Question

why is partitioning a directed line segment into a ratio of 1:3 not the same as finding \\(\frac{1}{3}\\) the length of the directed line segment?
\\(\bigcirc\\) the ratio given is part to whole, but fractions compare part to part.
\\(\bigcirc\\) the ratio given is part to part. the total number of parts in the whole is \\(3 - 1 = 2\\).
\\(\bigcirc\\) the ratio given is part to part. the total number of parts in the whole is \\(1 + 3 = 4\\).
\\(\bigcirc\\) the ratio given is part to whole, but the associated fraction is \\(\frac{3}{1}\\).

Explanation:

To determine the correct answer, we analyze the concept of ratios in partitioning a line segment. A ratio of \(1:3\) for partitioning a directed line segment is a part - to - part ratio. This means we are dividing the line segment into two parts where the first part has 1 unit and the second part has 3 units. The total number of parts that make up the whole line segment is the sum of these two parts, so \(1 + 3=4\) parts.

• For the first option: A ratio of \(1:3\) is not a part - to - whole ratio. A part - to - whole ratio would be something like \(1:4\) (if we were considering one part out of the whole) or \(3:4\), so this option is incorrect.
• For the second option: The total number of parts is not calculated as \(3 - 1\). We add the two parts of the ratio (\(1\) and \(3\)) to get the total number of parts in the whole, so this option is incorrect.
• For the fourth option: The ratio \(1:3\) is not a part - to - whole ratio, and the associated fraction is not \(\frac{3}{1}\). The fraction corresponding to the first part of the ratio \(1:3\) (when considering the whole as \(1 + 3 = 4\) parts) is \(\frac{1}{4}\), so this option is incorrect.

Answer:

C. The ratio given is part to part. The total number of parts in the whole is \(1+3 = 4\).