Suman bought `12(1)/(2)m` of cloth and gave it to the tailor to stitch shirts. If each shirt requires `2(1)/(2)m` of cloth, how many shirts did the tailor stitch?

Answer

To solve the problem step by step, we will first convert the mixed numbers into improper fractions, perform the division, and then interpret the result.

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- Suman bought \(12 \frac{1}{2} m\) of cloth.
- To convert this to an improper fraction:
\[ 12 \frac{1}{2} = \frac{12 \times 2 + 1}{2} = \frac{24 + 1}{2} = \frac{25}{2} m \]
- Each shirt requires \(2 \frac{1}{2} m\) of cloth.
- To convert this to an improper fraction:
\[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} m \]

2. **Set Up the Division**:
- We need to find out how many shirts can be made with the total cloth. This is done by dividing the total cloth by the cloth required for one shirt:
\[ \text{Number of shirts} = \frac{\text{Total cloth}}{\text{Cloth per shirt}} = \frac{\frac{25}{2}}{\frac{5}{2}} \]

3. **Perform the Division**:
- When dividing fractions, we multiply by the reciprocal of the divisor:
\[ \frac{25}{2} \div \frac{5}{2} = \frac{25}{2} \times \frac{2}{5} \]
- Now, we can simplify:
\[ = \frac{25 \times 2}{2 \times 5} = \frac{25}{5} = 5 \]

4. **Conclusion**:
- Therefore, the tailor can stitch **5 shirts**.