A piece of cake: this is a nice image to say that something is very easy to do.
"I have my piano exam tomorrow! Don't worry, you practise so much that it will be a piece of cake!"
"Once you know how to do it, it's a piece of cake."
Half-baked: if you bake a cake only halfway then it won't be properly cooked. So this adjective means a plan or an idea that has not been thought out. In fact, it usually has a stronger meaning of stupid, daft or ridiculous.
"He wanted to be an inventor but all his ideas were half-baked."
"Let's go on a massive road trip tomorrow! What kind of half-baked idea is that?!"
To eat humble pie: this is a little more unusual and means to admit in front of people that you have been very wrong about something; it usually feels humiliating.
"She told everyone that her sports team would easily beat us, but when our team won instead, she had to eat humble pie."
A slice of the cake: this means a share of something profitable; it might be money or things or some other kinds of benefits.
"He tried to keep the profits for himself but we all wanted a slice of the cake."
Interestingly we usually say "a slice of THE cake" and not "a slice of cake" here.
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