Basically you're trying to say "I'm perfect in math - but I have problems with other subjects." Sentence B is not expressing this idea. "(B) Math lets me avoid careless mistakes more often than other subjects." "Math" cannot 'let' you avoid mistakes一unless you are building a rocket or designing some engineering project. "Math" can 'let' you solve a hard problem, math 'lets' you figure out how electricity works, etc. Sentence B is grammatically correct, but does not contain the original meaning of sentence A.

Ah-huh!!
Your examples made it very clear to me.
Thank you very much, jve_84-san!!

By the way, I say "mathematics" and not "math" because I am a mathematician. In UK English, the short form is "maths", not "math." The short form "math" is only used in the US.

I think I missed some points about the nuance of "let" and "avoid" here.
Thank you so much as always, tony-san!

"Let someone do" and "make someone do" are difficult for speakers of Japanese because they are both translations of causative forms. I'm going to give you a list of close equivalents, although you probably know most of this already:

(1) let someone do something (interpreting "let" as present tense)
allow someone to do something
permit someone to do something
enable someone to do something
help someone to do something

(2) make someone do something
cause someone to do something
force someone to do something
result (inevitably) in someone doing something

These tend not to be used with negative verbs. There are other expressions which are usually used in place of letting/making someone not do something:

(1')
help/allow/permit/enable someone to avoid doing something

(2')
keep/prevent/hinder someone from doing something

Tony先生 hits the nail on the head here. In other words; math lets me ~x = math helps me to ~x.