Why do you think it is more important to look at "lived density" than overall population density?

Portugal ⇒ Ruled east of the line of demarcation

After the New World was rediscovered by the European powers and saw competition between the Spanish and the Portuguese, Pope Alexander VI came up with a Line of Demarcation to divide the New World. Portugal was to rule over every land east of the line which is why they colonized Brazil.

Russia ⇒ Controlled what is Alaska today.

Russia controlled what is Alaska today but then decided to sell it to the United States rather than risking the British taking it by forced and adding it to Canada.

Britain ⇒ Controlled the area of today's eastern United States.

Britain ruled the eastern part of today's United States and it was here that they established the colonies that became the first states of the United States of America when these colonies defeated the British in the American Revolution.

Spain ⇒ Ruled west of the land of demarcation

As explained above, Pope Alexander VI came up with a Line of Demarcation. This allowed Spain to rule lands west of this line such that they gained colonies such as Mexico and countries to the west of South America.