I-3-7-4-9-11-7-7-9- ii-2-3-4-5-1-3-2-5- iii-4-7-8-9-13-7-17-9

(i) 3/7+ 4/9 11/7 7/9 ⇒(3/7 11/7 )+( 4/9 7/9 ) ⇒(3/7 11/7 )+( 4/9 7/9 ) ⇒14/7+ 11/9 ⇒ 2 11/9 ⇒2×9 11/9⇒18 11/9⇒7/9 (ii) 2/3+ 4/5 1/3 2/5 ⇒(2/3 1/3 )+( 4/5 2/ ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

i 3/7+-4/9--1...

Question

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

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Solution

$(i) \frac{3}{7} + \frac{- 4}{9} - \frac{- 11}{7} - \frac{7}{9} \Rightarrow (\frac{3}{7} - \frac{- 11}{7}) + (\frac{- 4}{9} - \frac{7}{9}) \Rightarrow (\frac{3}{7} - \frac{11}{7}) + (\frac{- 4}{9} - \frac{7}{9}) \Rightarrow \frac{14}{7} + \frac{- 11}{9} \Rightarrow 2 - \frac{11}{9} \Rightarrow \frac{2 \times 9 - 11}{9} \Rightarrow \frac{18 - 11}{9} \Rightarrow \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} - \frac{1}{3} - \frac{2}{5} \Rightarrow (\frac{2}{3} - \frac{1}{3}) + (\frac{- 4}{5} - \frac{2}{5}) \Rightarrow \frac{1}{3} + \frac{- 6}{5} \Rightarrow \frac{1}{3} - \frac{6}{5} \Rightarrow \frac{(1 \times 5) - (6 \times 3)}{15} (∵ LCM of 3 and 5=15) \Rightarrow \frac{5 - 18}{15} \Rightarrow - \frac{13}{15} (i i i) \frac{4}{7} - \frac{- 8}{9} - \frac{- 13}{7} + \frac{17}{9} \Rightarrow (\frac{4}{7} - \frac{- 13}{7}) - (\frac{- 8}{9} - \frac{17}{9}) \Rightarrow (\frac{4}{7} + \frac{13}{7}) - (\frac{- 8}{9} - \frac{17}{9}) \Rightarrow \frac{17}{7} - (\frac{- 25}{9}) \Rightarrow \frac{17}{7} + \frac{25}{9} (∵ LCM of 7 and 9=63) \Rightarrow \frac{17 \times 9 + 25 \times 7}{63} \Rightarrow \frac{153 + 175}{63} \Rightarrow \frac{328}{63} \Rightarrow 5 \frac{13}{63}$

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Similar questions

Evaluate :

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

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}

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

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

Without adding find the sum

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

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(i) 37+−49−−117−79(ii) 23+−45−13−25(iii) 47−−89−−137+179

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