Verify the following- 5 7 - 12 13 - 7 18 - 5 7 12 13 - 7 18

L.H.S = ( 57×1213 #10;) ×718 #10; #10; = 6011×718 #10; #10; = 4201638 #10; #10; R.H.S = 57( 1213×718 #10;) = 57( 84234) = 42 ...

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Standard VIII

Mathematics

Associative Property of Rational Numbers

Verify the fo...

Question

Verify the following:
$(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} (\frac{12}{13} \times \frac{7}{18})$

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Solution

$L . H . S = (\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18}$

$= \frac{60}{11} \times \frac{7}{18}$

$= \frac{420}{1638}$

$R . H . S = \frac{5}{7} (\frac{12}{13} \times \frac{7}{18}) = \frac{5}{7} (\frac{84}{234}) = \frac{420}{1638}$

$S i n c e L . H . S = R . H . S p r o v e d$

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Similar questions

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

Verify the following:

(i) $18 \times [9 + (- 7)] = 18 \times 9 + 18 \times (- 7)$

(ii) $(- 13) \times [(- 6) + (- 19)] = (- 13) \times (- 6) + (- 13) \times (- 19)$

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

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

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

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

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

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Verify the following:(57×1213)×718=57(1213×718)

L.H.S=(57×1213)×718 =6011×718 =4201638 R.H.S=57(1213×718)=57(84234)=4201638 SinceL.H.S=R.H.Sproved

Verify the following:
$(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} (\frac{12}{13} \times \frac{7}{18})$

$L . H . S = (\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18}$

$= \frac{60}{11} \times \frac{7}{18}$

$= \frac{420}{1638}$

$R . H . S = \frac{5}{7} (\frac{12}{13} \times \frac{7}{18}) = \frac{5}{7} (\frac{84}{234}) = \frac{420}{1638}$

$S i n c e L . H . S = R . H . S p r o v e d$