To determine the correct algebraic expression that represents "Mica shared her oranges equally with five friends," let's analyze the situation step-by-step.
1. Understanding the Scenario:
- Mica has a certain number of oranges, denoted by [tex]\( w \)[/tex].
- She shares these oranges equally with five friends. Sharing equally means dividing the total number of oranges by the number of friends.
2. Translating the Scenario into a Mathematical Expression:
- Since Mica is sharing her oranges equally with five friends, we need to divide the number of oranges [tex]\( w \)[/tex] by the number of friends, which is 5.
- The fraction [tex]\(\frac{w}{5}\)[/tex] represents the number of oranges each friend gets.
3. Evaluating the Given Options:
- [tex]\( 5 + w \)[/tex]: This represents adding 5 to the number of oranges Mica has, which does not correspond to sharing the oranges.
- [tex]\( 5w \)[/tex]: This represents multiplying the number of oranges by 5, which again does not fit the description.
- [tex]\( \frac{5}{w} \)[/tex]: This represents dividing 5 by the number of oranges, which is not correct here.
- [tex]\( \frac{w}{5} \)[/tex]: This represents dividing the number of oranges by 5, which correctly matches the situation of sharing the oranges equally with five friends.
Hence, the correct algebraic expression that represents "Mica shared her oranges equally with five friends" is [tex]\( \frac{w}{5} \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
