Re-arrange suitably and find the sum in each of the following - i11-12-17-3-11-2-25-2 ii-6-7-5-6-4-9-15-7 iii3-5-7-3-9-5-13-15-7-3 iv 4-13-5-8-8-13-9-13 v2-3-4-5-1-3-2-5 vi 1-8-5-12-2-7-7-12-9-7-5-16

(i)11/12+ 17/3+11/2+ 25/2 = ( 11/12+ 17/3 )+ (11/2+ 25/2 ) =11 68/12+11 25/2 = 57/12+ 14/2 = 57 84/12= 141/12 (ii) 6/7+ 5/6+ 4/9+ 15/7 = ( 6/7+ 15/7 )+ ( 5 ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

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) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2} = (\frac{11}{12} + \frac{- 17}{3}) + (\frac{11}{2} + \frac{- 25}{2}) = \frac{11 - 68}{12} + \frac{11 - 25}{2} = \frac{- 57}{12} + \frac{- 14}{2} = \frac{- 57 - 84}{12} = \frac{- 141}{12}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7} = (\frac{- 6}{7} + \frac{- 15}{7}) + (\frac{- 5}{6} + \frac{- 4}{9}) = \frac{- 6 - 15}{7} + \frac{- 15 - 8}{18} = \frac{- 21}{7} + \frac{- 23}{18} = \frac{- 373 - 161}{126} = \frac{- 539}{126} = \frac{- 539 \div 7}{126 \div 7} = \frac{- 77}{18}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3} = (\frac{3}{5} + \frac{9}{5}) + (\frac{7}{3}) + \frac{- 13}{15} = \frac{3 + 9}{5} + \frac{7 - 7}{3} + \frac{- 13}{15} = \frac{12}{5} + 0 + \frac{- 13}{15} = \frac{12}{5} + \frac{- 13}{15} = \frac{36 - 13}{15} = \frac{23}{15}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13} = \frac{4}{13} + \frac{- 8}{13} + \frac{9}{13} + \frac{- 5}{8} = \frac{4 - 8 + 9}{13} + \frac{- 5}{8} = \frac{5}{13} + \frac{- 5}{8} = \frac{40 - 65}{104} (L C M o f 13, 8 = 104) = \frac{- 25}{104}$

(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) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16} = (\frac{1}{8} + \frac{- 5}{16}) + (\frac{5}{12} + \frac{7}{12}) + (\frac{2}{7} + \frac{9}{7}) = \frac{2 - 5}{16} + \frac{5 + 7}{12} + \frac{2 + 9}{7} = \frac{- 3}{16} + \frac{12}{12} + \frac{11}{7} = \frac{- 3}{16} + 1 + \frac{11}{7} = \frac{- 21 + 112 + 176}{112} = \frac{- 21 + 288}{112} = \frac{267}{117}$

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Similar questions

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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