Evaluate - i-3-7-4-9-11-7-7-9- ii-2-3-4-5-1-3-2-5- iii-4-7-0-8-9-13-7-17-9-iv-3-8-5-12-3-7-3-12-5-8-2-7

(i) 3/7+ 4/9+ 11/7+7/9 =(3/7+ 11/7+ )+( 4/9+7/9 ) =3 11/7+ 4+7/9 = 8/7+3/9 = 8/7+1/3 ∴LCM of 3 and 2=3×7 =21 = 8×3/7× 3+1× 7/3× 7 (∵ LC ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

Evaluate : i ...

Question

Evaluate :

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

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Solution

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} = (\frac{3}{7} + \frac{- 11}{7} +) + (\frac{- 4}{9} + \frac{7}{9}) = \frac{3 - 11}{7} + \frac{- 4 + 7}{9} = \frac{- 8}{7} + \frac{3}{9} = \frac{- 8}{7} + \frac{1}{3}$

$∴ L C M o f 3 a n d 2 = 3 \times 7 = 21 = \frac{- 8 \times 3}{7 \times 3} + \frac{1 \times 7}{3 \times 7} (∵ L C M o f 7 a n d 3 = 21) = \frac{- 24 + 7}{21} = \frac{- 17}{21} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} = (\frac{2}{3} + \frac{1}{3}) + (\frac{- 4}{5} + \frac{2}{5}) = \frac{2 + 1}{3} + \frac{- 4 + 2}{5} = \frac{3}{3} + (\frac{- 2}{5})$

$∴ L C M o f 3 a n d 5 = 3 \times 5 = 15 = \frac{3 \times 5}{3 \times 5} + \frac{- 2 \times 3}{5 \times 3} (∵ L C M o f 3 a n d 5 = 15) = \frac{15 - 6}{15} = \frac{9}{15} = \frac{3}{5} (i i i) \frac{4}{7} + 0 \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} = \frac{4}{7} + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} = [\frac{4}{7} + (\frac{- 13}{7})] + (\frac{- 8}{9} + \frac{17}{9}) = (\frac{4}{7}) - \frac{13}{7} + (\frac{- 8}{9}) + \frac{17}{9} = \frac{- 9}{7} + \frac{9}{9} = \frac{- 9}{7} + 1 = \frac{- 9 \times 1}{7 \times 1} + \frac{1 \times 7}{1 \times 7} (∵ L C M o f 1 a n d 7 = 7) = \frac{- 9}{7} + \frac{7}{7} = \frac{- 2}{7} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7} = (\frac{3}{8} - \frac{5}{8}) + (\frac{- 5}{12} + \frac{3}{12}) + (\frac{3}{7} - \frac{2}{7}) = \frac{- 2}{8} - \frac{2}{12} + \frac{1}{7} = \frac{- 1}{4} + \frac{1}{6} + \frac{1}{7}$

$∴ L C M o f 4.6 a n d 7 = 2 \times 2 \times 3 \times 7 = 84 = \frac{- 1 \times 21}{4 \times 21} - \frac{1 \times 14}{6 \times 14} + \frac{1 \times 12}{7 \times 12} (∵ L C M o f 4, 6 a n d 7 = 84) = \frac{- 21 - 14 + 12}{84} = \frac{- 35 + 12}{84} = \frac{- 23}{84}$

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Similar questions

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

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

Q. 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} - \frac{- 8}{9} - \frac{- 13}{7} + \frac{17}{9}

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) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Fill in the blanks:

$(i) - 4 \times \frac{7}{9} = \frac{7}{9} \times$ ___

$(i i) \frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times$ ___

$(i i i) \frac{1}{2} \times (\frac{3}{4} + \frac{- 5}{12}) = \frac{1}{2} \times$ ____ $+ (\times) \frac{- 5}{12}$

$(i v) \frac{- 4}{5} \times \frac{5}{7} \times$ ___ $= (\frac{- 4}{5} \times \frac{5}{7}) \times \frac{- 8}{9}$

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Evaluate : (i) 37+−49+−117+79(ii) 23+−45+13+25(iii) 47+0+−89+−137+179(iv) 38+−512+37+312+−58+−27