To determine the word class of the underlined word "half" in the sentence "He claimed his half share of the booty," we need to analyze the function and usage of the word within the context.

Step 1: Understanding "Half" as an Adjective

• In this sentence, "half" is describing the noun "share." It specifies the portion of the share that is being claimed. In grammatical terms, when a word describes or qualifies a noun, it functions as an adjective.

Step 2: Explanation of Adjective Usage

• Adjectives are words that modify nouns. They provide more information about a noun's quantity, quality, size, etc.
• In the given sentence, "half" answers the question "What kind of share?" by specifying the portion, thus qualifying the noun "share."

Step 3: Eliminating Other Options

• Adverb: Adverbs modify verbs, adjectives, or other adverbs. "Half" is not modifying any of these in the sentence.
• Determiner: Determiners specify nouns but usually include words like "a," "an," "the," "this," "that." "Half" can occasionally be a determiner, but in this context, it specifically acts as an adjective.
• Noun: Nouns are names of people, places, things, or ideas. "Half" is not functioning as a noun here; it does not act as a subject or object.

Conclusion: Based on the above analysis, "half" in this context is an adjective because it modifies the noun "share" by specifying its portion. Thus, the correct answer is:

Adjective