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`

1. Is the rational number expressing the amount of paper recycled more than `1/2` or less than `1/2`?
2. Which items have a recycled amount less than `1/2`?
3. Is the quantity of aluminium cans recycled more (or less) than half of the quantity of aluminium cans?
4. Arrange the rate of recycling the materials from the greatest to the smallest.

Answer 1

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.