To determine the length of the other piece of rope, follow these steps carefully:
1. Convert the mixed fraction to an improper fraction:
The initial length of the rope is [tex]\(5 \frac{2}{3}\)[/tex] meters.
- Convert [tex]\(5 \frac{2}{3}\)[/tex] to an improper fraction:
[tex]\[
5 \frac{2}{3} = 5 + \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{15 + 2}{3} = \frac{17}{3}
\][/tex]
2. Evaluate the total length in decimal form:
Convert [tex]\( \frac{17}{3} \)[/tex] to a decimal:
[tex]\[
\frac{17}{3} = 5.666666666666667 \text{ meters}
\][/tex]
3. Given length of one piece:
The length of one piece is given as [tex]\( \frac{1}{4} \)[/tex] meters.
- Convert [tex]\( \frac{1}{4} \)[/tex] to a decimal:
[tex]\[
\frac{1}{4} = 0.25 \text{ meters}
\][/tex]
4. Calculate the length of the other piece:
The total original length of the rope is the sum of the lengths of the two pieces. Therefore, to find the length of the other piece, subtract the length of the given piece from the total length:
[tex]\[
\text{Length of the other piece} = 5.666666666666667 - 0.25
\][/tex]
- Perform the subtraction:
[tex]\[
5.666666666666667 - 0.25 = 5.416666666666667 \text{ meters}
\][/tex]
So, the length of the other piece of rope is [tex]\(5.416666666666667\)[/tex] meters.
