Evaluate - i-5-9-7-6- ii-4-3-5- iii-1-15-5-12- iv-5-9-3-4- v-8-9-5-12- vi-0-2-7- vii-5-11-0- viii-2-3-5- ix-4-9-1

(i) 5/9+ 7/6 ∴LCM of 9 and 6=2×3×3=18 =5×2/9×2 7×3/6×3 (∵LCM of 9 and 6=18) =10 21/18= 11/8 (ii) 4+3/ 5 =4/1+(3/ 5 ) =4/1 3/5 =4×5/1×5 3×1/5 ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

Evaluate : i ...

Question

Evaluate : $(i) \frac{5}{9} + \frac{- 7}{6} (i i) 4 + \frac{3}{- 5} (i i i) \frac{1}{- 15} + \frac{5}{- 12} (i v) \frac{5}{9} + \frac{3}{- 4} (v) \frac{- 8}{9} + \frac{- 5}{12} (v i) 0 + \frac{- 2}{7} (v i i) \frac{5}{- 11} + 0 (v i i i) 2 + \frac{- 3}{5} (i x) \frac{4}{- 9} + 1$

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Solution

$(i) \frac{5}{9} + \frac{- 7}{6}$

$∴ L C M o f 9 a n d 6 = 2 \times 3 \times 3 = 18 = \frac{5 \times 2}{9 \times 2} - \frac{7 \times 3}{6 \times 3} (∵ L C M o f 9 a n d 6 = 18) = \frac{10 - 21}{18} = \frac{- 11}{8} (i i) 4 + \frac{3}{- 5} = \frac{4}{1} + (\frac{3}{- 5}) = \frac{4}{1} - \frac{3}{5} = \frac{4 \times 5}{1 \times 5} - \frac{3 \times 1}{5 \times 1} (∵ L C M o f 1 a n d 5 = 5) = \frac{20 - 3}{5} - \frac{17}{5} = 3 \frac{2}{5} (i i i) \frac{1}{- 15} + \frac{5}{- 12} = \frac{- 1}{15} + (\frac{5}{- 12}) = \frac{- 1}{15} - \frac{5}{12}$

$∴ L C M o f 15 a n d 12 = 2 \times 2 \times 3 \times 5 = 60 = \frac{- 1 \times 4}{15 \times 4} - \frac{5 \times 5}{12 \times 5} (∵ L C M o f 15 a n d 12 = 60) = \frac{- 4 - 25}{60} = \frac{- 29}{60} (i v) \frac{5}{9} + \frac{3}{- 4}$

$= \frac{5}{9} - \frac{3}{4} (∴ L C M o f 9 a n d 4 = 2 \times 2 \times 3 \times 3 = 36) = \frac{5 \times 4}{9 \times 4} - \frac{3 \times 9}{4 \times 9} = \frac{20 - 27}{36} = \frac{- 7}{36} (∵ L C M o f 9 a n d 4 = 36) = \frac{- 7}{36} (v) \frac{- 8}{9} + \frac{- 5}{12}$

$(∴ L C M o f 9, 12 = 2 \times 2 \times 3 \times 3 = 36) = \frac{- 8 \times 4}{9 \times 4} - \frac{5 \times 3}{12 \times 3} = \frac{- 32 - 15}{36} (∵ L C M o f 9 a n d 12 = 36) = \frac{- 47}{36} (v i) 0 + \frac{- 2}{7} = \frac{0 \times 7}{1 \times 7} - \frac{2 \times 1}{7 \times 1} (∵ L C M o f 0 a n d 7 = 7) = \frac{0 - 2}{7} = \frac{- 2}{7} (v i i) \frac{5}{- 11} + 0 = \frac{- 5 \times 1}{11 \times 1} + \frac{0 \times 11}{1 \times 11} (∵ L C M o f 0 a n d 11 = 11) = \frac{- 5 + 0}{11} = \frac{- 5}{11} (v i i i) 2 + \frac{- 3}{5} = \frac{2}{1} - \frac{3}{5} (∵ L C M o f 1 a n d 5 = 5) = \frac{2 \times 5}{1 \times 5} - \frac{3 \times 1}{5 \times 1} = \frac{10 - 3}{5} = \frac{7}{5} = 1 \frac{2}{5} (i x) \frac{4}{- 9} + 1 = \frac{- 4}{9} - \frac{1}{1} (∵ L C M o f 9 a n d 1 = 9) = \frac{- 4 \times 1}{1 \times 9} + \frac{1 \times 9}{1 \times 9} = \frac{- 4 + 9}{9} = \frac{5}{9}$

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Similar questions

Evaluate :

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

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

source $(i) \frac{8}{9} + \frac{- 11}{6} (i i) 3 + \frac{5}{- 7} (i i i) \frac{1}{- 12} a n d \frac{2}{- 15} (i v) \frac{- 8}{19} + \frac{- 4}{57} (v) \frac{7}{9} + \frac{3}{- 4} (v i) \frac{5}{26} + \frac{11}{- 39} (v i i) \frac{- 16}{9} + \frac{- 5}{12} (v i i i) \frac{- 13}{8} + \frac{5}{36} (i x) 0 + \frac{- 3}{5} (x) 1 + \frac{- 4}{5} (x i) \frac{- 5}{16} + \frac{7}{24}$

Fill in the blanks:

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

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

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

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

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

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Evaluate : $(i) \frac{5}{9} + \frac{- 7}{6} (i i) 4 + \frac{3}{- 5} (i i i) \frac{1}{- 15} + \frac{5}{- 12} (i v) \frac{5}{9} + \frac{3}{- 4} (v) \frac{- 8}{9} + \frac{- 5}{12} (v i) 0 + \frac{- 2}{7} (v i i) \frac{5}{- 11} + 0 (v i i i) 2 + \frac{- 3}{5} (i x) \frac{4}{- 9} + 1$