Mathematics, 28.06.2019 15:30 mitetwojr

Why is partitioning a directed line segment into a ratio of 1: 3 not the same as finding 1/3 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 1/3.

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Answer from: sabrinarea041904

The length of the directed line segment is partitioned into the ratio of 1:3 is $\boxed{{\mathbf{not\ same}}}$ as the one third length of the directed line segment.

Further explanation:

Ratio is the quantitative relation between two different things.

Given:

It is given that a directed line segment is partitioned in the ratio of 1:3 .

Step by step explanation:

Step 1

The directed line segment is partitioned in the ratio of 1:3 .

First part is before the desired point and 3 parts are after the desired point.

It means that there are total 4 shares as it contains four pieces.

Step 2:

The one third length of the directed line segment means there are three shares of equal size.

Step 3:

Consider an example a cloth has length of 12cm.

Now divide the cloth into the ratio of 1:3 .

$\begin{aligned}{\text{first part}}&=\frac{1}{4}\times12=3\hfill\\{\text{second part}}&=\frac{3}{4}\times12=9\hfill\\\end{aligned}$

Therefore, the cloth is divided in the ratio of 1:3 as ${\text{3cm, 9cm}}$

Now divide the cloth equally in three parts that is $\frac{1}{3}$ of the cloth.

$\frac{1}{3}\times12=4$

Therefore, the cloth is divided into one third as $4{\text{cm, }}4{\text{cm}}$ .

Thus, it has been proved the given explanation.

Learn more:

Learn more about why is partitioning a directed line segment into a ratio of 1:2 not the same as finding the length of the directed line segment? link Learn more about one solution contains 2 parts salt to 8 parts water, and another solution contains 3 parts salt to 5 parts water. how much of each should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water? link Learn more about the whole value of for which the solution of the equation link

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.

Answer from: angel182

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

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer from: Quest

Horizontal change or the change of x

Answer from: Quest

answer: 1722

step-by-step explanation:

given: the mass of saturn= $5.685\times10^{26}\ kgs$

the mass of mercury= $3.302\times10^{23}\ kgs$

the number of times the mass of saturn is greater than the mass of mercury

$=\frac{\text{mass of saturn}}{\text{mass of mercury}}\\=\frac{5.685\times10^{26}}{3.302\times10^{23}}\\\\=1.72168\times10^{26-23}{by using law of exponent}]\\=1.72168\times10^3=1721.68\approx1722$

hence, the mass of saturn is 1722 times greater than the mass of mercury.

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