Question
A piece of fabric is 4 14 yards long. If it’s cut into pieces that are each 34 yard long, there will be ____ pieces.
Answers
GPT-4o mini
To find out how many pieces of fabric you can cut from a piece that is \(4 \frac{1}{4}\) yards long, we first need to convert \(4 \frac{1}{4}\) yards into an improper fraction.
1. Convert \(4 \frac{1}{4}\) to an improper fraction:
\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4}
\]
2. The length of each piece is \(\frac{3}{4}\) yard. We need to divide the total length by the length of each piece:
\[
\text{Number of pieces} = \frac{\text{Total length}}{\text{Length of each piece}} = \frac{\frac{17}{4}}{\frac{3}{4}}
\]
3. Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{17}{4} \div \frac{3}{4} = \frac{17}{4} \times \frac{4}{3} = \frac{17 \times 4}{4 \times 3} = \frac{17}{3}
\]
4. Now we can convert \(\frac{17}{3}\) to a mixed number:
\[
17 \div 3 = 5 \quad \text{(with a remainder of 2)}
\]
So, \(\frac{17}{3} = 5 \frac{2}{3}\).
This tells us that you can cut **5 full pieces** of fabric, with a remainder of \(\frac{2}{3}\) yards left over, which is not enough for another full piece.
Thus, the answer is that there will be **5 pieces**.
1. Convert \(4 \frac{1}{4}\) to an improper fraction:
\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4}
\]
2. The length of each piece is \(\frac{3}{4}\) yard. We need to divide the total length by the length of each piece:
\[
\text{Number of pieces} = \frac{\text{Total length}}{\text{Length of each piece}} = \frac{\frac{17}{4}}{\frac{3}{4}}
\]
3. Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{17}{4} \div \frac{3}{4} = \frac{17}{4} \times \frac{4}{3} = \frac{17 \times 4}{4 \times 3} = \frac{17}{3}
\]
4. Now we can convert \(\frac{17}{3}\) to a mixed number:
\[
17 \div 3 = 5 \quad \text{(with a remainder of 2)}
\]
So, \(\frac{17}{3} = 5 \frac{2}{3}\).
This tells us that you can cut **5 full pieces** of fabric, with a remainder of \(\frac{2}{3}\) yards left over, which is not enough for another full piece.
Thus, the answer is that there will be **5 pieces**.