Question

find three rational number between 1/4 and 1/2 by mean method ​

Answer 1

Answer:

3/8 , 4/8 , 5/8

Working rule :

★ Let the smaller number be x and greater number be y .

★ Then find the common difference d using the formula ; d = (y - x)/(n + 1) , where n is the number of Rational numbers to be found between x and y .

★ The the required rational numbers will be given as ;

1st rational no. = x + d

2nd rational no. = x + 2d

3rd rational no. = x + 3d

:

:

nth rational no. = x + nd

Solution:

Here,

We need to find three rational numbers between 1/4 and 1/2 .

Thus,

x = 1/4 , y = 1/2 , n = 3

Now,

=> d = (y - x)/(n + 1)

=> d = (1/2 - 1/4) / (3 + 1)

=> d = [ (4 - 2)/4 ] / 4

=> d = (2/4) / 4

=> d = (1/2) / 4

=> d = 1/(2×4)

=> d = 1/8

Thus,

The required rational numbers will be ;

• 1st rational number = x + d

= 1/4 + 1/8

= (2 + 1)/8

= 3/8

• 2nd rational number = x + 2d

= 1/4 + 2/8

= (2 + 2)/8

= 4/8

• 3rx rational number = x + 3d

= 1/4 + 3/8

= (2 + 3)/8

= 5/8

Hence,

The required rational numbers are :

3/8 , 4/8 , 5/8