The best explanation for the spelling of smiled during a lesson on rules for adding suffixes to base words is that words ending in silent e drop the e when a vowel suffix is added.
A suffix refers to an affix that is placed after the stem of a word.
For words that end with the e when a vowel suffix is added, there is no principle or rule to explain this every word must be learned separately. Words ending in silent e drop the e when a vowel suffix is added.
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