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:

(iii)  (-7)/9,2/3 and (-5)/18

Solution

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 = 3

=((-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.

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 5.3 | Page 9