A rope of length `9 3/4`m is cut into 6 pieces of equal length. Find the length of each piece

Answer

To find the length of each piece of rope when a rope of length \(9 \frac{3}{4}\) meters is cut into 6 equal pieces, we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The length of the rope is given as \(9 \frac{3}{4}\) meters. We need to convert this mixed number into an improper fraction.

\[ 9 \frac{3}{4} = \frac{(9 \times 4) + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4} \]

### Step 2: Divide the improper fraction by the number of pieces
Now that we have the length of the rope as an improper fraction, we will divide it by the number of pieces (which is 6).

\[ \text{Length of each piece} = \frac{39}{4} \div 6 \]

### Step 3: Convert the division into multiplication
To divide by a whole number, we can multiply by its reciprocal. The reciprocal of 6 is \(\frac{1}{6}\).

\[ \frac{39}{4} \div 6 = \frac{39}{4} \times \frac{1}{6} \]

### Step 4: Multiply the fractions
Now we multiply the numerators and the denominators.

\[ \frac{39 \times 1}{4 \times 6} = \frac{39}{24} \]

### Step 5: Simplify the fraction
Next, we need to simplify \(\frac{39}{24}\). We can find the greatest common divisor (GCD) of 39 and 24, which is 3.

\[ \frac{39 \div 3}{24 \div 3} = \frac{13}{8} \]

### Step 6: Convert back to a mixed number (if necessary)
The fraction \(\frac{13}{8}\) can be converted back to a mixed number:

\[ \frac{13}{8} = 1 \frac{5}{8} \]

### Final Answer
Thus, the length of each piece of rope is \(1 \frac{5}{8}\) meters.

---