A morpheme is the smallest single unit of language that has meaning.

Example
The word 'uneconomical' has three morphemes, 'un-', 'economy' and '-al'. 'un-' is a negative and a bound morpheme (appearing only with other morphemes), 'economy' is a free morpheme, and '-al' is a bound morpheme which forms an adjective.

In the classroom
The most common bound morphemes are prefixes and suffixes. They are frequently taught by looking at word families based on the same free morpheme.

Further links:

https://www.teachingenglish.org.uk/article/how-new-words-are-created

https://www.teachingenglish.org.uk/article/conveying-meaning

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