Verify whether the given statement is true or false:
(i) `(13)/(5) divide (26)/(10) = (26)/(10) divide (13)/(5)`
(ii) `-9 divide (3)/(4)=(3)/(4) divide (-9)`
(iii) `(-8)/(9) divide (-4)/(3)=(-4)/(3) divide (-8)/(9)`
(iv) `(-7)/(24) divide (3)/(-16) = (3)/(-16) divide (-7)/(24)`

Answer

Let's verify each of the statements step by step.

### (i) Verify if \( \frac{13}{5} \div \frac{26}{10} = \frac{26}{10} \div \frac{13}{5} \)

1. **Calculate \( \frac{13}{5} \div \frac{26}{10} \)**:
- Dividing by a fraction is the same as multiplying by its reciprocal.
- So, \( \frac{13}{5} \div \frac{26}{10} = \frac{13}{5} \times \frac{10}{26} \).
- Simplifying \( \frac{10}{26} = \frac{5}{13} \).
- Therefore, \( \frac{13}{5} \times \frac{5}{13} = 1 \).

2. **Calculate \( \frac{26}{10} \div \frac{13}{5} \)**:
- Similarly, \( \frac{26}{10} \div \frac{13}{5} = \frac{26}{10} \times \frac{5}{13} \).
- Simplifying \( \frac{26}{10} = \frac{13}{5} \).
- Therefore, \( \frac{13}{5} \times \frac{5}{13} = 1 \).

3. **Conclusion**:
- Since both sides equal 1, the statement is **True**.

### (ii) Verify if \( -9 \div \frac{3}{4} = \frac{3}{4} \div -9 \)

1. **Calculate \( -9 \div \frac{3}{4} \)**:
- This is the same as \( -9 \times \frac{4}{3} = -\frac{36}{3} = -12 \).

2. **Calculate \( \frac{3}{4} \div -9 \)**:
- This is the same as \( \frac{3}{4} \times \frac{-1}{9} = -\frac{3}{36} = -\frac{1}{12} \).

3. **Conclusion**:
- Since \( -12 \neq -\frac{1}{12} \), the statement is **False**.

### (iii) Verify if \( \frac{-8}{9} \div \frac{-4}{3} = \frac{-4}{3} \div \frac{-8}{9} \)

1. **Calculate \( \frac{-8}{9} \div \frac{-4}{3} \)**:
- This is the same as \( \frac{-8}{9} \times \frac{3}{-4} = \frac{8 \times 3}{9 \times 4} = \frac{24}{36} = \frac{2}{3} \).

2. **Calculate \( \frac{-4}{3} \div \frac{-8}{9} \)**:
- This is the same as \( \frac{-4}{3} \times \frac{9}{-8} = \frac{4 \times 9}{3 \times 8} = \frac{36}{24} = \frac{3}{2} \).

3. **Conclusion**:
- Since \( \frac{2}{3} \neq \frac{3}{2} \), the statement is **False**.

### (iv) Verify if \( \frac{-7}{24} \div \frac{3}{-16} = \frac{3}{-16} \div \frac{-7}{24} \)

1. **Calculate \( \frac{-7}{24} \div \frac{3}{-16} \)**:
- This is the same as \( \frac{-7}{24} \times \frac{-16}{3} = \frac{7 \times 16}{24 \times 3} = \frac{112}{72} = \frac{14}{9} \).

2. **Calculate \( \frac{3}{-16} \div \frac{-7}{24} \)**:
- This is the same as \( \frac{3}{-16} \times \frac{24}{-7} = \frac{3 \times 24}{16 \times 7} = \frac{72}{112} = \frac{9}{14} \).

3. **Conclusion**:
- Since \( \frac{14}{9} \neq \frac{9}{14} \), the statement is **False**.

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