Final answer:
If each child receives the same number of orange slices, then there is a proportional relationship between the number of children and the number of oranges with a specific constant of proportionality. However, without information on the number of slices each child gets, the correct constant cannot be determined from the options provided.
Step-by-step explanation:
There is a proportional relationship between the number of children and the number of orange slices if every child receives the same number of orange slices. To find the constant of proportionality, you would divide the total number of orange slices by the number of children. This would give you the number of orange slices per child. If the ratio is the same regardless of the number of children, you have a proportional relationship, and the ratio is the constant of proportionality.
Without additional details about how many orange slices each child receives, we cannot determine which option is correct. However, the question provides four different options for the constant of proportionality, which are all below 1. This suggests that not every child receives a whole orange, but a fraction of it, assuming each orange provides multiple slices. Therefore, if each child receives the same fraction of an orange in slices, it would establish a proportional relationship between the number of children and the number of oranges, with a specific constant of proportionality.