Verify each of the following - i 5-7-12-13 -7-18 - 5-7- 12-13-7-18 ii -13-24- -12-5-35-36 - -13-24-12-5 -35-36 iii -9-5-10-3 -21-4 - -9-5- -10-3-21-4

(i) L.H.S. = (5/7×12/13) ×7/18 = 5 × 12/7 × 13×7/18 = 5 × 12/7 × 13×7/18 = 60/91×7/18 = 420/1638 = 420 ÷ 21/1638 ÷ 21 = 20/78 R.H.S = 5/7× (12/13×7/18) = 5 × ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Associative Property of Rational Numbers

Verify each o...

Question

Verify each of the following :

(i) $(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} \times (\frac{12}{13} \times \frac{7}{18})$
(ii) $\frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36}) = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36}$
(iii) $(\frac{- 9}{5} \times \frac{- 10}{3}) \times \frac{21}{- 4} = \frac{- 9}{5} \times (\frac{- 10}{3} \times \frac{21}{- 4})$

Open in App

Solution

(i) $L . H . S . = (\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5 \times 12}{7 \times 13} \times \frac{7}{18}$
$= \frac{5 \times 12}{7 \times 13} \times \frac{7}{18} = \frac{60}{91} \times \frac{7}{18} = \frac{420}{1638} = \frac{420 \div 21}{1638 \div 21} = \frac{20}{78} R . H . S = \frac{5}{7} \times (\frac{12}{13} \times \frac{7}{18}) = \frac{5 \times 84}{7 \times 234} = \frac{420}{1638} = \frac{420 \div 21}{1638 \div 21} = \frac{20}{78} ∴ (\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} \times (\frac{12}{13} \times \frac{7}{18})$

(ii) $L . H . S . \frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36})$
$= \frac{- 13}{24} \times \frac{- 12 \times 35}{5 \times 36} = \frac{- 13}{24} \times \frac{- 420}{180} = \frac{- 13 \times (- 420)}{24 \times 180} = \frac{5460}{4320} = \frac{5460 \div 60}{4320 \div 60} = \frac{91}{72} R . H . S . = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36} = \frac{- 13 \times (- 12)}{24 \times 5} \times \frac{35}{36} = \frac{156 \times 35}{120 \times 36} = \frac{5460}{4320} = \frac{5460 \div 60}{4320 \div 60} = \frac{91}{72} ∴ \frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36}) = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36}$

(iii) $L . H . S . = (\frac{- 9}{5} \times \frac{- 10}{3}) \times \frac{21}{- 4}$

$= \frac{- 9 \times (- 10)}{5 \times 3} \times \frac{21}{- 4} = \frac{90}{15} \times \frac{21}{- 4}$

$= \frac{90 \times 21}{15 \times (- 4)} = \frac{1890}{- 60}$

$= \frac{1890 \div 30}{- 60 \div 30} = \frac{63}{- 2} = \frac{- 63}{2}$

$R . H . S . = \frac{- 9}{5} \times (\frac{- 10}{3} \times \frac{21}{- 4})$

$= \frac{- 9}{5} \times \frac{- 10 \times 21}{3 \times (- 4)} = \frac{- 9}{5} \times \frac{- 210}{- 12}$

$\frac{- 9 \times (- 210)}{5 \times (- 12)} = \frac{1890}{- 60}$

$= \frac{1890 \div 30}{- 60 \div 30} = \frac{63}{- 2} = \frac{- 63}{2}$

$∴ (\frac{- 9}{5} \times \frac{- 10}{3}) \times \frac{21}{- 4} = \frac{- 9}{5} \times (\frac{- 10}{3} \times \frac{21}{- 4})$

Suggest Corrections

Similar questions

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

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

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

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:

(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} (\frac{12}{13} \times \frac{7}{18})

Join BYJU'S Learning Program

Verify each of the following : (i) (57×1213)×718=57×(1213×718) (ii) −1324×(−125×3536)=(−1324×−125)×3536 (iii) (−95×−103)×21−4=−95×(−103×21−4)