Question

Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Answer 1

Write required examples :

Rational numbers: A rational number has the form $\frac{p}{q}$where $p$ and $q$ are both integers and $q\ne 0$, the rational numbers are closed under addition, subtraction and multiplication but rational numbers are not closed under division.

Examples of closure property under

(i) Addition: $\frac{3}{4}+\frac{1}{2}=\frac{5}{4}$

(ii) Subtraction: $\frac{7}{1}-\frac{3}{4}=\frac{25}{4}$

(iii)Multiplication: $\frac{5}{2}\times \frac{3}{7}=\frac{15}{14}$

Rational numbers are not closed under division.

Example 1: Let us take two rational numbers $3$ and $0$. Then their division $\frac{3}{0}$is not defined,

Example 2: Let us take two rational numbers $9$ and $0$. Then their division $\frac{9}{0}$ is not defined.

Hence, above are the required examples.