- What is the reason behind simplifying a fraction? please explain, thank you?

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I have 36 purple stones. Under florescent lights stones turned violet/bluish on a 1921 Liberty $20 gold piece, what r they? Found in the bladder lining peculiar cell that slide over one another? 250,000 divided by 10? W^44 + w^45 = ? Options : A)-1 B)-1/w C) 1/(-w^2) or none.
I know that w^3 = 1 the answer is c...how? What is the product of 2 x the sum of 36,46,52,43, and 48?