Question

insert 6 rational number between 1 and 2 upon 5 by 2 different methods

Answer 1

6 rational no. between 1/2 and 5/2are
1/2×10/10=10/20
5/2×10/10=50 /20
6 rational no. are = 11/20 22/20,23/20,30/20, 36/20 39/20

Answer 2

2×5 = 10
so we have to find out 6 rational numbers between 1 and 5 × 2 =10
Let a = 1 and b = 10
First method
D = (b - a)/n + 1
and we have to find out 6 rational numbers so n = 6
D = ( 10 - 1 )/ 6 + 1 = 9/7
D = 9/7
now,
First rational number = a + d = 1 + 9/7
= ( 7 + 9 )/7 = 16/9.
second rational number = a + 2d = 1 + 2×9/7
=1 + 18/7 = ( 7 + 18 )/7 =25/7
Third rational number = a + 3d = 1 + 3×9/7
= 1 + 27/7 = ( 7 +27 )/7 = 34/7
Fourth rational number = a + 4d = 1 + 4×9/7
= 1 + 36/7 = ( 7 + 36 )/7 =43/7
Fifth rational number = a + 5d = 1 + 5×9/7
= 1 + 45/7 = ( 7 + 45 )/8 = 52/7
Sixth rational number = a + 6d = 1 + 6×9/7
=1 + 54/7 = ( 7 + 54 )/7 = 61/7.
Second method,
One rational number betwee n 1 and 10 =
( a + b)/2 =( 1 + 10 ) / 2 = 11/2
now,
11/2 is a rational number between 1 and 10 so,
second rational number =( 11/2 + 10 ) / 2
= 31/4
similarly, third = (31/4 + 10)/2
Fourth = {(31/4 + 10)/2}/2
Fifth =[ {(31/4 + 10)/2}/2 ] /2
sixth = [[ {(31/4 + 10)/2}/2 ] /2]/2.