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Question
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.
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Solution
a. Here, `1/2 = 1/2 xx 11/11 = 11/22`
And `5/11 = 5/11 xx 2/2 = 10/22`
So, paper recycled is less than `1/2`.
b. Similarly, `5/8` is greater than `1/2 (= 4/8)`
Also, `2/5 = (2 xx 2)/(5 xx 2) = 4/10 < 1/2 (= 5/10)`
And `3/4 > 1/2 (= 2/4)`
So, the quantity of paper and glass recycled is less than `1/2`.
c. Quantity of aluminium cans = `5/8 (= 10/16)` is more than `1/2` of the quantity of aluminim cans
= `5/8 xx 1/2`
= `5/16`
d. Taking LCM of 11, 8, 5, 4 = 440
Now, `5/11 = 5/11 xx 40/40 = 200/440`
`5/8 = 5/8 xx 55/55 = 275/440`
`2/5 = 2/5 xx 88/88 = 176/440`
`3/4 = 3/4 xx 110/110 = 330/440`
As, `330/440 > 275/440 > 200/440 > 176/440`
i.e. `3/4 > 5/8 > 5/11 > 2/5`
That means, Scrap > Aluminium cans > Paper > Glass.
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