(i)
\(\frac{4}{-9}=\frac{4\times-1}{-9\times-1}=\frac{-4}{9}\)
And,
\(\frac{7}{-18}=\frac{7\times-1}{-18\times-1}=\frac{-7}{18}\)
Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. LCM of 9, 12, 18 and 3 = 36
\(\frac{-4}{9}=\frac{-4\times4}{9\times4}=\frac{-16}{36}\)
\(\frac{-5}{12}=\frac{-5\times3}{12\times3}=\frac{-15}{36}\)
\(\frac{-7}{18}=\frac{-7\times2}{18\times2}=\frac{-14}{36}\)
\(\frac{-2}{3}=\frac{-2\times12}{3\times12}=\frac{-24}{36}\)
Clearly,
-24 < -16 < -15 < -14
Therefore,
\(\frac{-24}{36}<\frac{-16}{36}<\frac{-15}{36}<\frac{-14}{36}\)
Hence,
\(\frac{-2}{3}<\frac{4}{-9}<\frac{-5}{12}<\frac{7}{-18}\)
(ii)
\(\frac{5}{-12}=\frac{5\times-1}{-12\times-1}=\frac{-5}{12}\)
And,
\(\frac{9}{-24}=\frac{9\times-1}{-24\times-1}=\frac{-9}{24}\)
Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. LCM of 4, 12, 16 and 24 = 48
\(\frac{-3}{4}=\frac{-3\times12}{4\times12}=\frac{-36}{48}\)
\(\frac{-5}{12}=\frac{-5\times4}{12\times4}=\frac{-20}{48}\)
\(\frac{-7}{16}=\frac{-7\times3}{16\times3}=\frac{-21}{48}\)
\(\frac{-9}{24}=\frac{-9\times2}{24\times2}=\frac{-18}{48}\)
Clearly, -36 < -21 < -20 < -18
Therefore,
\(\frac{-36}{48}<\frac{-21}{48}<\frac{-20}{48}<\frac{-18}{48}\)
Hence,
\(\frac{-3}{4}<\frac{-7}{16}<\frac{5}{-12}<\frac{9}{24}\)
(iii)
\(\frac{3}{-5}=\frac{3\times-1}{-5\times-1}=\frac{-3}{5}\)
Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. LCM of 5, 10, 15 and 20 = 60
\(\frac{-3}{5}=\frac{-3\times12}{5\times12}=\frac{-36}{60}\)
\(\frac{-7}{10}=\frac{-7\times6}{10\times6}=\frac{-42}{60}\)
\(\frac{-11}{15}=\frac{-11\times4}{15\times4}=\frac{-44}{60}\)
\(\frac{-13}{20}=\frac{-13\times3}{20\times3}=\frac{-39}{60}\)
Clearly, -44 < -42 < -39 < -36
Therefore,
\(\frac{-44}{60}<\frac{-42}{60}<\frac{-39}{60}<\frac{-36}{60}\)
Hence,
\(\frac{-11}{15}<\frac{-7}{10}<\frac{-13}{20}<\frac{3}{-5}\)
(iv)
\(\frac{13}{-28}=\frac{13\times-1}{-28\times-1}=\frac{-13}{28}\)
Since, the denominators of all the numbers are different therefore we will take LCM of the denominators. LCM of 7, 14, 28 and 42 = 84
\(\frac{-4}{7}=\frac{-4\times12}{7\times12}=\frac{-48}{84}\)
\(\frac{-9}{14}=\frac{-9\times-6}{14\times6}=\frac{-54}{84}\)
\(\frac{-13}{28}=\frac{-13\times3}{28\times3}=\frac{-39}{84}\)
\(\frac{-23}{42}=\frac{-23\times2}{42\times2}=\frac{-46}{84}\)
Clearly, -54 < -48 < -46 < -39
Therefore,
\(\frac{-54}{84}<\frac{-48}{84}<\frac{-46}{84}<\frac{-39}{84}\)
Hence,
\(\frac{-9}{14}<\frac{-4}{7}<\frac{-23}{42}<\frac{13}{-28}\)
