The difference between As a rule and For the most part
When used as adverbs, as a rule means in general, whereas for the most part means mostly.
check bellow for the other definitions of As a rule and For the most part
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As a rule as an adverb (idiomatic):
In general; most often.
Examples:
"We go fishing every Sunday as a rule, but today the lake is frozen."
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For the most part as an adverb (idiomatic):
Mostly; in general; usually
Examples:
"She talked about her kids, for the most part."