The average of the two middle rational numbers if 4/7, 1/3, 2/3,5/9 are arranged in ascending order is ------------. (a) 4/9 (b) 71/63 (c) 4/18 (d) 71/126 . please show the method

Solution:

First to arrange the fractions in ascending order we have to make the denominators common.

So the LCM of the fractions : 4/7, 1/3, 2/3 5/9 = 63

4/7 = (4x9)/(7x9) = 36/63

1/3 = (1x21)/(3x21) = 21/63

2/3 = (2x21)/(3x21) = 42/63

5/9 = (5x7)/(9x7) = 35/63

So the ascending order is 21/63, 35/63, 36/63 42/63 i.e. 1/3, 5/9, 4/7 2/3. The two middle fractions are 5/9 4/7.

So Average = Sum total of all numbers / Total no. of numbers.

= (5/9 + 4/7) / 2

= ( 35 + 36 / 63) / 2

= 71 / 63 x 1/2

= 71 / 126.

Ans.: 71/126.

Hope you have understood.