Why is partitioning a directed line segment into a ratio of ratio of 1 to 3 not the same as finding 1 third the length of the directed line segment?

A ratio of 1 to 3 compares the two parts of the segment: one part on one side of the partition point and three parts on the other. Together, those parts make 1 + 3 = 4 equal parts of the whole segment, so the first part is one-fourth of the length, not one-third. Thus, the correct choice is “The ratio given is part to part. The total number of parts in the whole is 1 plus 3 is equal to 4.”

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