Question

Which of the rational numbers $\frac{4}{-3}$, $\frac{5}{-6}$, $\frac{7}{-18}$, $\frac{2}{-12}$ is the smallest?

• A. $\frac{4}{-3}$
• B. $\frac{5}{-6}$
• C. $\frac{7}{-18}$
• D. $\frac{2}{-12}$

Answer 1

The correct option is A $\frac{4}{-3}$

LCM of 3, 6, 18, 12 is 36.

Using LCM make the denominator equal.

$\frac{4}{-3}$ = $\frac{48}{-36}$

$\frac{5}{-6}$ = $\frac{30}{-36}$

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

$\frac{2}{-12}$ = $\frac{6}{-36}$
By comparing the numerators,
$\frac{6}{-36}$ > $\frac{14}{-36}$ > $\frac{30}{-36}$, >$\frac{48}{-36}$

$\frac{48}{-36}$ = $\frac{4}{-3}$ is smallest.