Certainly! Let's go through the solution step by step to determine the length of the remaining rope.
### Given:
1. Initial length of the rope: [tex]\(20 \frac{1}{2} \, \text{meters}\)[/tex]
2. Length of the piece cut off: [tex]\(3 \frac{5}{8} \, \text{meters}\)[/tex]
### Step 1: Convert the mixed numbers to improper fractions (decimal form is also acceptable):
- Initial length of the rope:
[tex]\[
20 \frac{1}{2} = 20 + \frac{1}{2} = 20.5 \, \text{meters}
\][/tex]
- Length of the piece cut off:
[tex]\[
3 \frac{5}{8} = 3 + \frac{5}{8} = 3.625 \, \text{meters}
\][/tex]
### Step 2: Subtract the length of the piece cut off from the initial length of the rope to find the remaining length:
[tex]\[
\text{Remaining length of the rope} = 20.5 \, \text{meters} - 3.625 \, \text{meters}
\][/tex]
### Step 3: Perform the subtraction:
[tex]\[
20.5 - 3.625 = 16.875 \, \text{meters}
\][/tex]
### Final Answer:
The length of the remaining rope is [tex]\(16.875 \, \text{meters}\)[/tex].
