Which of the following statements are true?
(i) `frac(-3)(5)` lies to the left of 0 on the number line.
(ii) `frac(-12)(7)` lies to the right of 0 on the number line.
(iii) `frac(1)(3)("and")frac(-5)(2)` lies to opposite side of 0 on the number line.
(iv) `frac(-18)(-13)` lies to the left of 0 on the number line.
(v) `frac(-5)(-8)` lies on the right of `frac(-5)(7)` on the number line.

Answer

To determine which of the statements are true, we will analyze each statement one by one.

**Step 1: Analyze Statement (i)**
Statement: \(-\frac{3}{5}\) lies to the left of 0 on the number line.
- Since \(-\frac{3}{5}\) is a negative number, it will indeed lie to the left of 0.
**Conclusion:** This statement is **True**.

**Step 2: Analyze Statement (ii)**
Statement: \(-\frac{12}{7}\) lies to the right of 0 on the number line.
- \(-\frac{12}{7}\) is also a negative number, so it will lie to the left of 0.
**Conclusion:** This statement is **False**.

**Step 3: Analyze Statement (iii)**
Statement: \(\frac{1}{3}\) and \(-\frac{5}{2}\) lie on opposite sides of 0 on the number line.
- \(\frac{1}{3}\) is positive and will be to the right of 0, while \(-\frac{5}{2}\) is negative and will be to the left of 0.
**Conclusion:** This statement is **True**.

**Step 4: Analyze Statement (iv)**
Statement: \(-\frac{18}{-13}\) lies to the left of 0 on the number line.
- \(-\frac{18}{-13}\) simplifies to \(\frac{18}{13}\), which is positive and will lie to the right of 0.
**Conclusion:** This statement is **False**.

**Step 5: Analyze Statement (v)**
Statement: \(-\frac{5}{-8}\) lies on the right of \(-\frac{5}{7}\) on the number line.
- \(-\frac{5}{-8}\) simplifies to \(\frac{5}{8}\), which is positive and lies to the right of 0.
- \(-\frac{5}{7}\) is negative and lies to the left of 0. Since \(\frac{5}{8}\) is positive, it will indeed lie to the right of \(-\frac{5}{7}\).
**Conclusion:** This statement is **True**.

**Final Results:**
1. True
2. False
3. True
4. False
5. True