Which of the following are negative rational numbers?
(i) `-16/5`, (ii) `-10/(-11)`, (iii) -21, (iv) `0/(-3)`, (v) 17

Answer

To determine which of the given numbers are negative rational numbers, we will analyze each option step by step.

### Step 1: Analyze the first number `-16/5`
- The numerator is `-16` (negative) and the denominator is `5` (positive).
- Since the numerator and denominator have different signs, `-16/5` is a negative rational number.

### Step 2: Analyze the second number `-10/(-11)`
- The numerator is `-10` (negative) and the denominator is `-11` (negative).
- Both the numerator and denominator are negative, so we can simplify this as `10/11`, which is a positive rational number.
- Therefore, `-10/(-11)` is **not** a negative rational number.

### Step 3: Analyze the third number `-21`
- We can express `-21` as `-21/1`.
- The numerator is `-21` (negative) and the denominator is `1` (positive).
- Since the numerator and denominator have different signs, `-21` is a negative rational number.

### Step 4: Analyze the fourth number `0/(-3)`
- The numerator is `0` and the denominator is `-3` (negative).
- A number with a numerator of `0` is neither positive nor negative, so `0/(-3)` is **not** a negative rational number.

### Step 5: Analyze the fifth number `17`
- We can express `17` as `17/1`.
- The numerator is `17` (positive) and the denominator is `1` (positive).
- Since both the numerator and denominator are positive, `17` is **not** a negative rational number.

### Conclusion:
The negative rational numbers from the given options are:
- (i) `-16/5`
- (iii) `-21`

### Summary of Results:
- Negative Rational Numbers: `-16/5`, `-21`
- Not Negative Rational Numbers: `-10/(-11)`, `0/(-3)`, `17`

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