To determine how many full [tex]\( 4 \frac{3}{4} \)[/tex]-inch sheets can be cut from a [tex]\( 23 \frac{5}{8} \)[/tex]-inch stock, we need to follow these steps:
1. Convert the mixed fractions to improper fractions or decimals:
- First, convert [tex]\( 23 \frac{5}{8} \)[/tex] to a decimal format:
[tex]\[
23 + \frac{5}{8} = 23 + 0.625 = 23.625 \text{ inches}
\][/tex]
- Similarly, convert [tex]\( 4 \frac{3}{4} \)[/tex] to a decimal:
[tex]\[
4 + \frac{3}{4} = 4 + 0.75 = 4.75 \text{ inches}
\][/tex]
2. Divide the total stock length by the length of one sheet:
[tex]\[
\frac{23.625}{4.75}
\][/tex]
When you perform the division, you get the number of full sheets that can be cut:
[tex]\[
23.625 \div 4.75 = 4.0
\][/tex]
This means we can cut 4 full [tex]\( 4.75 \)[/tex]-inch sheets from the [tex]\( 23.625 \)[/tex]-inch stock.
3. Calculate the remaining stock after cutting full sheets:
- Multiply the number of full sheets by the length of one sheet:
[tex]\[
4 \times 4.75 = 19 \text{ inches}
\][/tex]
- Subtract this from the total stock length to find the remaining stock:
[tex]\[
23.625 - 19 = 4.625 \text{ inches}
\][/tex]
So, the detailed results are:
- The total stock length is [tex]\( 23.625 \)[/tex] inches.
- Each sheet is [tex]\( 4.75 \)[/tex] inches long.
- We can cut [tex]\( 4 \)[/tex] full sheets.
- The remaining stock after cutting the full sheets is [tex]\( 4.625 \)[/tex] inches.
Therefore, you can cut 4 full [tex]\( 4 \frac{3}{4} \)[/tex]-inch sheets from the [tex]\( 23 \frac{5}{8} \)[/tex]-inch stock, with [tex]\( 4 \frac{5}{8} \)[/tex] inches of stock remaining.
