peace, piece

Peace or peace means tranquility, calm, or quiet; the absence of strife or war--
When the war was over, both sides signed a peace treaty.
The peace symbol is still popular on t-shirts after all these years.
Those children never give their mother any peace.

Piece or piece ( rhymes with peace ) means a section or segment of, or a part of something that has been divided or even torn--
She cut the cake equally, and gave each of them a piece.
He tried to sew the piece of his torn shirt back on.
Can we have a piece of pie?
Pie? Those children never give their mother a piece.

Now that you know that, you can say--
"This is so nice--peace and quiet and a piece of pizza for everyone."

Note--not to be confused with "peas", the plural of "pea", as in the green vegetable that grows in a pod--
They are as like as two peas in  a pod.
Note #2--"apiece" means each--
Those apples cost fifty cents apiece.
They were paid $100 apiece for the day's work.
"Apiece", meaning each, is one word--but "a piece" ( two words ) may also be part of a sensible sentence--
The candy is twenty cents a piece. ( Each piece of candy costs twenty cents. )
They paid twenty cents apiece for candy.  ( Each person paid twenty cents. )
Note # 3--"peace of mind" means contentment or mental tranquility--
She always checked the gas before they left, for her own peace of mind.
Not to be confused with "a piece of one's mind", meaning an angry outburst or rebuke--
I'm so mad; I would like to give him a piece of my mind.