Final answer:
The Great Compromise and the Three-Fifths Compromise were key to determining representation by population in the U.S. House of Representatives, with the former establishing a bicameral legislature and the latter affecting the balance of power between states.
Step-by-step explanation:
The states reached significant compromises regarding representation by population in the House of Representatives during the Constitutional Convention. The Great Compromise, also known as the Connecticut Compromise, proposed a bicameral legislature consisting of two houses. In the Senate, each state would have equal representation with two senators, while in the House of Representatives, representation would be proportional to the population of each state. Additionally, the Three-Fifths Compromise was agreed upon to count enslaved individuals as three-fifths of a person for representation and taxation purposes, which significantly affected the balance of power between northern and southern states.