A construction worker needs to cut a board that is 7 1/4 feet long into pieces that are each 1/8 of a foot. How many pieces can the worker cut from the board?

To determine how many pieces the construction worker can cut from the board, we need to divide the total length of the board by the length of each piece.

### Given:
- The length of the board is 7 1/4 feet.
- Each piece is 1/8 of a foot.

### Step-by-step solution:
1. **Convert the mixed fraction 7 1/4 to an improper fraction:**
   \[
   7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}
   \]

2. **Set up the division:**
   We need to divide \(\frac{29}{4}\) by \(\frac{1}{8}\):
   \[
   \frac{29}{4} \div \frac{1}{8}
   \]

3. **Multiply by the reciprocal:**
   Dividing by a fraction is the same as multiplying by its reciprocal:
   \[
   \frac{29}{4} \times \frac{8}{1} = \frac{29 \times 8}{4 \times 1} = \frac{232}{4}
   \]

4. **Simplify the result:**
   \[
   \frac{232}{4} = 58
   \]

Thus, the worker can cut **58 pieces** from the board.

Would you like further details on this or have any other questions?

Here are 5 related questions you could explore:
1. What if the board was 8 1/2 feet long instead?
2. How many pieces can be cut if each piece is 1/4 of a foot?
3. If the worker needs an extra foot of board, how many more pieces can be cut?
4. How would the number of pieces change if each piece were 1/16 of a foot?
5. How many total pieces can be cut from 3 boards of the same length?

**Tip:** Converting mixed numbers to improper fractions simplifies division involving fractions.

Find out how many pieces can be cut from a 7 1/4 feet long board if each piece is 1/8 of a foot. This problem teaches fraction division, including converting mixed numbers to improper fractions and multiplying by reciprocals. Perfect for students in Grades 5-7.

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