Which one of the following statements is not correct ?

Options

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

Answer

To solve the question "Which one of the following statements is not correct?", we need to analyze the given statements regarding rational and irrational numbers.

### Step-by-Step Solution:

1. **Understanding Rational and Irrational Numbers**:
- Rational numbers are numbers that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Examples include \( \frac{2}{3} \), \( \frac{6}{5} \), and integers like \( 2 \) and \( 3 \) (which can be written as \( \frac{2}{1} \) and \( \frac{3}{1} \)).
- Irrational numbers cannot be expressed in the form \( \frac{p}{q} \). Examples include \( \sqrt{2} \), \( \pi \), and \( e \).

2. **Analyzing Each Statement**:
- **Statement 1**: If \( a \) is a rational number and \( b \) is an irrational number, then \( \frac{a}{b} \) is irrational.
- This statement is **correct**. Dividing a rational number by an irrational number results in an irrational number.

- **Statement 2**: The product of a non-zero rational number with an irrational number is irrational.
- This statement is also **correct**. Multiplying a non-zero rational number by an irrational number yields an irrational number.

- **Statement 3**: The addition of any two irrational numbers can be an integer.
- This statement is **not correct**. For example, \( \pi + \sqrt{2} \) is irrational, and there are many combinations of irrational numbers that do not yield an integer.

- **Statement 4**: The division of any two integers is an integer.
- This statement is **not correct** as well. For example, \( \frac{3}{2} = 1.5 \), which is not an integer.

3. **Conclusion**:
- The statements that are not correct are Statements 3 and 4. However, since the question asks for one statement that is not correct, we can conclude that Statement 3 is the most commonly misunderstood one.

### Final Answer:
The statement that is not correct is: "The addition of any two irrational numbers can be an integer."