Question

For each set of rational number, given below, verify the associative property of addition of rational number:

(i) `1/2 , 2/3 "and"-1/6`

Answer 1

`1/2,2/3 and -1/6`

Show that:

`1/2+ (2/3+(-1)/6)=(1/2+2/3)+(-1)/6`

∴`1/2+(2/3+(-1)/6)`         

2	3, 6
3	3, 3
	1, 1

∴LCM of 3 and 6=6

=`1/2+((2 xx2)/(3xx2)+(-1xx1)/(6xx1))`

=`1/2+(4/6-1/6)`

=`1/2+((4-1)/6)`

=`1/2+(3/6)`

=`(1xx3)/(2xx3)+(3xx1)/(6xx1)`  (∴LCM of 2 and 6=3)

=`(3+3)/6=6/6=1`

And, `(1/2+2/3)+(-1)/6`     

2	2, 3
3	1, 3
	1, 1

∴LCM of 2 and 3=6

=`((1xx3)/(2xx3)+(2xx2)/(3xx2))+(-1)/6`

=`(3+4)/6+(-1)/6`

=`(7-1)/6=6/6=1`

∴`1/2+(2/3+(-1)/6)=(1/2+2/3)+(-1)/6`

This verifies associative property of the addition of rational numbers.