A cord of length `71(1)/(2)m` has been cut into 26 pieces of equal length. What is the length of each piece?

Answer

To find the length of each piece of the cord, we need to divide the total length of the cord by the number of pieces it has been cut into.

### Step-by-step Solution:

**Step 1: Convert the mixed number to an improper fraction.**

The length of the cord is given as \( 71 \frac{1}{2} \) meters.

To convert this mixed number to an improper fraction:
- Multiply the whole number (71) by the denominator (2):
\[ 71 \times 2 = 142 \]
- Add the numerator (1) to this result:
\[ 142 + 1 = 143 \]
- Therefore, \( 71 \frac{1}{2} \) can be written as:
\[ \frac{143}{2} \text{ meters} \]

**Step 2: Divide the total length by the number of pieces.**

Now we need to divide \( \frac{143}{2} \) by 26. This can be expressed as:
\[ \text{Length of each piece} = \frac{143}{2} \div 26 \]

Dividing by a number is the same as multiplying by its reciprocal:
\[ \frac{143}{2} \div 26 = \frac{143}{2} \times \frac{1}{26} = \frac{143 \times 1}{2 \times 26} = \frac{143}{52} \]

**Step 3: Simplify the fraction if possible.**

Now we check if \( \frac{143}{52} \) can be simplified. The numerator (143) and the denominator (52) do not have any common factors other than 1, so this fraction is already in its simplest form.

**Step 4: Convert the improper fraction back to a mixed number (if needed).**

To convert \( \frac{143}{52} \) back to a mixed number:
- Divide 143 by 52:
\[ 143 \div 52 = 2 \quad \text{(whole number part)} \]
- Calculate the remainder:
\[ 143 - (52 \times 2) = 143 - 104 = 39 \]
- Therefore, \( \frac{143}{52} \) can be expressed as:
\[ 2 \frac{39}{52} \]

Thus, the length of each piece of the cord is \( 2 \frac{39}{52} \) meters.