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The pronunciation of any word in English (or any language at all) is not Universal.  This is because there are many different dialects of The English Language — both throughout America, and also world-wide.  The pronunciations that are presented on GiveMeSomeEnglish!!! are based-upon a combination of both “common usage”, and the most neutral accent used in The International Common Tongue — a.k.a. “American English”.
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Awfully – For this word:  the “Aw” combination is pronounced like in the word “Law” or “Awesome” (this is the standard pronunciation of this letter combination in The Common Tongue);  for the “-fully” suffix – the “u” is pronounced as a true-schwa;  the “ll” combination is pronounced simply like the single letter “l” (this is the standard pronunciation of this letter combination in The Common Tongue);  and the final “y” is pronounced like the long letter “e” (this is the standard pronunciation of this suffix in The Common Tongue).

– /AW-fə-lee/ – /ˈɔ.fə.liː/ – Notice also that the stress is on the second syllable –

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Learn More About The Word “Awfully” On Wiktionary

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