Question
Alex has a piece of fabric that is 56 inches long and 3 inches wide. He cuts it into pieces that are each 7 inches long and 1 inch wide.
What is the greatest number of 7 inch by 1 inch pieces that Alex can get?
What is the greatest number of 7 inch by 1 inch pieces that Alex can get?
Answers
GPT-4o mini
To find the greatest number of 7-inch by 1-inch pieces that Alex can cut from a piece of fabric that is 56 inches long and 3 inches wide, we need to consider both the length and the width of the fabric.
**Step 1: Calculate the length.**
Alex's fabric is 56 inches long, and each piece he wants to cut is 7 inches long. To find out how many 7-inch pieces he can cut from 56 inches, we perform the following division:
\[
\text{Number of pieces by length} = \frac{56 \text{ inches}}{7 \text{ inches per piece}} = 8
\]
**Step 2: Calculate the width.**
The width of the fabric is 3 inches, and since each piece is 1 inch wide, we can determine how many 1-inch wide pieces can fit across the width of the fabric:
\[
\text{Number of pieces by width} = \frac{3 \text{ inches}}{1 \text{ inch per piece}} = 3
\]
**Step 3: Calculate the total pieces.**
Now, to find the total number of pieces Alex can obtain, we multiply the number of pieces he can get by length and the number he can get by width:
\[
\text{Total number of pieces} = (\text{Number of pieces by length}) \times (\text{Number of pieces by width}) = 8 \times 3 = 24
\]
Therefore, the greatest number of 7-inch by 1-inch pieces that Alex can get is \(\boxed{24}\).
**Step 1: Calculate the length.**
Alex's fabric is 56 inches long, and each piece he wants to cut is 7 inches long. To find out how many 7-inch pieces he can cut from 56 inches, we perform the following division:
\[
\text{Number of pieces by length} = \frac{56 \text{ inches}}{7 \text{ inches per piece}} = 8
\]
**Step 2: Calculate the width.**
The width of the fabric is 3 inches, and since each piece is 1 inch wide, we can determine how many 1-inch wide pieces can fit across the width of the fabric:
\[
\text{Number of pieces by width} = \frac{3 \text{ inches}}{1 \text{ inch per piece}} = 3
\]
**Step 3: Calculate the total pieces.**
Now, to find the total number of pieces Alex can obtain, we multiply the number of pieces he can get by length and the number he can get by width:
\[
\text{Total number of pieces} = (\text{Number of pieces by length}) \times (\text{Number of pieces by width}) = 8 \times 3 = 24
\]
Therefore, the greatest number of 7-inch by 1-inch pieces that Alex can get is \(\boxed{24}\).