Which of the two rational numbers is greater in each of the following pairs?
(i) `3/(-8)` or 0, (ii) `1/19` or 0

Answer

Let's solve the question step by step.

### Step 1: Compare the first pair of rational numbers: \( \frac{3}{-8} \) and 0.

1. **Identify the sign of \( \frac{3}{-8} \)**:
- The numerator is 3 (positive) and the denominator is -8 (negative).
- When a positive number is divided by a negative number, the result is negative.
- Therefore, \( \frac{3}{-8} = -\frac{3}{8} \).

2. **Compare \( -\frac{3}{8} \) with 0**:
- We know that all negative numbers are less than 0.
- Since \( -\frac{3}{8} \) is negative, it is less than 0.

**Conclusion for the first pair**:
- \( 0 \) is greater than \( -\frac{3}{8} \).

### Step 2: Compare the second pair of rational numbers: \( \frac{1}{19} \) and 0.

1. **Identify the sign of \( \frac{1}{19} \)**:
- The numerator is 1 (positive) and the denominator is 19 (positive).
- When a positive number is divided by another positive number, the result is positive.
- Therefore, \( \frac{1}{19} \) is a positive number.

2. **Compare \( \frac{1}{19} \) with 0**:
- We know that all positive numbers are greater than 0.
- Since \( \frac{1}{19} \) is positive, it is greater than 0.

**Conclusion for the second pair**:
- \( \frac{1}{19} \) is greater than \( 0 \).

### Final Answers:
- For the first pair: \( 0 > -\frac{3}{8} \)
- For the second pair: \( \frac{1}{19} > 0 \)

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