Answer:
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Step-by-step explanation:
We know that partitioning a directed line segment into a ratio of 1:3 means that we are dividing the given line segment into two parts whose first part is 1 times the of some quantity while the another part is 3 times of the same quantity. So basically we are comparing part to part in by ratio. And total number of parts in the whole will be just sum of both so we get 1+3=4
Hence choice (3) is correct answer.
"The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4."
The one third length of the directed line segment is [tex]\boxed{{\mathbf{not\ same}}}[/tex] as the length of the directed line segment is divided into the ratio of [tex]1:3[/tex] .
Further explanation:
Ratio is the numerical relation between two different things.
Given:
It is given that a directed line segment is separated in the ratio of [tex]1:3[/tex] .
Step by step explanation:
Step 1 :
The directed line segment is separated in the ratio of [tex]1:3[/tex] .
It means that there are total 4 shares as it contains four pieces.
One part is before the required point and 3 remaining parts are after the required point.
Step 2:
The one third length of the directed line segment means there are three parts of equal size.
Step 3:
Consider an example a ribbon has length of 8cm.
Now divide the ribbon into the ratio of [tex]1:3[/tex] .
[tex]\begin{aligned}{\text{first part}}&=\frac{1}{4}\times8=2\hfill\\{\text{second part}}&=\frac{3}{4}\times 8=6\hfill\\\end{aligned}[/tex]
Therefore, the ribbon is separated in the ratio of [tex]1:3[/tex] as [tex]{\text{2cm, 6cm}}[/tex]
Now divide the ribbon equally in three parts that is [tex]\frac{1}{3}[/tex] of the ribbon.
[tex]\frac{1}{3}\times8=\frac{8}{3}[/tex]
Therefore, the ribbon is partitioned into one third as [tex]\frac{8}{3}{\text{cm, }}\frac{8}{3}{\text{cm}}[/tex] .
Thus, it has been proved the given explanation.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Fractions
Keywords: directed, line segment, length, one third, ratio, units, line, thing, quantitative relation, number, comparison, different things, ribbon, equally divided.
