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For Each Set of Rational Number, Given Below, Verify the Associative Property of Addition of Rational Number: - Mathematics

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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`

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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.

Concept: Addition of Rational Number
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APPEARS IN

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