(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, 6 and 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,
\(\frac{1}{3}>\frac{-2}{1}>\frac{-13}{6}>\frac{-8}{6}\)
(ii)
\(\frac{7}{-15}=\frac{7\times-1}{-15\times-1}=\frac{-7}{15}\)
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
\(\frac{-10}{11}=\frac{-10\times12}{11\times12}=\frac{-120}{132}\)
\(\frac{-19}{22}=\frac{-19\times6}{22\times6}=\frac{-114}{132}\)
\(\frac{-23}{33}=\frac{-23\times4}{33\times4}=\frac{-92}{132}\)
\(\frac{-39}{44}=\frac{-39\times3}{44\times3}=\frac{-117}{132}\)
Clearly, -92>-114>-117>-120
Therefore,
\(\frac{-92}{132}>\frac{-114}{132}>\frac{-117}{132}>\frac{-120}{132}\)
Hence,
\(\frac{-23}{33}>\frac{-19}{22}>\frac{-39}{44}>\frac{-10}{11}\)
