A cable o f length 257 `1/4` m has to be cut into 21 pieces o f equal length. Fin d the length o f each piece.

Answer

To solve the problem of finding the length of each piece of cable when a total length of 257 \( \frac{1}{4} \) meters is cut into 21 equal pieces, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The total length of the cable is given as \( 257 \frac{1}{4} \) meters. We need to convert this mixed number into an improper fraction.

To convert \( 257 \frac{1}{4} \):
- Multiply the whole number (257) by the denominator (4):
\[ 257 \times 4 = 1028 \]
- Add the numerator (1) to this result:
\[ 1028 + 1 = 1029 \]
- Therefore, \( 257 \frac{1}{4} = \frac{1029}{4} \).

### Step 2: Set up the division
Now, we need to divide the total length by the number of pieces (21):
\[ \text{Length of each piece} = \frac{1029}{4} \div 21 \]

### Step 3: Convert the division into multiplication
To divide by a whole number, we can multiply by its reciprocal:
\[ \frac{1029}{4} \div 21 = \frac{1029}{4} \times \frac{1}{21} \]

### Step 4: Multiply the fractions
Now, we multiply the numerators and the denominators:
\[ \frac{1029 \times 1}{4 \times 21} = \frac{1029}{84} \]

### Step 5: Simplify the fraction
Next, we simplify \( \frac{1029}{84} \). We can find the greatest common divisor (GCD) of 1029 and 84.
- Dividing both by 21 (since 21 is a common factor):
\[ \frac{1029 \div 21}{84 \div 21} = \frac{49}{4} \]

### Step 6: Convert back to a mixed number (if needed)
The fraction \( \frac{49}{4} \) can be converted back to a mixed number:
- Divide 49 by 4:
\[ 49 \div 4 = 12 \quad \text{(whole number)} \]
with a remainder of 1. Thus, we have:
\[ 12 \frac{1}{4} \]

### Final Answer
The length of each piece is \( 12 \frac{1}{4} \) meters.

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