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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`
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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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The average life expectancies of males for several states are shown in the table. Express each decimal in the form `p/q` and arrange the states from the least to the greatest male life expectancy. State-wise data are included below; more indicators can be found in the “FACTFILE” section on the homepage for each state.
| State | Male | `bb(p/q)` form | Lowest terms |
| Andhra Pradesh | 61.6 | ||
| Assam | 57.1 | ||
| Bihar | 60.7 | ||
| Gujarat | 61.9 | ||
| Haryana | 64.1 | ||
| Himachal Pradesh | 65.1 | ||
| Karnataka | 62.4 | ||
| Kerala | 70.6 | ||
| Madhya Pradesh | 56.5 | ||
| Maharashtra | 64.5 | ||
| Orissa | 57.6 | ||
| Punjab | 66.9 | ||
| Rajasthan | 59.8 | ||
| Tamil Nadu | 63.7 | ||
| Uttar Pradesh | 58.9 | ||
| West Bengal | 62.8 | ||
| India | 60.8 |
Source: Registrar General of India (2003) SRS Based Abridged Lefe Tables. SRS Analytical Studies, Report No. 3 of 2003, New Delhi: Registrar General of India. The data are for the 1995-99 period; states subsequently divided are therefore included in their pre-partition states (Chhatisgarh in MP, Uttaranchal in UP and Jharkhand in Bihar)
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