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प्रश्न
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`
उत्तर
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 = 9
=`((-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.
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State, True Or False
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Zero is a rational number.
Put the (√), wherever applicable
| Number | Natural Number |
Whole Number |
Integer | Fraction | Rational Number |
| (a) – 114 | |||||
| (b) `19/27` | |||||
| (c) `623/1` | |||||
| (d) `-19 3/4` | |||||
| (e) `73/71` | |||||
| (f) 0 |
