**Question:**

**The table shows the portion of some common materials that are recycled.**

**(a) Is the rational number expressing the amount of paper recycled more than ½ or less than ½?**

**(b) Which items have a recycled amount less than ½?**

**(c) Is the quantity of aluminium cans recycled more (or less) than half of the quantity of aluminium cans?**

**(d) Arrange the rate of recycling the materials from the greatest to the smallest.**

**Solution:**

**(a) Is the rational number expressing the amount of paper recycled more than ½ or less than ½?**

The rational number expressing the amount of paper recycled is less than ½.

**(b) Which items have a recycled amount less than ½?**

Paper and Glass have a recycled amount less than ½.

**(c) Is the quantity of aluminium cans recycled more (or less) than half of the quantity of aluminium cans?**

The quantity of aluminium cans recycled is more than half of the quantity of aluminium cans.

**(d) Arrange the rate of recycling the materials from the greatest to the smallest.**

The LCM of the denominators 11, 8, 5 and 4 is 440

∴ 5/11 = [(5×40)/ (11×40)] = (200/440)

(5/8) = [(5×55)/ (8×55)] = (275/440)

(2/5) = [(2×88)/ (5×88)] = (176/440)

(3/4) = [(3×110)/ (4×110)] = (330/440)

Then,

Now, 330 > 275 > 200 > 176

Hence, ⇒ 3/4 > 5/8 > 5/11 > 2/5

∴Scrap > Aluminium > Cans > Paper > Glass.