Which of these sentences using eating as a participle?
a. i enjoy eating foods that i have prepared myself.
b. my eating habits are a lot healthier than they used to be.
c. i would have to say that eating is my favorite pastime.
d. this problem has been eating away at me, and i can't sleep.

Two sentences use "eating" as a participle:

B. My eating habits are a lot healthier than they used to be.

D. This problem has been eating away at me, and I can't sleep.

Explanation:

The gerund and the present participle are identical to the eye. They both are formed by adding -ing to a verb root. Thus, "eating" can be a gerund or a participle, according to the context.

The difference between them is quite simple. The gerund acts like a noun, having the same functions a noun would have in a sentence: subject, object of a verb or of a preposition, and subject complement. The present participle, on the other hand, will either act as an adjective, modifying a noun or a pronoun, or be a part of a continuous tense.

That is precisely what we have in options B and D. In option B, "eating" is an adjective modifying the noun "habits". In letter D, "eating" is a part of the Present Perfect Continuous tense. Therefore, in options B and D, "eating" is a participle:

B. My eating habits are a lot healthier than they used to be.

D. This problem has been eating away at me, and I can't sleep.