Final answer:
The territories that were divided between the British and French are present-day Pennsylvania and Ohio, over which the French and Indian War erupted due to conflicting territorial claims.
Step-by-step explanation:
The modern states whose territories were contested between the British and the French before the start of the French and Indian War are Pennsylvania and Ohio. This conflict arose over rival claims along the frontier in present-day western Pennsylvania, which resulted in military engagements such as the building of Fort Duquesne by the French and confrontations involving key figures like George Washington from Virginia. The British had granted land to the Ohio Company, including Virginians expanding westward, while the French aimed to protect their claims as well. Ultimately, the war expanded into a greater conflict known as the Seven Years' War in Europe, and post-war, the British emerged as the dominant power in eastern North America with the signing of the Treaty of Paris in 1763.