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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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संबंधित प्रश्न
Add the following rational numbers:
Simplify:
Subtract the first rational number from the second in each of the following:
What number should be subtracted from \[\frac{- 5}{3}\] to get\[\frac{5}{6}?\]
What number should be subtracted from \[\frac{3}{7}\] to get\[\frac{5}{4}?\]
Simplify:
For each set of rational number, given below, verify the associative property of addition of rational number:
(iv) `-1, 5/6 and (-2)/3`
State, True Or False
`7/9=(7÷5)/(9÷5)`
Compare: `-1 1/2 and 0 or -3/2 and 0`
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` |
Arrange the rate of recycling the materials from the greatest to the smallest.
