To solve this problem step-by-step, follow these instructions:
1. Convert the Mixed Number to an Improper Fraction:
- The length of the wire is given as [tex]\(6 \frac{1}{2}\)[/tex] meters.
- A mixed number can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction part, then adding the numerator of the fraction part to the product.
- [tex]\(6 \frac{1}{2}\)[/tex] can be converted as follows: [tex]\(6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2}\)[/tex].
2. Calculate the Total Length in Decimal Form:
- Now, convert [tex]\(\frac{13}{2}\)[/tex] to decimal form.
- [tex]\(\frac{13}{2} = 6.5\)[/tex].
- Therefore, the length of the wire is [tex]\(6.5\)[/tex] meters.
3. Understand the Number of Equal Pieces:
- The wire is to be cut into 13 equal pieces.
- This means we need to divide the total length of the wire by the number of pieces to find the length of each piece.
4. Divide the Total Length by the Number of Pieces:
- Our total length is [tex]\(6.5\)[/tex] meters, and we need to divide this by the 13 pieces.
- [tex]\(\text{Length of each piece} = \frac{6.5}{13}\)[/tex].
5. Simplify the Division:
- When we divide [tex]\(6.5\)[/tex] by 13, we get [tex]\(0.5\)[/tex].
Therefore, the length of each piece when the [tex]\(6.5\)[/tex] meters wire is divided into 13 equal pieces is [tex]\(0.5\)[/tex] meters.
