Which of the two rational number is greater in each of the following pairs?
(i) `frac(5)(6)("or")0`
(ii) `frac(-3)(5)("or")0`
(iii) `frac(5)(8)("or")frac(3)(8)`
(iv) `frac(7)(9)("or")frac(-5)(9)`
(v) `frac(-6)(11)("or")frac(5)(-11)`
(vi) `frac(-15)(4)("or")frac(-17)(4)`

Answer

Let's solve the question step by step.

### Step 1: Compare `frac(5)(6)` and `0`
- **Solution**: `frac(5)(6)` is a positive rational number (approximately 0.833), and `0` is neither positive nor negative. Since all positive numbers are greater than zero, we conclude that:
\[ \frac{5}{6} > 0 \]

### Step 2: Compare `frac(-3)(5)` and `0`
- **Solution**: `frac(-3)(5)` is a negative rational number (approximately -0.6). Since zero is greater than all negative numbers, we conclude that:
\[ \frac{-3}{5} < 0 \]

### Step 3: Compare `frac(5)(8)` and `frac(3)(8)`
- **Solution**: Both fractions have the same denominator (8). To compare them, we only need to look at the numerators. Since `5` is greater than `3`, we conclude that:
\[ \frac{5}{8} > \frac{3}{8} \]

### Step 4: Compare `frac(7)(9)` and `frac(-5)(9)`
- **Solution**: `frac(7)(9)` is a positive rational number, while `frac(-5)(9)` is a negative rational number. Since all positive numbers are greater than negative numbers, we conclude that:
\[ \frac{7}{9} > \frac{-5}{9} \]

### Step 5: Compare `frac(-6)(11)` and `frac(5)(-11)`
- **Solution**: The fraction `frac(5)(-11)` can be rewritten as `frac(-5)(11)`. Now we compare `frac(-6)(11)` and `frac(-5)(11)`. Both are negative, and since `-6` is less than `-5`, we conclude that:
\[ \frac{-6}{11} < \frac{-5}{11} \]

### Step 6: Compare `frac(-15)(4)` and `frac(-17)(4)`
- **Solution**: Both fractions have the same denominator (4). To compare them, we only need to look at the numerators. Since `-15` is greater than `-17` (in the context of negative numbers), we conclude that:
\[ \frac{-15}{4} > \frac{-17}{4} \]

### Summary of Results:
1. \( \frac{5}{6} > 0 \)
2. \( \frac{-3}{5} < 0 \)
3. \( \frac{5}{8} > \frac{3}{8} \)
4. \( \frac{7}{9} > \frac{-5}{9} \)
5. \( \frac{-6}{11} < \frac{-5}{11} \)
6. \( \frac{-15}{4} > \frac{-17}{4} \)