Question

The smallest number among $-\frac{2}{3}$,$-\frac{9}{6}$,$-\frac{5}{2}$ and $-\frac{3}{4}$ is:
$\left[2\right]$

Answer 1

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

$-\frac{2}{3}$ = $-\frac{8}{12}$

$-\frac{9}{6}$ = $-\frac{18}{12}$

$-\frac{5}{2}$ = $-\frac{30}{12}$

$-\frac{3}{4}$ = $-\frac{9}{12}.$

$-\frac{30}{12}<-\frac{18}{12}<-\frac{9}{12}<-\frac{8}{12}$
$\left[1\right]$
$\Rightarrow -\frac{5}{2}<-\frac{9}{6}<-\frac{3}{4}<-\frac{2}{3}$
Thus, the smallest out of the given rational numbers is $-\frac{5}{2}.$
$\left[1\right]$