Which of the following are rational numbers?
(i) `5/15`, (ii) `-6/23`, (iii) 17, (iv) -25, (v) 0

Answer

To determine which of the given numbers are rational numbers, we will follow the definition of rational numbers. A rational number is defined as a number that can be expressed in the form of \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

Let's analyze each number one by one:

1. **Number: \( \frac{5}{15} \)**
- This is already in the form \( \frac{p}{q} \) where \( p = 5 \) and \( q = 15 \).
- Since \( q \neq 0 \), \( \frac{5}{15} \) is a rational number.

2. **Number: \( -\frac{6}{23} \)**
- This is also in the form \( \frac{p}{q} \) where \( p = -6 \) and \( q = 23 \).
- Again, \( q \neq 0 \), so \( -\frac{6}{23} \) is a rational number.

3. **Number: 17**
- We can express 17 as \( \frac{17}{1} \).
- Here, \( p = 17 \) and \( q = 1 \), and since \( q \neq 0 \), 17 is a rational number.

4. **Number: -25**
- We can express -25 as \( \frac{-25}{1} \).
- Here, \( p = -25 \) and \( q = 1 \), and since \( q \neq 0 \), -25 is a rational number.

5. **Number: 0**
- We can express 0 as \( \frac{0}{1} \).
- Here, \( p = 0 \) and \( q = 1 \), and since \( q \neq 0 \), 0 is a rational number.

Now, we can conclude that all the given numbers are rational numbers.

### Summary:
- (i) \( \frac{5}{15} \) - Rational
- (ii) \( -\frac{6}{23} \) - Rational
- (iii) 17 - Rational
- (iv) -25 - Rational
- (v) 0 - Rational