Multiplication of rational number

The multiplication of a rational number x and an irrational number y is

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.

CLOSURE PROPERTY The product or multiplication of any two rational numbers is always a rational number.

Representation of rational numbers on the number line

What is the multiplicative identity of rational number?

Multiplication by 0every rational number when multiplied with 0given 0.

Which of the following is an example of distributive property of multiplication over addition for rational numbers.

Multiplication of a non-zero rational number with an irrational number is an irrational number.