A rope of length `13 1/2` m has been divided into 9 pieces of the same length. What is the length of each piece?

Answer

To find the length of each piece of the rope, we need to divide the total length of the rope by the number of pieces. Let's go through the steps together.

### Step-by-Step Solution:

1. **Convert the Mixed Number to an Improper Fraction:**
The length of the rope is given as \( 13 \frac{1}{2} \) meters. To convert this into an improper fraction:
\[ 13 \frac{1}{2} = \frac{(13 \times 2) + 1}{2} = \frac{26 + 1}{2} = \frac{27}{2} \text{ meters} \]

2. **Determine the Number of Pieces:**
The rope is divided into 9 equal pieces.

3. **Calculate the Length of Each Piece:**
To find the length of each piece, we divide the total length of the rope by the number of pieces:
\[ \text{Length of each piece} = \frac{\text{Total Length}}{\text{Number of Pieces}} = \frac{\frac{27}{2}}{9} \]

4. **Simplify the Division:**
Dividing by a whole number can be done by multiplying by the reciprocal:
\[ \frac{\frac{27}{2}}{9} = \frac{27}{2} \times \frac{1}{9} = \frac{27 \times 1}{2 \times 9} = \frac{27}{18} \]

5. **Reduce the Fraction:**
Now we simplify \( \frac{27}{18} \):
\[ \frac{27}{18} = \frac{3}{2} \text{ (dividing both numerator and denominator by 9)} \]

6. **Convert Back to a Mixed Number (if needed):**
The fraction \( \frac{3}{2} \) can be converted back to a mixed number:
\[ \frac{3}{2} = 1 \frac{1}{2} \text{ meters} \]

### Final Answer:
The length of each piece of the rope is \( 1 \frac{1}{2} \) meters.

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