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

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

The ratio given is part to whole, but fractions compare part to part.

The ratio given is part of the part. The total number of parts in the whole is 3 – 1 = 2.

The ratio given is part of the part. The total number of parts in the whole is 1 + 3 = 4.

The ratio given is part to whole, but the associated fraction is.

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