Answer :
Certainly! Let's solve the problem step-by-step:
Melissa has a piece of ribbon that is [tex]\(1 \frac{2}{3}\)[/tex] feet long, and she wants to cut it into 10 equal pieces.
1. Convert the mixed number to an improper fraction:
- [tex]\(1 \frac{2}{3}\)[/tex] is the same as [tex]\(1 + \frac{2}{3}\)[/tex].
- Converting this to an improper fraction: [tex]\(1\)[/tex] is the same as [tex]\(\frac{3}{3}\)[/tex].
- Add [tex]\(\frac{3}{3} + \frac{2}{3} = \frac{5}{3}\)[/tex].
2. Divide the total length by the number of pieces:
- We need to divide the total length of [tex]\(\frac{5}{3}\)[/tex] feet by 10.
- This is the same as multiplying [tex]\(\frac{5}{3}\)[/tex] by [tex]\(\frac{1}{10}\)[/tex].
3. Perform the multiplication:
- [tex]\(\frac{5}{3} \times \frac{1}{10} = \frac{5 \times 1}{3 \times 10} = \frac{5}{30}\)[/tex].
4. Simplify the fraction:
- The fraction [tex]\(\frac{5}{30}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 5.
- [tex]\(\frac{5}{30} = \frac{1}{6}\)[/tex].
So, each piece of the ribbon should be [tex]\(\frac{1}{6}\)[/tex] foot long.
Therefore, the correct answer is: A [tex]\(\frac{1}{6}\)[/tex] ft.
Melissa has a piece of ribbon that is [tex]\(1 \frac{2}{3}\)[/tex] feet long, and she wants to cut it into 10 equal pieces.
1. Convert the mixed number to an improper fraction:
- [tex]\(1 \frac{2}{3}\)[/tex] is the same as [tex]\(1 + \frac{2}{3}\)[/tex].
- Converting this to an improper fraction: [tex]\(1\)[/tex] is the same as [tex]\(\frac{3}{3}\)[/tex].
- Add [tex]\(\frac{3}{3} + \frac{2}{3} = \frac{5}{3}\)[/tex].
2. Divide the total length by the number of pieces:
- We need to divide the total length of [tex]\(\frac{5}{3}\)[/tex] feet by 10.
- This is the same as multiplying [tex]\(\frac{5}{3}\)[/tex] by [tex]\(\frac{1}{10}\)[/tex].
3. Perform the multiplication:
- [tex]\(\frac{5}{3} \times \frac{1}{10} = \frac{5 \times 1}{3 \times 10} = \frac{5}{30}\)[/tex].
4. Simplify the fraction:
- The fraction [tex]\(\frac{5}{30}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 5.
- [tex]\(\frac{5}{30} = \frac{1}{6}\)[/tex].
So, each piece of the ribbon should be [tex]\(\frac{1}{6}\)[/tex] foot long.
Therefore, the correct answer is: A [tex]\(\frac{1}{6}\)[/tex] ft.
