Question

Compare the following rational numbers and choose the correct option(s):
$\frac{4}{-9}$, $\frac{5}{-12}$, $\frac{7}{-18}$, $\frac{2}{-3}$

• A. -4/9
• B. 5/-12
• C. 7/-18
• D. 2/-3

Answer 1

Answer: (C), (D)

The correct options are
C

7/-18

D

2/-3

When we have to compare two rational numbers, we first make their denominators equal and then compare their numerators.
LCM of 9, 12, 18, 3 is 36.
Using LCM make the denominator equal.

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

$\frac{5}{-12}$ = $\frac{5\times 3}{-12\times 3}$ = $\frac{15}{-36}$

$\frac{7}{-18}$ = $\frac{7\times 2}{-18\times 2}$ = $\frac{14}{-36}$

$\frac{2}{-3}$ = $\frac{2\times 12}{-3\times 12}$ = $\frac{24}{-36}$

Among $\frac{16}{-36}$, $\frac{15}{-36}$, $\frac{14}{-36}$ and $\frac{24}{-36}$;
$\frac{14}{-36}$ is greatest and $\frac{24}{-36}$ is smallest.