Match column I to column II in the following:
`{:("Column I","Column II"),((i) (3)/(4) div (3)/(4) , (a) -1),((ii) (1)/(2) div (4)/(4) , (b) (-2)/(3) ),((iii) (2)/(3) div (-1) , (c) (3)/(2) ),((iv) (3)/(4) div (1)/(2), (d) (3)/(8)),((v) (5)/(7) div ((-5)/(7)), (e) 1):}`

Answer

To solve the problem of matching Column I to Column II, we will go through each division step by step.

### Step-by-Step Solution:

1. **First Part: \( \frac{3}{4} \div \frac{3}{4} \)**
To divide fractions, we multiply by the reciprocal of the second fraction:
\[ \frac{3}{4} \times \frac{4}{3} = \frac{3 \times 4}{4 \times 3} = \frac{12}{12} = 1 \]
**Match:** \( E \) (1)

2. **Second Part: \( \frac{1}{2} \div \frac{4}{4} \)**
Again, we multiply by the reciprocal:
\[ \frac{1}{2} \times \frac{4}{4} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} = \frac{1}{2} \]
**Match:** Not present in Column II, so we note it as \( \frac{1}{2} \).

3. **Third Part: \( \frac{2}{3} \div (-1) \)**
Dividing by -1 means we multiply by -1:
\[ \frac{2}{3} \times \frac{1}{-1} = -\frac{2}{3} \]
**Match:** \( B \) \( (-\frac{2}{3}) \)

4. **Fourth Part: \( \frac{3}{4} \div \frac{1}{2} \)**
Multiply by the reciprocal:
\[ \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2} \]
**Match:** \( C \) \( (\frac{3}{2}) \)

5. **Fifth Part: \( \frac{5}{7} \div \left(-\frac{5}{7}\right) \)**
Multiply by the reciprocal:
\[ \frac{5}{7} \times \left(-\frac{7}{5}\right) = -\frac{5 \times 7}{7 \times 5} = -1 \]
**Match:** \( A \) \( (-1) \)

### Final Matches:
- (i) \( \frac{3}{4} \div \frac{3}{4} \) → \( E \) (1)
- (ii) \( \frac{1}{2} \div \frac{4}{4} \) → Not present (1/2)
- (iii) \( \frac{2}{3} \div (-1) \) → \( B \) \( (-\frac{2}{3}) \)
- (iv) \( \frac{3}{4} \div \frac{1}{2} \) → \( C \) \( (\frac{3}{2}) \)
- (v) \( \frac{5}{7} \div \left(-\frac{5}{7}\right) \) → \( A \) \( (-1) \)