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

Sum

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

#### Solution

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.

Concept: Concept of Rational Numbers
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 1 Rational Numbers
Exercise 1 (A) | Q 5.2 | Page 9