Question

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

(iii)  `(-7)/9,2/-3 and (-5)/18`

Answer 1

Show that:

`(-7)/9+(2/(-3)+(-5)/18)=((-7)/9+2/(-3))+(-5)/18`

∴`(-7)/9+(2/(-3)+(-5)/18)`       

2	3, 18
3	3, 9
5	3, 3
	1, 1

∴ LCM of 3 and 18 = 2 x 3 x 3 = 18

=`(-7)/9 + ((-2xx6)/(3xx6)+(-5xx1)/(18xx1))`

= `(-7)/9+(-12-5)/18`  (∴ LCM of 3 and 18 = 18)

=`(-7)/9+(-17)/18`      

=`(-7xx2)/(9xx2)-(17xx1)/(18xx1)`    (∴ LCM of 9 and 18 = 18)

= `(-14-17)/18=(-31)/18`

And, `((-7)/9+2/3)+(-5)/18` 

3	3, 9
3	3, 3
	1, 1

∴ LCM of 3 and 9 = 9

=`((-7xx1)/(9xx1)+(-2xx3)/(3xx3))+(-5)/18`   (∴LCM=9 and3=9)

= `(-7-6)/9+(-5)/18`

=`(-13)/9+(-5)/18`

=`(-13xx2)/(9xx2)+(-5xx1)/(18xx1)=(-26xx-5)/18=(-31)/18`

∴`(-7)/9+(2/(-3)+(-5)/18)=((-7)/9+2/(-3))+(-5)/18`

This verifies associtive property of the addition of rational numbers.