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Cross Multiplication for Proportionalities

An electrician needs to be able to use proportionality to solve a problem about conductor resistance at length. Here's how it works. If a certain conductor has a resistance of 18 ohms per 1000 feet, what will the resistance be for, say, 500 feet? 9 ohms, you come up with. Right. But if the length is not an exact half, or some other common fraction, how is the solution determined? 

Cross multiplication can do it.

A over B equals C over D

Or, A times D divided by B equals C. Sound difficult? Let me explain.

If a conductor is  (A)18 ohms per (B) 1000 feet, then what is the resistance (C) at (d)500 feet?

So it is A times D divided by B equals C.

Or 18 times 500 divided by 1000 equals 9.

Works every time.

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