Tamil Nadu Board Solutions for Chapter: Numbers, Exercise 13: Exercise 1.3

Check whether associative property holds for subtraction and division of rational numbers.

Verify the commutative property for addition and multiplication for the rational numbers $\frac{-10}{11}$ and $\frac{-8}{33}$.

Verify the associative property for addition and multiplication for the rational numbers $\frac{-7}{9}, \frac{5}{6}$ and $\frac{-4}{3}$.

Verify the identity property for addition and multiplication for the rational numbers $\frac{15}{19}$ and $\frac{-18}{25}$.

Verify the additive and multiplicative inverse property for the rational numbers $\frac{-7}{17}$ and $\frac{17}{27}$.

Closure property is not true for division of rational numbers because of the number.

$\frac{1}{2}-\left(\frac{3}{4}-\frac{5}{6}\right)\ne \left(\frac{1}{2}-\frac{3}{4}\right)-\frac{5}{6}$ illustrates that subtraction does not satisfy the______ law of rational numbers.

$\frac{3}{4}\times \left(\frac{1}{2}-\frac{1}{4}\right)=\frac{3}{4}\times \frac{1}{2}-\frac{3}{4}\times \frac{1}{4}$ illustrates multiplication is distributive over