Which of the following are negative rational number?
(i) `frac(-15)(-4)`
(ii) 0
(iii) `frac(-5)(7)`
(iv) `frac(4)(-9)`
(v) -6
(vi) `frac(1)(-2)`

Answer

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

### Step 1: Analyze `frac(-15)(-4)`
- The fraction `frac(-15)(-4)` has both the numerator and denominator as negative numbers.
- When we divide two negative numbers, the result is positive.
- Therefore, `frac(-15)(-4)` is **not a negative rational number**.

### Step 2: Analyze 0
- The number 0 is neither positive nor negative.
- It is considered a rational number but not a negative rational number.
- Therefore, 0 is **not a negative rational number**.

### Step 3: Analyze `frac(-5)(7)`
- The fraction `frac(-5)(7)` has a negative numerator and a positive denominator.
- A negative divided by a positive is negative.
- Therefore, `frac(-5)(7)` is a **negative rational number**.

### Step 4: Analyze `frac(4)(-9)`
- The fraction `frac(4)(-9)` has a positive numerator and a negative denominator.
- A positive divided by a negative is also negative.
- Therefore, `frac(4)(-9)` is a **negative rational number**.

### Step 5: Analyze -6
- The number -6 is a negative integer.
- It can be expressed as `frac(-6)(1)`, which is a negative rational number.
- Therefore, -6 is a **negative rational number**.

### Step 6: Analyze `frac(1)(-2)`
- The fraction `frac(1)(-2)` has a positive numerator and a negative denominator.
- A positive divided by a negative is negative.
- Therefore, `frac(1)(-2)` is a **negative rational number**.

### Summary of Results
- Negative rational numbers from the options are:
- (iii) `frac(-5)(7)`
- (iv) `frac(4)(-9)`
- (v) -6
- (vi) `frac(1)(-2)`

### Final Answer
The negative rational numbers are:
- `frac(-5)(7)`,
- `frac(4)(-9)`,
- -6,
- `frac(1)(-2)`.

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