Question

Which of the following expressions show that rational numbers are associative under multiplication?

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

Answer 1

The correct option is A

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

Associative property states that if a,b and c are three rational numbers, then
$(a\times b)\times c=a\times (b\times c).$

Hence the expression:
$\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}$
represents associative property.