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Answers
Step-by-step explanation:
Given :-
Two rational numbers 5/7 and 8/9
To find :-
Find two rational numbers between them ?
Solution :-
Using Mean Method :-
Given numbers are 5/7 and 8/9
We know that
The rational number between two numbers a and b is (a+b)/2
First rational number between 5/7 and 8/9
Let a = 5/7 , b = 8/9
The first rational number
= [(5/7)+(8/9)]/2
LCM of 7 and 9 = 63
=[ [(5×9)+(8×7)]/63]/2
=> [(45+56)/63]/2
=> (101/63)/2
=>101/(63×2)
=> 101/126
The second rational number between 5/7 and 101/126
=> [(5/7)+(101/126)]/2
LCM of 7 and 126 is 126
=> [[(5×18)+(101)]/126]/2
=> [(90+101)/126]/2
=> (191/126)/2
=> 191/(126×2)
=> 191/252
The two Rational numbers = 101/126 , 191/252
Short cut method :-
Given numbers are 5/7 and 8/9
on writing them as like fractions then
5/7 = (5/7)×(9/9) = (5×9)/(7×9) = 45/63
8/9 = (8/9)×(7/7)=(8×7)/(9×7) = 56/63
Required rational numbers between them are 46/63,47/63,48/63,49/63,50/63,51/63,52/63,
53/63,54/63,55/63
Answer:-
The two rational numbers between 5/7 and 8/9 by mean method are 101/126 , 191/252
The rational numbers between 5/7 and 8/9 are
46/63,47/63,48/63,49/63,50/63,51/63,52/63,
53/63,54/63,55/63
Used formulae:-
Mean Method:-
- The rational number between two numbers a and b is (a+b)/2
- There are infinitely number many rational numbers between two numbers .This property is called Densitive Property.