Which of the following statements are true and which are false?
(i) `(-3)/(5)` lies to the left of 0 on the number line.
(ii) `(-12)/(7)` lies to the right of 0 on the number line.
(iii) The rational numbers `(1)/(3) and (-5)/(2)` are on opposite sides of 0 on the number line.
(iv) The rational number `(-18)/(-13)` lies to the left of 0 on the number line.

Answer

To determine whether each statement is true or false, we will analyze each statement step by step.

### Step 1: Analyze Statement (i)
**Statement:** `(-3)/(5)` lies to the left of 0 on the number line.

- **Analysis:** The number `(-3)/(5)` is a negative number because it has a negative numerator. On the number line, negative numbers lie to the left of 0.
- **Conclusion:** This statement is **True**.

### Step 2: Analyze Statement (ii)
**Statement:** `(-12)/(7)` lies to the right of 0 on the number line.

- **Analysis:** The number `(-12)/(7)` is also a negative number since it has a negative numerator. Negative numbers lie to the left of 0 on the number line.
- **Conclusion:** This statement is **False**.

### Step 3: Analyze Statement (iii)
**Statement:** The rational numbers `(1)/(3)` and `(-5)/(2)` are on opposite sides of 0 on the number line.

- **Analysis:** The number `(1)/(3)` is positive, while `(-5)/(2)` is negative. Positive numbers lie to the right of 0, and negative numbers lie to the left of 0. Since one is positive and the other is negative, they are indeed on opposite sides of 0.
- **Conclusion:** This statement is **True**.

### Step 4: Analyze Statement (iv)
**Statement:** The rational number `(-18)/(-13)` lies to the left of 0 on the number line.

- **Analysis:** The expression `(-18)/(-13)` simplifies to a positive number because a negative divided by a negative is positive. Positive numbers lie to the right of 0 on the number line.
- **Conclusion:** This statement is **False**.

### Summary of Results
- (i) True
- (ii) False
- (iii) True
- (iv) False

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