To solve the problem, we need to determine how many boxes Jette has left to unpack after already unpacking a certain number of boxes.
1. Convert the mixed fractions to improper fractions for ease of calculation:
- Jette initially had [tex]\(5 \frac{1}{2}\)[/tex] boxes. This can be converted to an improper fraction as follows:
[tex]\[
5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} = 5.5 \text{ boxes}
\][/tex]
- Jette unpacked [tex]\(3 \frac{1}{3} \frac{1}{2}\)[/tex] boxes. This needs to be handled cautiously since it's not a standard representation of mixed fractions. We should interpret it as:
[tex]\[
3 + \frac{1}{3} + \frac{1}{2}
\][/tex]
First, find a common denominator for the fractions:
[tex]\[
\frac{1}{3} + \frac{1}{2}
\][/tex]
- The least common multiple of 3 and 2 is 6. Thus, we convert the fractions:
[tex]\[
\frac{1}{3} = \frac{2}{6}
\][/tex]
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
- Add the fractions together:
[tex]\[
\frac{2}{6} + \frac{3}{6} = \frac{5}{6}
\][/tex]
- Now add this to the whole number 3:
[tex]\[
3 + \frac{5}{6} = 3.8333333333333335 \text{ boxes}
\][/tex]
2. Subtract the number of unpacked boxes from the initial number of boxes to find the remaining boxes to unpack:
[tex]\[
\text{Remaining boxes} = 5.5 - 3.8333333333333335 = 1.6666666666666665 \text{ boxes}
\][/tex]
Therefore, Jette needs to unpack approximately [tex]\(1.67\)[/tex] more boxes to finish unpacking.
