Question

Arrange the following rational numbers in descending order:

(i) $\frac{-2}{5},\frac{7}{-10},\frac{-11}{15},\frac{19}{-30}$
(ii) $-2,\frac{-13}{6},\frac{8}{-3},\frac{1}{3}$
(iii) $\frac{-4}{9},\frac{5}{-12},\frac{-7}{18},\frac{2}{-3}$
(iv) $\frac{17}{-30},\frac{11}{-15},\frac{-7}{10},\frac{3}{5}$

Answer 1

$\begin{array}{l}\\ \left(\text{i}\right)\frac{-2}{5},\frac{7}{-10},\frac{-11}{15},\frac{19}{-30}\\ \mathrm{First},\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{convert}\mathrm{each}\mathrm{negative}\mathrm{denominator}\mathrm{into}\mathrm{positive}.\\ \frac{-2}{5},\frac{7\times -1}{-10\times -1},\frac{-11}{15},\frac{19\times -1}{-30\times -1}\\ \frac{-2}{5},\frac{-7}{10},\frac{-11}{15},\frac{-19}{30}\\ \end{array}$


$\begin{array}{l}\begin{array}{l}\text{L}.\text{C}.\text{M. of 5},\text{1}0,1\text{5 and 3}0\mathrm{is}\text{3}0.\\ \frac{-2\times 6}{5\times 6}=\frac{-12}{30},\\ \frac{-7\times 3}{10\times 3}=\frac{-21}{30},\\ \frac{-11\times 2}{15\times 2}=\frac{-22}{30},\\ \frac{-19\times 1}{30\times 1}=\frac{-19}{30},\end{array}\\ \\ \text{Correct order:}\frac{-2}{5}>\frac{19}{-30}>\frac{7}{-10}>\frac{-11}{15}\\ \left(\text{ii}\right)-2,\frac{-13}{6},\frac{8}{-3},\frac{1}{3}\\ \mathrm{First},\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{convert}\mathrm{each}\mathrm{negative}\mathrm{denominator}\mathrm{into}\mathrm{positive}.\\ -2,\frac{-13}{6},\frac{8\times -1}{-3\times -1},\frac{1}{3}\\ -2,\frac{-13}{6},\frac{-8}{3},\frac{1}{3}\end{array}$



$\begin{array}{l}\begin{array}{l}\text{L}.\text{C}.\text{M. of 6},\text{3 and 3 is 6.}\\ \frac{-2\times 6}{1\times 6}=\frac{-12}{6},\\ \frac{-13\times 1}{6\times 1}=\frac{-13}{6},\\ \frac{-8\times 2}{3\times 2}=\frac{-16}{6},\end{array}\\ \frac{1\times 2}{3\times 2}=\frac{2}{6},\\ \text{Correct order:}\frac{1}{3}>-2>\frac{-13}{6}>\frac{-8}{3}\end{array}$
$\begin{array}{l}\left(\text{iii}\right)\frac{-4}{9},\frac{5}{-12},\frac{-7}{18},\frac{2}{-3}\\ \mathrm{First},\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{convert}\mathrm{each}\mathrm{negative}\mathrm{denominator}\mathrm{into}\mathrm{positive}.\\ \frac{-4}{9},\frac{5\times -1}{-12\times -1},\frac{-7}{18},\frac{2\times -1}{-3\times -1}\\ \frac{-4}{9},\frac{-5}{12},\frac{-7}{18},\frac{-2}{3}\end{array}$


$\begin{array}{l}\begin{array}{l}\text{L}.\text{C}.\text{M. of 9},\text{12},\text{18 and 3 is}36.\\ \frac{-4\times 4}{9\times 4}=\frac{-16}{36},\\ \frac{-5\times 3}{12\times 3}=\frac{-15}{36},\\ \frac{-7\times 2}{18\times 2}=\frac{-14}{36},\\ \frac{-2\times 12}{3\times 12}=\frac{-24}{36}\end{array}\\ \\ \text{Correct order:}\frac{-7}{18}>\frac{-5}{12}>\frac{-4}{9}>\frac{-2}{3}\\ \left(\text{iv}\right)\frac{17}{-30},\frac{11}{-15},\frac{-7}{10},\frac{3}{5}\\ \mathrm{First},\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{convert}\mathrm{each}\mathrm{negative}\mathrm{denominator}\mathrm{into}\mathrm{positive}.\\ \frac{17\times -1}{-30\times -1},\frac{11\times -1}{-15\times -1},\frac{-7}{10},\frac{3}{5}\\ \frac{-17}{30},\frac{-11}{15},\frac{-7}{10},\frac{3}{5}\\ \begin{array}{l}\\ \\ \\ \\ \\ \end{array}\end{array}$


$\begin{array}{l}\text{L}.\text{C}.\text{M. of 3}0,\text{15},\text{1}0\mathrm{and}\text{5 is 3}0.\\ \frac{-17\times 1}{30\times 1}=\frac{-17}{30},\\ \frac{-11\times 2}{15\times 2}=\frac{-22}{30},\\ \frac{-7\times 3}{10\times 3}=\frac{-21}{30},\\ \frac{3\times 6}{5\times 6}=\frac{18}{30},\\ \text{Correct order:}\frac{3}{5}>\frac{17}{-30}>\frac{-7}{10}>\frac{11}{-15}\end{array}$