Do you know the difference? These three words are homophones and they confuse many people.
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Use _er, _est if the adjective has one or two syllables, e.g. happy, happier, happiest; high, higher, highest.
Positive degree: high
Comparative degree: higher
Superlative degree; highest
Use more or most if the adjective has more than two syllables, e.g. beautiful, more beautiful, most beautiful.
There are also some words that have special comparative forms, e.g. good, better, best; bad, worse, worst.
Adjectives in English do not become plural if they are followed by plural nouns. The only exception is demonstrative adjectives. Occasionally, a plural noun will be made into an adjective but this is not because of agreement with the noun but because of what the noun refers to, e.g. The Twin Tours disaster led to the deaths of many people.