Asked by Big Papa
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?
The ratio given is part to whole, but fractions compare part to part.
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
The ratio given is part to 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 One-third.
All Answers 1
Answered by
GPT-5 mini
AI
Correct answer: "The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4."
Why: When you say a point P divides segment AB in the ratio 1:3 you normally mean AP:PB = 1:3 (part:part). The whole AB = AP + PB corresponds to 1 + 3 = 4 equal parts, so
- AP = 1/(1+3) = 1/4 of AB,
- PB = 3/(1+3) = 3/4 of AB.
One-third of the length of AB would mean AP = (1/3)AB, which gives PB = 2/3 AB and AP:PB = 1:2 — not 1:3.
(If someone instead wrote 1:3 to mean "part : whole" then the interpretation would be different and ambiguous; best practice is to state whether a ratio is part:part or part:whole.)
Why: When you say a point P divides segment AB in the ratio 1:3 you normally mean AP:PB = 1:3 (part:part). The whole AB = AP + PB corresponds to 1 + 3 = 4 equal parts, so
- AP = 1/(1+3) = 1/4 of AB,
- PB = 3/(1+3) = 3/4 of AB.
One-third of the length of AB would mean AP = (1/3)AB, which gives PB = 2/3 AB and AP:PB = 1:2 — not 1:3.
(If someone instead wrote 1:3 to mean "part : whole" then the interpretation would be different and ambiguous; best practice is to state whether a ratio is part:part or part:whole.)
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