Question

Find the greatest rational number among the following.
$-\frac{4}{9}$, $-\frac{5}{12}$, $-\frac{7}{18}$ and $-\frac{2}{3}$ [3 marks]

Answer 1

Note that LCM of 9, 12, 18, 3 is 36. (1 mark)

Using LCM to convert each of the given rational numbers to equivalent forms,

$-\frac{4}{9}$ = $-\frac{16}{36}$

$-\frac{5}{12}$ = $-\frac{15}{36}$

$-\frac{7}{18}$ = $-\frac{14}{36}$

$-\frac{2}{3}$ = $-\frac{24}{36}$ (1 mark)

Since the denominators are equal, we now compare the rational numbers using its numerators.
Thus, $-\frac{24}{36}<-\frac{16}{36}<-\frac{15}{36}<-\frac{14}{36}$
i.e., $-\frac{2}{3}<-\frac{4}{9}<-\frac{5}{12}<-\frac{7}{18}$
$\therefore -\frac{7}{18}$ is the greatest among the given numbers. (1 mark)