To determine which expression would be most helpful in solving the area model described, we need to analyze the given information: The area model has 5 shaded parts and 1 unshaded part, with the shaded part represented as \( \frac{5}{6} \).
The representation suggests that the total area is divided into parts, where 5 parts represent shaded area, and the unshaded area is 1 part. This indicates a total of 6 parts (5 shaded + 1 unshaded), suggesting that the area model illustrates a fraction of the whole.
Given the fractions and their context, we can examine the provided choices:
- One-sixth divided by \( \frac{5}{6} \) - This expression finds how many times \( \frac{5}{6} \) fits into \( \frac{1}{6} \).
- \( \frac{5}{6} \) divided by one-sixth - This expression calculates how many sixths are in \( \frac{5}{6} \). Since there are 5 shaded parts of \( \frac{5}{6} \), this matches the context of the model.
- 6 divided by one-sixth - This would calculate how many sixths are in 6, which doesn't directly pertain to the area model provided.
- 6 divided by \( \frac{5}{6} \) - This calculates how many portions of the shaded area \( \frac{5}{6} \) fit into 6 but is less relevant than the second option.
The most relevant expression regarding the area model is the second one:
\( \frac{5}{6} \) divided by one-sixth.
This expression aligns well with the given parts in the area model (the shaded and unshaded parts) and will help determine how many one-sixth parts fit into the shaded area \( \frac{5}{6} \), which is directly applicable to the situation described.