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प्रश्न
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`
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उत्तर
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.
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