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प्रश्न
Find the greatest and the smallest rational number among the following.
`(-2)/(3) , (-7)/(9) and (-5)/(6)`
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उत्तर
Given numbers : `(-2)/(3) , (-7)/(9) and (-5)/(6)`
The L.C.M. of 3, 9 and 6 is 18.
Thus, numbers are :
`(-2)/(3) = (-2 xx 6)/(3 xx 6)`
= `(-12)/(18); (-7)/(9)`
= `(-7 xx 2)/(9 xx 2)`
= `(-14)/(18); (-5)/(6)`
= `(-5 xx 3)/(6 xx 3)`
= `(-15)/(18)`
Since -12 > -14 > -15, we have `(-2)/(3) > (-7)/(9) > (-5)/(6)`.
Hence, the greatest rational number is `(-2)/(3)` and the smallest rational number is `(-5)/(6)`.
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संबंधित प्रश्न
Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]
Express each of the following as a rational number of the form \[\frac{p}{q}:\]
Multiply:
Simplify:
Fill in the blanks:
Insert a rational number between:
`(5)/(9) and (6)/(7)`
The table shows the portion of some common materials that are recycled.
| Material | Recycled |
| Paper | `5/11` |
| Aluminium cans | `5/8` |
| Glass | `2/5` |
| Scrap | `3/4` |
- Is the rational number expressing the amount of paper recycled more than `1/2` or less than `1/2`?
- Which items have a recycled amount less than `1/2`?
- Is the quantity of aluminium cans recycled more (or less) than half of the quantity of aluminium cans?
- Arrange the rate of recycling the materials from the greatest to the smallest.
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)
Write the following numbers in the form `p/q`, where p and q are integers:
Six-eighths
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 |
