Scaled Drawing Question

[JoshuaS]

[FONT=arial,helvetica,sans-serif] The answer to the question below is 28 feet. I am having trouble understanding the answer is not in inches if both of these numbers (8 inch is 3.5 inches) are in inches. Can some help explain this to me?



The total length of a measurement from a US Customary scaled drawing of 1/8 inch is 3.5 inches. What is the actual length?[/FONT]
[FONT=arial,helvetica,sans-serif] [/FONT]
[FONT=arial,helvetica,sans-serif]Step one:[/FONT]
[FONT=arial,helvetica,sans-serif]Convert the scale (1/8 inch) into a decimal format.[/FONT]
[FONT=arial,helvetica,sans-serif] [/FONT]
[FONT=arial,helvetica,sans-serif]1/8 inch scale is 1 divided by 8 = 0.125 inches[/FONT]
[FONT=arial,helvetica,sans-serif] [/FONT]
[FONT=arial,helvetica,sans-serif]Step two:[/FONT]
[FONT=arial,helvetica,sans-serif]Determine the measurement on the scale drawing using a ruler. In this example our measurement is 3.5 inches.[/FONT]
[FONT=arial,helvetica,sans-serif] [/FONT]
[FONT=arial,helvetica,sans-serif]Step three:[/FONT]
[FONT=arial,helvetica,sans-serif]Divide the measurement by the scale decimal value. In other words, how many 0.125 units go into the measured length?[/FONT]
[FONT=arial,helvetica,sans-serif] [/FONT]
[FONT=arial,helvetica,sans-serif]3.5 / 0.125 = 28 feet[/FONT]

 

[Deleted member 4993]

The answer to the question below is 28 feet. I am having trouble understanding the answer is not in inches if both of these numbers (8 inch is 3.5 inches) are in inches. Can some help explain this to me?



The total length of a measurement from a US Customary scaled drawing of 1/8 inch is 3.5 inches. What is the actual length?

Step one:
Convert the scale (1/8 inch) into a decimal format.

1/8 inch scale is 1 divided by 8 = 0.125 inches

Step two:
Determine the measurement on the scale drawing using a ruler. In this example our measurement is 3.5 inches.

Step three:
Divide the measurement by the scale decimal value. In other words, how many 0.125 units go into the measured length?

3.5 / 0.125 = 28 feet

Is your scale factor:

1/8 inch ≡ 1 ft → 1 in ≡ 8 ft → 3.5 in ≡ 8*3.5 ft = 28 ft

 

[DrPhil]

Try being more explicit with the units. The scale factor is "inches per foot"

The answer to the question below is 28 feet. I am having trouble understanding the answer is not in inches if both of these numbers (8 inch is 3.5 inches) are in inches. Can some help explain this to me?



The total length of a measurement from a US Customary scaled drawing of 1/8 inch is 3.5 inches. What is the actual length?

Step one:
Convert the scale (1/8 inch) into a decimal format.

1/8 inch scale is 1 divided by 8 = 0.125 inches per foot

Step two:
Determine the measurement on the scale drawing using a ruler. In this example our measurement is 3.5 inches.

Step three:
Divide the measurement by the scale decimal value. In other words, how many 0.125 units go into the measured length?

(3.5 inches)/ (0.125 inches/foot) = 28 feet

The inches in the numerator cancel inches in the denominator, and 1/foot in the denominator becomes foot in the numerator

 

[JoshuaS]

The scale factor is "inches per foot"

How would I know from the given information that the answer is in inches per foot? I cut and pasted the information directly from the example I was given. Is this just a standard that is assumed or am I misreading something somewhere because I still don't see it.

 

[JeffM]

The scale factor is "inches per foot"

How would I know from the given information that the answer is in inches per foot? I cut and pasted the information directly from the example I was given. Is this just a standard that is assumed or am I misreading something somewhere because I still don't see it.

I think the example is confusing.

Question, given the customary US scaled drawing, where 1/8th of a scaled inch represents 1 actual foot, how many actual feet are represented by 3.5 scaled inches?

So here is what I would do. I get rid of the stupid fraction, what used to be called denis's rule but is now Jeff's rule.

If each 1/8th of an inch on the scale means 1 foot in reality, then every inch on the scale means 8 feet in reality. Correct? No fractions, no decimals.

So how many actual feet are represented by 3.5 inches on the scale? Simple: 3.5 times 8 = 28 actual feet.

Edit: Mathematically, multiplying by 8 gives the same answer as dividing by 0.125 so my method and your book's method end up in the same place. I just think my method is more intuitive for most people. Furthermore, if you are being taught a technique called dimensional analysis, then my method is too simplistic to teach that technique, and you should ignore my answer and follow up with with Subhotosh Khan and Dr. Phil.