Question

Which of the following expressions shows that rational numbers are associative under
multiplication.
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Answer 1

GIVEN :

The expressions are

a) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{3}{5}\times \frac{2}{3})\times \frac{-6}{7}$

b) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=\frac{2}{3}\times (\frac{3}{5}\times \frac{-6}{7})$

c) $(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}=(\frac{-6}{7}\times \frac{2}{3})\times \frac{3}{5}$

d) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}$

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TO FIND :

The expressions that rational numbers are associative under  multiplication

SOLUTION :

Given expressions are

a) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{3}{5}\times \frac{2}{3})\times \frac{-6}{7}$

b) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=\frac{2}{3}\times (\frac{3}{5}\times \frac{-6}{7})$

c) $(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}=(\frac{-6}{7}\times \frac{2}{3})\times \frac{3}{5}$

d) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}$

The rational numbers are associative under  multiplication is given by :

$(a\times b)\times c=a\times (b\times c)$

While comparing the formula of rational numbers are associative under  multiplication we have that the expression, option d) is correct.

$\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}$ is the rational numbers are associative under multiplication.