Question

Find the smallest number among $-\frac{2}{3}$,$-\frac{9}{6}$,$-\frac{5}{2}$ and $-\frac{3}{4}$.
[4 marks]

Answer 1

LCM of 3, 6, 2 and 4 is 12. ...(0.5 marks)
Converting the given numbers to equivalent rational numbers (having the same denominator), we get

$-\frac{2}{3}$ = $-\frac{8}{12}$ ...(0.5 marks)

$-\frac{9}{6}$ = $-\frac{18}{12}$ ...(0.5 marks)

$-\frac{5}{2}$ = $-\frac{30}{12}$ ...(0.5 marks)

$-\frac{3}{4}$ = $-\frac{9}{12}.$ ...(0.5 marks)

$-\frac{30}{12}<-\frac{18}{12}<-\frac{9}{12}<-\frac{8}{12}$ ...(0.5 marks)

$\Rightarrow -\frac{5}{2}<-\frac{9}{6}<-\frac{3}{4}<-\frac{2}{3}$ ...(0.5 marks)
Thus, the smallest out of the given rational numbers is $-\frac{5}{2}.$ ...(0.5 marks)