Question

Which of the following statements is incorrect?

• A. If 'a' is a rational number and 'b' is irrational, then a + b is irrational.
• B. The product of a non-zero rational number with an irrational number is always irrational.
• C. Addition of any two irrational numbers can be rational.
• D. Division of any two integers is an integer.

Answer 1

The correct option is D

Division of any two integers is an integer.

Sum of a rational number and an irrational number is always irrational So, If 'a' is a rational number and 'b' is irrational, then a + b is irrational.

The product of a non-zero rational number with an irrational number is always irrational.

Addition of any two irrational numbers can be rational. For example, $(4+\sqrt{3})+(4-\sqrt{3})=4+\sqrt{3}+4-\sqrt{3}=8$

But, Division of any two integers is always not an integer. For example $\frac{3}{4}$ is not an integer where 3 and 4 are integers.