1. Two-thirds of an apple is bad.

2. Most of an apple is bad.
3. Half of an apple is rotten.
4. The rest of an apple is rotten.
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What about the sentences? 'An' is used in each sentence. Can we use 'an' in this way?

It would be better to use "the" in place of "an" in all these. When you use "an," you're implying that it could be just any apple ... or maybe even all of them. But if you use "the," you are referring to a particular apple.

Yes, "an" can be used in this way in each of the given sentences. "An" is an indefinite article used before nouns that begin with a vowel sound, such as "apple." It indicates that the noun that follows is singular and nonspecific.

In the given sentences, "an" is used to introduce the noun "apple" in each case, helping to establish that the statements are referring to an individual apple, without specifying which one. This is a grammatically correct usage of the article "an" in English.