To determine how long each section of the wooden board is after it has been cut into 3 equal parts, we need to follow these steps:
1. Determine the total length of the board: We are given that the total length of the board is [tex]\(\frac{3}{5}\)[/tex] of a meter.
2. Identify the number of equal parts: We are told that Darren cuts the board into 3 equal parts.
3. Calculate the length of each part:
- To find the length of each individual part, we divide the total length of the board by the number of equal parts. This involves dividing [tex]\(\frac{3}{5}\)[/tex] by 3.
- In mathematical terms, this is:
[tex]\[
\text{Length of each part} = \frac{\frac{3}{5}}{3}
\][/tex]
4. Perform the division:
- Dividing a fraction by a whole number can be carried out by multiplying the fraction by the reciprocal of the whole number.
- The reciprocal of 3 is [tex]\(\frac{1}{3}\)[/tex].
- Therefore:
[tex]\[
\frac{\frac{3}{5}}{3} = \frac{3}{5} \times \frac{1}{3} = \frac{3 \times 1}{5 \times 3} = \frac{3}{15} = \frac{1}{5}
\][/tex]
Therefore, each part of the board is [tex]\(\frac{1}{5}\)[/tex] of a meter long. Hence, the correct answer is:
[tex]\[
\boxed{\frac{1}{5} \text{ m}}
\][/tex]
