Re-arrange suitably and find the sum in each of the following-i 1112-173-112-252ii -67-56-49-157iii 35-73-95-1315-73iv 413-58-813-913v 23-45-13-25vi 18-512-27-712-97-516

(i) #160;(112+ 252)+ 173+1112=11 252+ 173+1112= 142+ 173+1112= 7+ 173+1112= 84 68+1112= 14112= 474(ii) #160;( 67+ 157)+ 56+ 49= 6 157+ 56+ 49= 217+ 56+ 49= ...

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Byju's Answer

Standard VI

Mathematics

Importance of Brackets

Re-arrange su...

Question

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

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Solution

$(i) (\frac{11}{2} + \frac{- 25}{2}) + \frac{- 17}{3} + \frac{11}{12} = (\frac{11 - 25}{2}) + \frac{- 17}{3} + \frac{11}{12} = \frac{- 14}{2} + \frac{- 17}{3} + \frac{11}{12} = - 7 + \frac{- 17}{3} + \frac{11}{12} = \frac{- 84 - 68 + 11}{12} = \frac{- 141}{12} = \frac{- 47}{4} (ii) (\frac{- 6}{7} + \frac{- 15}{7}) + \frac{- 5}{6} + \frac{- 4}{9} = (\frac{- 6 - 15}{7}) + \frac{- 5}{6} + \frac{- 4}{9} = \frac{- 21}{7} + \frac{- 5}{6} + \frac{- 4}{9} = \frac{- 378 - 105 - 56}{126} = \frac{- 539}{126} = \frac{- 77}{18} (iii) (\frac{3}{5} + \frac{9}{5}) + (\frac{- 7}{3} + \frac{7}{3}) + \frac{- 13}{15} = (\frac{3 + 9}{5}) + (\frac{- 7 + 7}{3}) + \frac{- 13}{15} = \frac{12}{5} + \frac{- 13}{15} = \frac{36 - 13}{15} = \frac{23}{15} (iv) (\frac{4}{13} - \frac{8}{13} + \frac{9}{13}) + \frac{- 5}{8} = (\frac{4 - 8 + 9}{13}) + \frac{- 5}{8} = \frac{5}{13} + \frac{- 5}{8} = \frac{40 - 65}{104} = \frac{- 25}{104} (v) (\frac{2}{3} + \frac{1}{3}) + (\frac{- 4}{5} + \frac{2}{5}) = \frac{3}{3} + \frac{- 2}{5} = \frac{15 - 6}{15} = \frac{9}{15} = \frac{3}{5} (vi) (\frac{1}{8} + \frac{- 5}{16}) + (\frac{5}{12} + \frac{7}{12}) + (\frac{2}{7} + \frac{9}{7}) = (\frac{2 - 5}{16}) + (\frac{5 + 7}{12}) + (\frac{2 + 9}{7}) = \frac{- 3}{16} + \frac{12}{12} + \frac{11}{7} = \frac{- 63 + 336 + 528}{336} = \frac{801}{336} = \frac{267}{112}$

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Similar questions

Q. Simplify:

(i)

\frac{2}{3} + \frac{3}{4} + \frac{1}{2}

(ii)

\frac{5}{8} + \frac{2}{5} + \frac{3}{4}

(iii)

\frac{3}{10} + \frac{7}{15} + \frac{3}{5}

(iv)

\frac{3}{4} + \frac{7}{16} + \frac{5}{8}

(v)

4 \frac{2}{3} + 3 \frac{1}{4} + 7 \frac{1}{2}

(vi)

7 \frac{1}{3} + 3 \frac{2}{3} + 5 \frac{1}{6}

(vii)

7 + \frac{7}{4} + 5 \frac{1}{6}

(viii)

\frac{5}{6} + 3 + \frac{3}{4}

(ix)

\frac{7}{18} + \frac{5}{6} + 1 \frac{1}{12}

Q. Verify the following:
(i)

\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}

(ii)

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

(iii)

3 + \frac{- 7}{12} = \frac{- 7}{12} + 3

(iv)

\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}

Q. Evaluate:

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\frac{- 3}{5} + \frac{7}{5} + \frac{- 1}{5}

(ii)

\frac{- 12}{7} + \frac{3}{7} + \frac{- 2}{7}

(iii)

\frac{11}{- 12} + \frac{3}{- 8} + \frac{1}{4}

(iv)

\frac{- 16}{9} + \frac{- 5}{12} + \frac{7}{18}

(v)

- 3 + \frac{1}{8} + \frac{- 2}{5}

(vi)

\frac{- 13}{8} + \frac{5}{16} + \frac{- 1}{4}

Simplify each of the following and write as a rational number of the form $\frac{p}{q}$ :
(i) $\frac{3}{4} + \frac{5}{6} + \frac{- 7}{8}$
(ii) $\frac{2}{3} + \frac{- 5}{6} + \frac{- 7}{9}$
(iii) $\frac{- 11}{2} + \frac{7}{6} + \frac{- 5}{8}$
(iv) $\frac{- 4}{5} + \frac{- 7}{10} + \frac{- 8}{15}$
(v) $\frac{- 9}{10} + \frac{22}{15} + \frac{13}{- 20}$
(vi) $\frac{5}{3} + \frac{3}{- 2} + \frac{- 7}{3} + 3$