To determine the leftover length after a carpenter cuts three pieces of 4 feet 6 inches from a 14-foot board, let's follow these steps:

1. Convert Measurements for Easier Calculation:

   • Each piece cut is 4 feet 6 inches. Converting this to inches: $4 \text{ feet} = 4 \times 12 = 48 \text{ inches}$ $4 \text{ feet 6 inches} = 48 + 6 = 54 \text{ inches}$
   • The board is 14 feet in total length. Converting this to inches: $14 \text{ feet} = 14 \times 12 = 168 \text{ inches}$

2. Calculate the Total Length Cut:

   • Three pieces of 4 feet 6 inches (54 inches) are cut: $3 \times 54 = 162 \text{ inches}$

3. Find the Remaining Length:

   • Subtract the total length cut from the original length of the board: $168 - 162 = 6 \text{ inches}$

4. Convert the Remaining Length Back to Feet and Inches:

   • The leftover piece is 6 inches.

Answer

The piece left over is 6 inches.

Would you like further details, or do you have any questions?

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Here are some related questions for further exploration:

1. How would the leftover piece change if each cut was 5 feet instead of 4 feet 6 inches?
2. How can we calculate remaining lengths quickly when given measurements in mixed units?
3. If the board length was increased to 20 feet, how much would be left over after the same cuts?
4. What is the advantage of converting lengths to a single unit before performing calculations?
5. How would you solve the problem if the cuts were 4 feet 8 inches instead of 4 feet 6 inches?

Tip: Converting all measurements to a single unit before calculating can simplify operations with mixed units.