Let’s solve the given problem step by step.

Problem Summary:

• An 8-meter rope is divided.
• First, 18 pieces, each of $\frac{2}{5} \, \text{m}$, are cut.
• The remaining length is then divided into smaller pieces, each of $\frac{1}{5} \, \text{m}$.
• We need to find how many pieces of $\frac{1}{5} \, \text{m}$ are obtained.

Step 1: Calculate the total length used in the first cut

Each piece is $\frac{2}{5} \, \text{m}$, and there are 18 pieces.
The total length of rope used is:

$18 \times \frac{2}{5} = \frac{36}{5} \, \text{m}$

Simplify:

$\frac{36}{5} = 7.2 \, \text{m}$

Step 2: Calculate the remaining length of the rope

The original length of the rope is 8 meters, and 7.2 meters have been used.
The remaining length is:

$8 - 7.2 = 0.8 \, \text{m}$

Step 3: Divide the remaining length into smaller pieces

Each piece of the smaller length is $\frac{1}{5} \, \text{m}$.
The number of such pieces is:

$\frac{0.8}{\frac{1}{5}} = 0.8 \times 5 = 4$

Final Answer:

The remaining rope is divided into 4 pieces of $\frac{1}{5} \, \text{m}$ each.

Would you like a detailed explanation of any step or have further questions?

5 Related Questions:

1. How is multiplication of fractions applied in such problems?
2. How can the total length of a rope be represented in mixed fractions?
3. What if the rope's original length was not exactly divisible by the lengths given?
4. How can such division problems be visualized using diagrams or models?
5. What is the practical significance of unit conversion in problems like this?

Tip:

When working with fractions, ensure you use common denominators or simplify operations step by step to avoid errors.