To find the maximum number of [tex]\(6 \frac{3}{4}\)[/tex]-inch strips that can be cut from a spool of ribbon that is 10 yards long, we need to follow several steps:
1. Convert the length of the ribbon from yards to inches.
- 1 yard is equal to 36 inches.
- Therefore, 10 yards is [tex]\(10 \times 36 = 360\)[/tex] inches.
2. Convert the length of each strip to a decimal for easier calculation.
- The length of each strip is [tex]\(6 \frac{3}{4}\)[/tex] inches.
- [tex]\(6 \frac{3}{4}\)[/tex] can be written as a mixed fraction, which is equal to [tex]\(6 + \frac{3}{4}\)[/tex].
- Converting [tex]\(\frac{3}{4}\)[/tex] to a decimal, we get [tex]\(0.75\)[/tex].
- So, [tex]\(6 \frac{3}{4} = 6 + 0.75 = 6.75\)[/tex] inches.
3. Calculate the maximum number of strips that can be cut from the ribbon.
- We take the total length of the ribbon in inches and divide it by the length of one strip.
- This gives us [tex]\(\frac{360}{6.75}\)[/tex].
The division of [tex]\(360\)[/tex] by [tex]\(6.75\)[/tex] results in approximately 53.3333. Since we are looking for the maximum number of complete strips that can be cut, we take the integer part of this result, which is 53.
Thus, the maximum number of [tex]\(6 \frac{3}{4}\)[/tex]-inch strips we can cut from a 10-yard long ribbon is [tex]\(\boxed{53}\)[/tex].
