Statement I: The rational numbers(Q)  is associative under addition.

Statement II: Multiplication is commutative for rational numbers

I): If  $a,b,c\in Q\text{and}a+\left(b+c\right)=\left(a+b\right)+c$ is called associative property of rational numbers under addition

For example  $\frac{2}{3},\frac{5}{6},\frac{7}{12}\in Q$

$\frac{2}{3}+\left(\frac{5}{6}+\frac{7}{12}\right)=\frac{2}{3}+\left(\frac{10+7}{12}\right)=\frac{2}{3}+\frac{17}{12}=\frac{8+17}{12}=\frac{25}{12}$

$\left(\frac{2}{3}+\frac{5}{6}\right)+\frac{7}{12}=\left(\frac{4+5}{6}\right)+\frac{7}{12}=\frac{9}{6}+\frac{7}{12}=\frac{18+7}{12}=\frac{25}{12}$

$\therefore \frac{2}{3}+\left(\frac{5}{6}+\frac{7}{12}\right)=\left(\frac{2}{3}+\frac{5}{6}\right)+\frac{7}{12}$

Hence, addition is associative for rational numbers

II) : If$a,b\in Q\text{and}a\times b=b\times a$ then it is called commutative property under multiplication.

For Ex:  $\frac{2}{3}\times \frac{7}{9}\in Q$

$\frac{2}{3}\times \frac{7}{9}=\frac{14}{27}$

$\frac{7}{9}\times \frac{2}{3}=\frac{14}{27}$

$\therefore \frac{2}{3}\times \frac{7}{9}=\frac{7}{9}\times \frac{2}{3}$

Hence, Multiplication is commutative for rotational numbers