Question
How many 5/16foot pieces of wood can you cut from a board that is 1 9/16 feet long?
A
1/5pieces of wood
B
125/256 pieces of wood
C
5 pieces of wood
D
3 pieces of wood
Answers
GPT-4o mini
To determine how many \( \frac{5}{16} \)-foot pieces of wood can be cut from a board that is \( 1 \frac{9}{16} \) feet long, we first need to convert \( 1 \frac{9}{16} \) into an improper fraction.
1. Convert \( 1 \frac{9}{16} \):
\[
1 \frac{9}{16} = \frac{16}{16} + \frac{9}{16} = \frac{25}{16}
\]
2. Now divide the total length by the length of each piece:
\[
\text{Number of pieces} = \frac{\frac{25}{16}}{\frac{5}{16}} = \frac{25}{16} \times \frac{16}{5}
\]
The \( \frac{16}{16} \) cancels out:
\[
\frac{25}{5} = 5
\]
Thus, you can cut **5 pieces** of wood that are \( \frac{5}{16} \) feet each from a board that is \( 1 \frac{9}{16} \) feet long.
The correct answer is:
**C. 5 pieces of wood**
1. Convert \( 1 \frac{9}{16} \):
\[
1 \frac{9}{16} = \frac{16}{16} + \frac{9}{16} = \frac{25}{16}
\]
2. Now divide the total length by the length of each piece:
\[
\text{Number of pieces} = \frac{\frac{25}{16}}{\frac{5}{16}} = \frac{25}{16} \times \frac{16}{5}
\]
The \( \frac{16}{16} \) cancels out:
\[
\frac{25}{5} = 5
\]
Thus, you can cut **5 pieces** of wood that are \( \frac{5}{16} \) feet each from a board that is \( 1 \frac{9}{16} \) feet long.
The correct answer is:
**C. 5 pieces of wood**