MHB Ratios and proportion: Scaling

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The discussion focuses on understanding ratios and proportions in the context of scaling. Participants express scales in ratio form, converting measurements like 1/2" = 1" to a ratio of 1:2 and 1/8" = 1'0" to 1:96. A job dimension of 24 inches is analyzed using a scale of 3" = 1'0", leading to a simplified ratio of 1:4, indicating that each unit on the drawing represents four units on the job. The final question involves calculating the corresponding drawing length for the job dimension. The conversation emphasizes the importance of converting units and simplifying ratios for clarity in scaling.
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Hi guys.

We're on a new topic in math now which has to do with ratios and proportions but with scaling.

A few questions I have are

How can I express the following scales in ratio?

1/2" = 1"
1/8" = 1'0"

Also we're doing a Job and Drawing scale

A dimension on a job is 24 in. Using scale of 3" = 1'0", compute the length of the same line for a drawing. How would that one look?

Thank you
 
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Eabzolid said:
Hi guys.

We're on a new topic in math now which has to do with ratios and proportions but with scaling.

A few questions I have are

How can I express the following scales in ratio?

1/2" = 1"

Since both measures are given in the same units, we can write:

$$\frac{1}{2}:1$$

Multiply through by 2:

$$1:2$$

Eabzolid said:
1/8" = 1'0"

First, convert both to the same units of measure...let's use inches:

$$\frac{1}{8}:12$$

Multiply through by 8:

$$1:96$$

Eabzolid said:
Also we're doing a Job and Drawing scale

A dimension on a job is 24 in. Using scale of 3" = 1'0", compute the length of the same line for a drawing. How would that one look?

Thank you

So, using the technique I outlined above, what ratio would you use for the given scale?
 
Would it look like this 3/1 : 24?

I really don't have an idea about this.
 
Eabzolid said:
Would it look like this 3/1 : 24?

I really don't have an idea about this.

Since 1' 0'' = 12'' we could express the scale as the ratio:

$$3:12$$

And then dividing through by 3 we get:

$$1:4$$

This means a length of $x$ on the drawing represents a length of $4x$ on the job. So if:

$$4x=24$$

Then what is $x$ in inches?
 
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