common sense: who, what, where, when, why? why do you think the colonists thought they should not depend on britain?
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They believed they didn't need Britian because Britian was taxing them enormous amounts of money and controlling their freedom.

Common Sense was pamphlet that Thomas Paine wrote to challenge the authority of the British government and advocate American independence. It was directed at the British monarchy and appealed to the common people of America. It was written before the Revolutionary war and its intent was to get the common man to support independence. It was written because the British government was being oppressive towards to colonists by passing certain laws and taxes without the colonists having a say in government. 
The colonists thought that they didn't depend on Britain because it was a small country over seas and they were the ones producing everything.