(10+9)/15]/2
=> (19/15)/2
=> 19/(15×2)
=> 19/30
II) The second rational number between 2/3 and 19/30
= [(2/3)+(19/30)]/2
LCM of 3 and 30 = 30
=> [20+19)/30]/2
=> (39/30)/2
=> 39/(30×2)
=> 39/60
III) The third rational number between 2/3 and 39/60
= [(2/3)+(39/60)]/2
LCM of 3 and 60 = 60
=> [(40+39)/60]/2
=> (79/60)/2
=> 79/(60×2)
=> 79/120
The three rational numbers are 19/30, 39/60, 79/120
Answer :-
I) The three rational numbers by general method are 37/60, 38/60 , 39/60
ii) The three rational numbers by mean method are 19/30, 39/60, 79/120
Used formulae :-
Mean Method:-
The rational number between the two numbers a and b is (a+b)/2
Points to know:-
There are infinitely number of many rational numbers between two rational numbers.This property is called Densitive Property of rational numbers.