Question

Marissa buys a licorice candy rope to share with some friends. The rope is 30 2/3 inches long. She begins to cut the rope into pieces that are 3 1/3 inches long.
If she continues until the entire rope is cut into pieces, how many 3 1/3 inch pieces will she have?

9 1/5
9 2/3
10 1/6
10 1/3

Answer 1

To find out how many pieces of 3 1/3 inches Marissa can cut from a rope that is 30 2/3 inches long, we need to follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Divide the total length of the rope by the length of each piece.

First, let's convert the mixed numbers:

1. The length of the rope:
\(30 \frac{2}{3} = \frac{30 \times 3 + 2}{3} = \frac{90 + 2}{3} = \frac{92}{3}\)

2. The length of each piece:
\(3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}\)

Now we can divide the total length of the rope by the length of each piece:
\[
\frac{92}{3} \div \frac{10}{3} = \frac{92}{3} \times \frac{3}{10} = \frac{92 \times 3}{3 \times 10} = \frac{92}{10} = \frac{46}{5}
\]

Now, we convert \(\frac{46}{5}\) into a mixed number:
\[
46 \div 5 = 9 \quad \text{(remainder is 1)}
\]
So, \(\frac{46}{5} = 9 \frac{1}{5}\).

Thus, the total number of pieces Marissa can cut is:
\[
\boxed{9 \frac{1}{5}}
\]