Question

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

(iv) `-1, 5/6 and (-2)/3` 

Answer 1

Show that :

This verifies associative  property  of the addition of rational numbers.

`(-1)/1+(5/6+(-2)/3)=((-1)/1+5/6)+(-2)/3`

∴`(-1)/1+(5/6+(-2)/3)`   

2	6, 3
3	3, 3
	1, 1

∴ LCM of 6 and 3 = 6

=`(-1)/1+((5xx1)/(6xx1)+(-2xx2)/(3xx2))`    (∴LCM of 6 and 3 = 6)

=`(-1)/1+((5-4)/6)`

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

=`(-1xx6)/(1xx6)+(1xx1)/(6xx1)`    (∴ LCM of 1 and 6 = 1)

=`(-6+1)/6=(-5)/6`

And, `((-1)/1+5/6)+(-2)/3`

=`((-1xx6)/(1xx6)+(5xx1)/(6xx1))+(-2)/3`  (∴LCM of 1 and 6 =6) 

=`((-6+5)/6)+(-2)/3`    

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

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

=`(-1-4)/6=(-5)/6`  (∴LCM of 6 and 3 = 6)

∴`(-1)/1+(5/6+(-2)/3)=((-1)/1+5/6)+(-2)/3`