Question

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

(ii) `(-2)/5, 4/15 and (-7)/10`

Answer 1

Show that :

`(-2)/5+(4/15+(-7)/10)=((-2)/5+4/15)+(-7)/10`

∴`(-2)/5+(4/15+(-7)/10)`   

2	15 ,10
3	15 ,5
5	5 ,5
	1 ,1

∴ LCM of 15, 10 =2 x 3 x 5 = 30

=`(-2)/5+((4xx2)/(15xx2)+(-7xx3)/(10xx3))` 

                 (∴LCM of 15 and 10 = 30)

=`(-2)/5+((8-21)/30)`    

=`(-2)/5-13/30=(-2xx6)/(5xx6)-(13xx1)/(30xx1)`

=`(-12-13)/30=(-25)/30=(-5)/6`

And, `((-2)/5+4/15)+(-7)/10` 

3	5, 15
5	5 ,5
	1, 1

∴ LCM  of 5 and 15 = 3 x 5 = 15

=`((-2xx3)/(5xx3)+(4xx1)/(15xx1))+(-7)/10`

∴LCM of 5 and  15 = 15

=`(-6+4)/15+(-7)/10`

=`(-2)/15+(-7)/10`

=`(-2xx2)/(15xx2)-(7xx3)/(10xx3)`

=`(-4)/30-21/30=(-25)/30=(-5)/6`

∴ `(-2)/5+(4/15+(-7)/10)=((-2)/5+4/15)+(-7)/10`

This verifies associative property of the addition of rational numbers.