Fill in the blanks- i -3-17 - -12-5 - -12-5 - - ii -9 - -21-8 - - - -9 iii -8-13 - 3-7 - -13-4 - - - -3-7 - -13-4- iv -12 - 7-12 - -9-11 - -12 - 7-12 - - v 19-5 - -3-11 - -7-8 - 19-5 - - - -7-8 vi -16-7 - - -16-7 - -16-7

(i) ( 3/17) + ( 12/5) = ( 12/5) + ( 3/17) (By commutative Law of addition) (ii) ( 9) + ( 21/8) +( 21/8) + ( 9) (By commutative Law of addition) (iii) ( 8/13 + 3 ...

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Byju's Answer

Standard VIII

Mathematics

Commutative Property of Rational Numbers

Fill in the b...

Question

Fill in the blanks.

(i) $(\frac{- 3}{17}) + (\frac{- 12}{5}) = (\frac{- 12}{5}) + (. . . . .)$

(ii) $- 9 + \frac{- 21}{8} = (. . . . . .) + (- 9)$

(iii) $(\frac{- 8}{13} + \frac{3}{7}) + (\frac{- 13}{4}) = (. . . . . .) + [\frac{3}{7} + (\frac{- 13}{4})]$

(iv) $- 12 + (\frac{7}{12} + \frac{- 9}{11}) = (- 12 + \frac{7}{12}) + (. . . . .)$

(v) $\frac{19}{- 5} + (\frac{- 3}{11} + \frac{- 7}{8}) = {\frac{19}{- 5} + (. . . . .)} + \frac{- 7}{8}$

(vi) $\frac{- 16}{7} + . . . . . = . . . . . . + \frac{- 16}{7} = \frac{- 16}{7}$

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Solution

(i) $(\frac{- 3}{17}) + (\frac{- 12}{5}) = (\frac{- 12}{5}) + (\frac{- 3}{17})$
(By commutative Law of addition)
(ii) $(- 9) + (\frac{- 21}{8}) + (\frac{- 21}{8}) + (- 9)$
(By commutative Law of addition)
(iii) $(\frac{- 8}{13} + \frac{3}{7}) + (\frac{- 13}{4}) = (\frac{- 8}{13}) + [\frac{3}{7} + (\frac{- 13}{4})]$
(By Associative Law of addition)
(iv) $- 12 + (\frac{7}{12} + \frac{- 9}{11}) = (- 12 + \frac{7}{12}) + (\frac{- 9}{11})$
(By Associative Law of addition)
(v) $\frac{19}{- 5} + (\frac{- 3}{11} + \frac{- 7}{8}) = {\frac{19}{- 5} + \frac{- 3}{11}} + \frac{- 7}{8}$
(By Associative Law of addition)
(vi) $\frac{- 16}{7} + 0 = 0 + \frac{- 16}{7} = \frac{- 16}{7}$
[Existance of Additive Identity (0)]

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

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

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) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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

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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Fill in the blanks. (i) (−317)+(−125)=(−125)+(.....) (ii) −9+−218=(......)+(−9) (iii) (−813+37)+(−134)=(......)+[37+(−134)] (iv) −12+(712+−911)=(−12+712)+(.....) (v) 19−5+(−311+−78)={19−5+(.....)}+−78 (vi) −167+.....=......+−167=−167