State whether the given statement is true or false:
(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) The quotient of two integers is always a rational number.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.

Answer

Let's analyze each statement one by one and determine whether they are true or false.

### Solution:

**(i) Zero is the smallest rational number.**
- **Explanation:** Rational numbers include all integers, fractions, and can be both positive and negative. On a number line, there are numbers less than zero (like -1, -2, etc.). Therefore, zero is not the smallest rational number.
- **Conclusion:** **False**

**(ii) Every integer is a rational number.**
- **Explanation:** An integer can be expressed as a fraction by placing it over 1. For example, the integer 5 can be written as 5/1, which is a rational number. Thus, all integers can be represented as rational numbers.
- **Conclusion:** **True**

**(iii) The quotient of two integers is always a rational number.**
- **Explanation:** The quotient of two integers (a/b) is a rational number as long as the denominator (b) is not zero. However, if the denominator is zero, the quotient is undefined. Therefore, this statement is not always true.
- **Conclusion:** **False**

**(iv) Every fraction is a rational number.**
- **Explanation:** A fraction is defined as the quotient of two integers, where the denominator is not zero. Therefore, all fractions are indeed rational numbers.
- **Conclusion:** **True**

**(v) Every rational number is a fraction.**
- **Explanation:** A rational number can be expressed as a fraction of two integers. For example, the rational number 3 can be expressed as 3/1. Thus, every rational number can be represented as a fraction.
- **Conclusion:** **True**

### Final Answers:
(i) False
(ii) True
(iii) False
(iv) True
(v) True