RATIONAL NUMBER
A rational number is in the form of a fraction, in which two integers will be in the form p/q where q ≠ 0.
Example:- (3/2), (5/3), (10/3)......etc.
How to find a rational number between two rational numbers?
We will use two ways to find a rational number-
- By equivalent fraction (easy method)
- By taking mean
Step I (By equivalent fraction)
In an equivalent fraction, we do multiply the same number to numerator & denominator of the rational number.
For understand how it is work take an example-
Example:-
Find five rational number between (1/4) & (1/2).
Solve:-
= (1/4) & (1/2)
{We will multiply 8 to rational number (1/4) in numerator 1 & denominator 4)
{Also multiply rational number (1/2) from 16 in numerator 1 & denominator 2}
{ From these, it will become the same denominator in both rational numbers as below}
= (1×8)/(4×8) & (1×16)/(2×16)
= 8/32 & 16/32
{Here you can see now both denominators are same & we may find another rational number between them as below}
= (8/32), (9/32), (10/32), (11/32), (12/32), (13/32), (14/32), (15/32), (16/32)
or
= (1/4), (9/32), (10/32), (11/32), (12/32), (13/32), (14/32), (15/32), (1/2)
{Here we have seven rational number between them, we may select any five from above}
{ So five rational number between (1/4) & (1/2) will be}
= (9/32), (10/32), (11/32), (12/32), (13/32)
Step 2 (By taking mean)
In this, we take mean of both rational numbers & find another rational number between them.
Now take an example & understand it. Let's discuss-
Example:-
Find three rational number between (1/4) & (1/2).
Solve:-
= (1/4) & (1/2)
{Now we take mean between (1/4) & (1/2)}
= { (1/4) + (1/2) } ÷2
= { (1+2)/4 } ÷ 2
= (3/4) ÷ 2
{Now we will do reciprocal of 2 & change sign}
= (3/4)×(1/2)
= (3/8)
{Here we get a rational number (3/8) between (1/4) & (1/2)}
= (1/4), (3/8), (1/2)
{Now take mean between (1/4) & (3/8)} &
{Take mean between (3/8) & (1/2) to get more rational numbers between them}
= {(1/4) + (3/8)} ÷2 & {(3/8) + (1/2)} ÷2
= { (2+3)/8 } ÷ 2 & { (3+4)/8 } ÷ 2
= (5/8)÷2 & (7/8)÷2
= (5/8)×(1/2) & (7/8)×(1/2)
= (5/16) & (7/16)
{Now we get two more rational number & our three rational will be between (1/4) & (1/2)}
= (1/4), (3/8), (5/16), (7/16), (1/2).
For any query, you may contact us & if it is helpful then please share.....