Question

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

• A. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{2}{3}\right)\times \left(\frac{-6}{7}\right)\right)\times \left(\frac{3}{5}\right)\right]$
• B. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{3}{5}\right)\times \left(\frac{-6}{7}\right)\right)\right]$
• C. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{3}{5}\right)\times \left(\frac{2}{3}\right)\right)\times \left(\frac{-6}{7}\right)\right]$
• D. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{-6}{7}\right)\times \left(\frac{2}{3}\right)\right)\times \left(\frac{3}{5}\right)\right]$

Answer 1

The correct option is A

$\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{2}{3}\right)\times \left(\frac{-6}{7}\right)\right)\times \left(\frac{3}{5}\right)\right]$

Determine the correct expression.

The associativity property states that in an expression with multiple factors, different ways of grouping the factors will not change the product of the expression.

That is $a\times \left(b\times c\right)=\left(a\times b\right)\times c$.

So, the expression that resembles the definition of associativity is $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{2}{3}\right)\times \left(\frac{-6}{7}\right)\right)\times \left(\frac{3}{5}\right)\right]$

.Hence, option $\left(\mathrm{A}\right)$ is correct.