(i) \(-2 = \frac{-2}{1}\)

And,

\(\frac{8}{-3} = \frac{8\times-1}{-3\times-1} = \frac{-8}{3}\)

Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. 

LCM of 1, 6and 3 = 6

\(\frac{-2}{1}= \frac{-2\times6}{1\times6} = \frac{-12}{6}\)

\(\frac{-13}{6}= \frac{-13\times1}{6\times1} = \frac{-13}{6}\)

\(\frac{-8}{3}= \frac{-8\times2}{3\times2} = \frac{-16}{6}\)

\(\frac{1}{3}= \frac{1\times2}{3\times2} = \frac{-2}{6}\)

Clearly,

2 > -12 > -13 > -16

Therefore,

\(\frac{2}{6}>\frac{-12}{6}>\frac{-13}{6}>\frac{-16}{6}\)

Hence,

\(\frac{1}{3}>\frac{-2}{1}>\frac{-13}{6}>\frac{-8}{3}\)

(ii) \(\frac{7}{-15}= \frac{7\times-1}{-30\times-1} = \frac{-17}{30}\)

And,

\(\frac{17}{-30}= \frac{17\times-1}{-30\times-1} = \frac{-17}{30}\)

Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. 

LCM of 10, 15, 20 and 30 = 60

\(\frac{-3}{10}= \frac{-3\times6}{10\times6} = \frac{-18}{60}\)

\(\frac{-7}{15}= \frac{-7\times4}{15\times4} = \frac{-28}{60}\)

\(\frac{-11}{20}= \frac{-11\times3}{20\times3} = \frac{-33}{60}\)

\(\frac{-17}{30}= \frac{-17\times2}{30\times2} = \frac{-34}{60}\)

Clearly, 

-18>-28>-33>-34

Therefore,

\(\frac{-18}{60}>\frac{-28}{60}>\frac{-33}{60}>\frac{-34}{60}\)

Hence,

\(\frac{-3}{10}>\frac{-7}{15}>\frac{-11}{20}>\frac{-17}{30}\)

(iii) \(\frac{23}{-24} = \frac{23\times-1}{-24\times-1} = \frac{-23}{24}\)

Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. 

LCM of 6, 12, 18 and 24 = 72

 \(\frac{-5}{6}= \frac{-5\times12}{6\times12} = \frac{-60}{72}\)

\(\frac{-7}{12}= \frac{-7\times6}{12\times6} = \frac{-42}{72}\)

\(\frac{-13}{18}= \frac{-13\times4}{18\times4} = \frac{-52}{72}\)

\(\frac{-23}{24}= \frac{-23\times3}{24\times3} = \frac{-69}{72}\)

Clearly, -42>-52>-60>-69 

Therefore,

\(\frac{-42}{72}>\frac{-52}{72}>\frac{-60}{72}>\frac{-69}{72}\)

Hence,

\(\frac{-7}{12}>\frac{-13}{18}>\frac{-5}{6}>\frac{-23}{24}\)

(iv) Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. 

LCM of 11, 22, 33 and 44 = 132

  \(\frac{-10}{11}= \frac{-10\times12}{11\times12} = \frac{-120}{132}\)

\(\frac{-19}{22}= \frac{-19\times6}{22\times6} = \frac{-144}{132}\)

\(\frac{-23}{33}= \frac{-23\times4}{33\times4} = \frac{-92}{132}\)

\(\frac{-39}{44}= \frac{-39\times3}{44\times3} = \frac{-117}{132}\)

Clearly, -92>-114>-117>-120 

Therefore,

\(\frac{-92}{132}>\frac{-114}{132}>\frac{-117}{132}>\frac{-120}{132}\)

Hence,

\(\frac{-23}{33}>\frac{-19}{22}>\frac{-39}{44}>\frac{-10}{11}\)