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 1/2 or less than 1/2? (b) Which items have a recycled amount less than 1/2? (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.

Material Recycled
Paper 5/11
Aluminium cans 5/8
Glass 2/5
Scrap 3/4

Solution

(a) 

Answer

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

(b) 

Answer

Paper and Glass have a recycled amount less than ½.

(c) 

Answer

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

(d)

Answer

Let us take the LCM of the given fractions

On taking 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)

200/440, 275/440, 176/440, 330/440

Now, 330 > 275 > 200 > 176

Hence, ⇒ 3/4 > 5/8 > 5/11 > 2/5

∴Scrap > Aluminium > Cans > Paper > Glass.

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