Question

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

Arrange the rate of recycling the materials from the greatest to the smallest.

Material	Recycled
Paper	$\frac{5}{11}$
Aluminium cans	$\frac{5}{8}$
Glass	$\frac{2}{5}$
Scrap	$\frac{3}{4}$

Answer 1

Desecending order :

The given table is

Material	Recycled
Paper	$\frac{5}{11}$
Aluminium cans	$\frac{5}{8}$
Glass	$\frac{2}{5}$
Scrap	$\frac{3}{4}$

Take the LCM of the given fractions

$LCM\left(11,8,5,4\right)=440$

So,

$$\begin{gathered} \frac{5}{11}=\frac{5\times 40}{11\times 40} \\ =\frac{200}{440} \\ \frac{5}{8}=\frac{5\times 55}{8\times 55} \\ =\frac{275}{440} \\ \frac{2}{5}=\frac{2\times 88}{5\times 88} \\ =\frac{176}{440} \\ \frac{3}{4}=\frac{2\times 110}{4\times 110} \\ =\frac{330}{440} \end{gathered}$$

Now, $330>275>200>176$

Thus,

$\frac{3}{4}>\frac{5}{8}>\frac{5}{11}>\frac{2}{5}$

Hence, $\mathrm{Scrap}>\mathrm{Aluminium}>\mathrm{Cans}>\mathrm{paper}>\mathrm{Glass}$.