<P> During the 1760s and early 1770s , relations between the Thirteen Colonies and Britain became increasingly strained , primarily because of resentment of the British Parliament 's attempts to govern and tax American colonists without their consent . This was summarised at the time by the slogan `` No taxation without representation '' , a perceived violation of the guaranteed Rights of Englishmen . The American Revolution began with rejection of Parliamentary authority and moves towards self - government . In response , Britain sent troops to reimpose direct rule , leading to the outbreak of war in 1775 . The following year , in 1776 , the United States declared independence . The entry of France into the war in 1778 tipped the military balance in the Americans ' favour and after a decisive defeat at Yorktown in 1781 , Britain began negotiating peace terms . American independence was acknowledged at the Peace of Paris in 1783 . </P>
during which time period did the largest number of former colonies become independent states
the 1760s and early 1770s