In a group of people, half of them wear glasses, and one-third of them wear contact lenses. What fraction of the group wears neither glasses nor contact lenses?
One-sixth of the group wears neither glasses nor contact lenses.

Here's the logic behind this:

1. Let's assume there are 6 people in the group (the least common multiple of 2 and 3).
2. Half of them wear glasses, which means 3 out of 6 people wear glasses.
3. One-third of them wear contact lenses, which means 2 out of 6 people wear contact lenses.
4. To find out how many people wear neither glasses nor contact lenses, we need to subtract those who wear glasses or contact lenses from the total number of people.
5. So, 6 - 3 (glasses) - 2 (contact lenses) = 1 person.
6. Therefore, 1 out of 6 people wears neither glasses nor contact lenses, which is equal to one-sixth of the group.