You can remember the meaning of 以为 with this easy mnemonic:
According to (以) some cultures it is considered rude to reject someone's offer clearly. It can be confusing because (为), "I have some leftover work. I will go when I can make it.", some think this response to a casual meet up invite means yes when the responder meant otherwise.
Using mnemonics to remember the meaning of Chinese characters like can have an enormous impact on how long to learn Mandarin it takes.