Question

Among the following rational numbers, which is the least?
P = $\frac{7}{8}$, Q = $\frac{8}{7}$, R= $\frac{3}{4}$,
S= $\frac{1}{14}$

• A. P
• B. Q
• C. R
• D. S

Answer 1

The correct option is D S

Converting all the given rational numbers to like fractions, by taking the LCM, we get, (LCM =56)
P = $\frac{7}{8}$ = $\frac{49}{56}$
Q= $\frac{8}{7}$ = $\frac{64}{56}$
R = $\frac{3}{4}$ = $\frac{42}{56}$
S = $\frac{1}{14}$ = $\frac{4}{56}$

from the above we infer that,
$\frac{4}{56}$ < $\frac{42}{56}$ < $\frac{49}{56}$ < $\frac{64}{56}$
$\therefore$ $S=\frac{1}{14}$ is the least rational number in the above given numbers.