# 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:

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

#### Solution

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.

Is there an error in this question or solution?

#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 1 Rational Numbers
Exercise 1 (A) | Q 5.1 | Page 9