Re-arrange suitably and find the sum in each of the following:
(i) $ \frac{11}{12}+\frac{-17}{3}+\frac{11}{2}+\frac{-25}{2} $
(ii) $ \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} $
(iii) $ \frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3} $
(iv) $ \frac{4}{13}+\frac{-5}{8}+\frac{-8}{13}+\frac{9}{13} $
(v) $ \frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5} $
(vi) $ \frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16} $

To do:

We have to find the sum by rearranging suitably in each case.

Solution:

(i) $\frac{11}{12}+\frac{-17}{3}+\frac{11}{2}+\frac{-25}{2}=(\frac{11}{12}+\frac{-17}{3})+(\frac{11}{2}+\frac{-25}{2})$

$=\frac{11-68}{12}+\frac{11-25}{2}$

$=\frac{-57}{12}+\frac{-14}{2}$

$=\frac{-57-84}{12}$

$=\frac{-141}{12}$

(ii) $\frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7}=(\frac{-6}{7}+\frac{-15}{7})+(\frac{-5}{6}+\frac{-4}{9})$

$=\frac{-6-15}{7}+\frac{-15-8}{18}$

$=\frac{-21}{7}+\frac{-23}{18}$

$=\frac{-378-161}{126}$

$=\frac{-539}{126}$

$=\frac{-77}{18}$

(iii) $\frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3}=(\frac{3}{5}+\frac{9}{5})+(\frac{7}{3}+\frac{-7}{3})+\frac{-13}{15}$

$=\frac{3+9}{5}+\frac{7-7}{3}+\frac{-13}{15}$

$=\frac{12}{5}+0+\frac{-13}{15}$

$=\frac{12}{5}+\frac{-13}{15}$

$=\frac{36-13}{15}$

$=\frac{23}{15}$

(iv) $\frac{4}{13}+\frac{-5}{8}+\frac{-8}{13}+\frac{9}{13}=\frac{4}{13}+\frac{-8}{13}+\frac{9}{13}+\frac{-5}{8}$

$=\frac{4-8+9}{13}+\frac{-5}{8}$

$=\frac{5}{13}+\frac{-5}{8}$

$=\frac{40-65}{104}$

$=\frac{-25}{104}$

(v) $\frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5}=(\frac{2}{3}+\frac{1}{3})+(\frac{-4}{5}+\frac{2}{5})$

$=\frac{2+1}{3}+\frac{-4+2}{5}$

$=\frac{3}{3}+\frac{-2}{5}$

$=1+\frac{-2}{5}$

$=\frac{5-2}{5}$

$=\frac{3}{5}$

(vi) $\frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16}=(\frac{1}{8}+\frac{-5}{16})+(\frac{5}{12}+\frac{7}{12})+(\frac{2}{7}+\frac{9}{7})$

$=\frac{2-5}{16}+\frac{5+7}{12}+\frac{2+9}{7}$

$=\frac{-3}{16}+\frac{12}{12}+\frac{11}{7}$

$=\frac{-3}{16}+1+\frac{11}{7}$

$=\frac{-21+112+176}{112}$

$=\frac{288-21}{112}$

$=\frac{267}{112}$ 

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Updated on: 10-Oct-2022

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