Question

Arrange the following rational numbers in descending order:
(i) $\frac{7}{8},\frac{64}{16},\frac{36}{-12},\frac{5}{-4},\frac{140}{28}$
(ii) $\frac{-3}{10},\frac{17}{-30},\frac{7}{-15},\frac{-11}{20}$

Answer 1

We have to arrange them in descending order.

(i)
$$\begin{gathered} \mathrm{Since},\mathrm{LCM}\hspace{0.17em}\mathrm{of}8,16,-12,-4,28\mathrm{is}336. \\ \mathrm{Multiplying}\mathrm{the}\mathrm{numerators}\mathrm{and}\mathrm{denominators},\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{denominator}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{LCM}, \\ \frac{7}{8}=\frac{7\times 42}{8\times 42}=\frac{294}{336}, \\ \frac{64}{16}=\frac{64\times 21}{16\times 21}=\frac{1344}{336}, \\ \frac{36}{-12}=\frac{-36\times 28}{12\times 28}=\frac{-1008}{336}, \\ \frac{5}{-4}=\frac{-5\times 84}{4\times 84}=\frac{-420}{336}, \\ \frac{140}{28}=\frac{140\times 12}{28\times 12}=\frac{1680}{336}. \\ \mathrm{Order}\mathrm{is}1680>1344>294>-420>-1008. \\ \mathrm{Order}\mathrm{is}\frac{140}{28}>\frac{64}{16}>\frac{7}{8}>\frac{5}{-4}>\frac{36}{-12}. \end{gathered}$$
(ii)

$$\begin{gathered} \mathrm{Since},\mathrm{LCM}\hspace{0.17em}\mathrm{of}10,-30,-15,20\mathrm{is}60. \\ \mathrm{Multiplying}\mathrm{the}\mathrm{numerators}\mathrm{and}\mathrm{denominators},\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{denominator}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{LCM}, \\ \frac{-3}{10}=\frac{-3\times 6}{10\times 6}=\frac{-18}{60}, \\ \frac{17}{-30}=\frac{-17\times 2}{30\times 2}=\frac{-34}{60}, \\ \frac{7}{-15}=\frac{-7\times 4}{15\times 4}=\frac{-28}{60}, \\ \frac{-11}{20}=\frac{-11\times 3}{20\times 3}=\frac{-33}{60}, \\ \mathrm{Order}\mathrm{is},-18>-28>-33>-34. \\ \mathrm{Order}\mathrm{is}\frac{-3}{10}>\frac{7}{-15}>\frac{-11}{20}>\frac{17}{-30}. \end{gathered}$$