MHB Ratios and proportion: Scaling

[Eabzolid]

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

 

[MarkFL]

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:

$$1:2$$

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:

$$1:96$$

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?

 

[Eabzolid]

Would it look like this 3/1 : 24?

I really don't have an idea about this.

 

[MarkFL]

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?