Verify whether the given statement is true or false - i 5-9-1-3 -5-2 - 5-9- 1-3-5-2 ii -16 -6-5-9-10 - -16 -6-5-9-10 iii -3-5-12-35 -1-14 - -3-5- -12-35-1-14

(i) L.H.S. = (5/9÷1/3) ÷5/2 = (5/9×3/1) ÷5/2 = 15/9÷5/2 = 15/9×2/5 = 30/45 = 30 ÷ 15/45 ÷ 15 = 2/3 R.H.S. = 5/9÷ [1/3÷5/2] = 5/9÷ [1/3×2/5] = 5/9÷ [2/15] = 5/9× ...

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Byju's Answer

Standard VIII

Mathematics

Associative Property of Rational Numbers

Verify whethe...

Question

Verify whether the given statement is true or false :

(i) $(\frac{5}{9} \div \frac{1}{3}) \div \frac{5}{2} = \frac{5}{9} \div (\frac{1}{3} \div \frac{5}{2})$

(ii) ${(- 16) \div \frac{6}{5}} \div \frac{- 9}{10} = (- 16) \div {\frac{6}{5} \div \frac{- 9}{10}}$

(iii) $(\frac{- 3}{5} \div \frac{- 12}{35}) \div \frac{1}{14} = \frac{- 3}{5} \div (\frac{- 12}{35} \div \frac{1}{14})$

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Solution

(i) $L . H . S . = (\frac{5}{9} \div \frac{1}{3}) \div \frac{5}{2}$

$= (\frac{5}{9} \times \frac{3}{1}) \div \frac{5}{2} = \frac{15}{9} \div \frac{5}{2}$

$= \frac{15}{9} \times \frac{2}{5} = \frac{30}{45} = \frac{30 \div 15}{45 \div 15} = \frac{2}{3}$

$R . H . S . = \frac{5}{9} \div [\frac{1}{3} \div \frac{5}{2}] = \frac{5}{9} \div [\frac{1}{3} \times \frac{2}{5}]$

$= \frac{5}{9} \div [\frac{2}{15}] = \frac{5}{9} \times \frac{15}{2} = \frac{75}{18}$

$= \frac{75 \div 3}{18 \div 3} = \frac{25}{6}$

$∵ L . H . S . \neq R . H . S .$

$∴$ It is false.

(ii) $L . H . S . = [(- 16) \div \frac{6}{5}] \div \frac{- 9}{10}$

$= [- 16 \times \frac{5}{6}] \div \frac{- 9}{10} = \frac{- 80}{6} \div \frac{- 9}{10}$

$= \frac{- 80}{6} \times \frac{10}{- 9} = \frac{- 800}{- 54} = \frac{800}{54} = \frac{800 \div 2}{54 \div 2} = \frac{400}{27}$

$R . H . S . = (- 16) \div [\frac{6}{5} \div \frac{- 9}{10}]$

$= (- 16) \div [\frac{6}{5} \times \frac{10}{- 9}] = - 16 \div [\frac{60}{- 45}]$

$= - 16 \times \frac{- 45}{60} = \frac{720}{60} = \frac{720 \div 60}{60 \div 60} = \frac{12}{1} = 12$

$∵ L . H . S . \neq R . H . S .$

$∴$ It is false.

(iii) $L . H . S . = [\frac{- 3}{5} \div \frac{- 12}{35}] \div \frac{1}{14}$

$= [\frac{- 3}{5} \times \frac{35}{- 12}] \div \frac{1}{14}$

$= \frac{- 105}{- 60} \div \frac{1}{14} = \frac{105}{60} \times \frac{14}{1}$

$= \frac{1470}{60} = \frac{1470}{60} = \frac{1470 \div 30}{60 \div 30} = \frac{49}{2}$

$R . H . S . = \frac{- 3}{5} \div [\frac{- 12}{35} \div \frac{1}{14}]$

$= \frac{- 3}{5} \div [\frac{- 12}{35} \times \frac{14}{1}]$

$= \frac{- 3}{5} \div [\frac{- 168}{35}]$

$= \frac{- 3}{5} \times \frac{35}{- 168} = \frac{- 105}{- 840}$

$= \frac{105}{840} = \frac{105 \div 105}{840 \div 105} = \frac{1}{8}$

$∵ L . H . S . \neq R . H . S .$

$∴$ It is false.

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Similar questions

Q. Mark whether true or false.
(a) 8 (7 + 3) = 8 × 7 + 8 × 3 ____
(b) 12 (16 + 4) = 12 × 16 + 12 × 4 ____
(c) 14 (5 + 2) = 14 × 5 + 14 × 2 ____
(d) 9 (8 − 3) = 9 × 8 − 9 × 3 ____

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

Q. Verify the following equality

(\frac{- 3}{5} + \frac{1}{6}) + \frac{9}{10} = \frac{- 3}{5} + (\frac{1}{6} + \frac{9}{10})

Add using number line:

(1) 5 and 3

(2) 6 and 2

(3) (−3) and (+5)

(4) 8 and (−12)

(5) (−7) and 5

(6) 10 and (−14)

(7) (−5) and (−2)

(8) (+6) and (−9)

(9) (−4) and (−1)

(10) 1 and (−5)

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Verify whether the given statement is true or false : (i) (59÷13)÷52=59÷(13÷52) (ii) {(−16)÷65}÷−910=(−16)÷{65÷−910} (iii) (−35÷−1235)÷114=−35÷(−1235÷114)