A log of wood 6 `2/7` m in length, was cut into 11 pieces. What is the length of each piece?

Answer

To find the length of each piece of wood when a log of wood measuring 6 \( \frac{2}{7} \) meters is cut into 11 pieces, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction.
The length of the log is given as \( 6 \frac{2}{7} \) meters. To convert this mixed fraction into an improper fraction, we can use the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]
Here, the whole number is 6, the numerator is 2, and the denominator is 7.

Calculating this gives:
\[ 6 \times 7 + 2 = 42 + 2 = 44 \]
So, the improper fraction is:
\[ \frac{44}{7} \text{ meters} \]

### Step 2: Divide the improper fraction by the number of pieces.
Next, we need to divide the total length of the log by the number of pieces (11):
\[ \text{Length of each piece} = \frac{44}{7} \div 11 \]

### Step 3: Convert the division into multiplication by the reciprocal.
To divide by a whole number, we can multiply by its reciprocal. The reciprocal of 11 is \( \frac{1}{11} \):
\[ \frac{44}{7} \div 11 = \frac{44}{7} \times \frac{1}{11} \]

### Step 4: Multiply the fractions.
Now, we can multiply the fractions:
\[ \frac{44 \times 1}{7 \times 11} = \frac{44}{77} \]

### Step 5: Simplify the fraction.
Next, we simplify \( \frac{44}{77} \). Both the numerator and the denominator can be divided by 11:
\[ \frac{44 \div 11}{77 \div 11} = \frac{4}{7} \]

### Conclusion:
The length of each piece of wood is \( \frac{4}{7} \) meters.

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