Question

3. Verify the associative law of multiplication for the following groups of rational numbers.
(1) -3/11,-7/4,-1/2​

Answer 1

Associative Law

( A x B ) x C = ( A x B ) x C

$A = \frac{ - 3}{4}$

$B = \frac{ - 7}{4}$

$C = \frac{ - 1}{2}$

Now,

( A x B ) x C

$( \frac{( - 3)}{4} \times \frac{( - 7)}{4} ) \times \frac{( - 1)}{2}$

$= ( \frac{21}{16} ) \times \frac{( - 1)}{2}$

$= \frac{ - 21}{32}$

Now,

A x ( B x C )

$\frac{ (- 3)}{4} ( \frac{( - 7)}{4} \times \frac{ (- 1)}{2} )$

$= \frac{ - 3}{4} ( \frac{7}{8} )$

$= \frac{ - 21}{32}$

$\frac{ - 21}{32} = \frac{ - 21}{32}$

( A x B ) x C = A x ( B x C )

Hence Associative Property Satisfied.

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