To determine the length of the remaining rope, we need to subtract the lengths of the two pieces that were cut off from the original length of the rope.

1. The original length of the rope is 11 meters.
2. The two pieces cut off are of lengths $\frac{13}{5}$ meters and $\frac{33}{10}$ meters.

Step 1: Convert both fractions to decimals or equivalent fractions.

• $\frac{13}{5} = 2.6$ meters
• $\frac{33}{10} = 3.3$ meters

Step 2: Add the lengths of the two cut pieces.

$2.6 + 3.3 = 5.9 \, \text{meters}$

Step 3: Subtract the total length of the cut pieces from the original length of the rope.

$11 - 5.9 = 5.1 \, \text{meters}$

Thus, the length of the remaining rope is 5.1 meters.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:

1. How do you convert fractions into decimals?
2. What are the steps to subtract mixed numbers from whole numbers?
3. How can we calculate the remaining length if the rope was cut into three pieces?
4. How would the problem change if one of the fractions was improper?
5. What if the original rope length was in a different unit like feet or inches?

Tip: Always double-check your units to ensure accuracy when working with measurements.