Understanding formulas involving divison and multiplication

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Discussion Overview

The discussion revolves around understanding how formulas involving division and multiplication apply to abstract concepts in physics and mathematics, such as Ohm's Law and the formula for speed. Participants explore the nature of these relationships and the implications of using mathematical operations in defining physical quantities.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how formulas like Ohm's Law (V = I•R) and the speed formula (Speed = distance / time) can involve multiplication and division of abstract concepts, questioning the underlying assumptions of these relationships.
  • Another participant suggests that equations like speed = distance / time are definitions, indicating that mathematics serves as a language to express these concepts, and emphasizes the need for practice to understand the subtleties of mathematical language.
  • A participant asks how to calculate speed, indicating a desire for clarity on the application of the formula rather than its definition.
  • One participant asserts that speed is a concept that cannot be separated from its mathematical representation, implying that mathematical operations are essential to understanding physical concepts.
  • A further inquiry is made about the acceptance of addition and subtraction in relation to abstract concepts, questioning the consistency of using different mathematical operations.
  • Another participant raises the topic of ratios and their relevance, suggesting a broader exploration of mathematical relationships.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and acceptance of mathematical operations in defining abstract concepts. There is no consensus on how to approach these formulas or the nature of their definitions, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants have not fully resolved their uncertainties regarding the application of division and multiplication in abstract contexts, and there are missing assumptions about the foundational understanding of mathematical operations.

Niaboc67
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I've never quite understood is how formula can involve division and multiplication while dealing with abstract concepts. Such as, ohm's law V = I•R where V=voltage applied I=current and R=resistance. How does that work exactly? how can you multiply two abstract concepts together to understand the equivalence to something else. Is this to assume we are evaluating for something, correct? if we know the certain number of volts and the current we can figure out the voltage? if this is correct can this be reversed in order to figure out the others alone, such as I and R?

Other formulas such as Speed = distance / time. Things like these have always confused me, maybe I just don't quite understand division but how can diving possible given you the outcome of speed?
Also anything dealing with infinities and pi in formulas I don't see how these are work together to form an understanding.

Please help
 
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Many times it is a definition. Like (speed = distance / time), that's just the definition of speed. Mathematics is just a language and that is the mathematical translation of "speed is distance per time" or "speed is how long it takes to go a distance" or "speed is how far you go in an amount of time"
Those are 3 verbal (english) ways of defining speed. Division is just part of the language used in the mathematical definition.

As with any language, you have to use it quite a bit before you can understand it fluently. You have to use it a lot to understand the subtle meanings involved, and you also have to use it a lot before you can think with it.
 
Niaboc67 said:
Other formulas such as Speed = distance / time. Things like these have always confused me,
How would you calculate speed instead?
 
Speed is a 'concept'. You can't avoid the Maths.
 
Niaboc67 said:
I've never quite understood is how formula can involve division and multiplication while dealing with abstract concepts.

What about ratios? How do you feel about them?

Your post implies that you accept addition and subtraction w.r.t. abstract concepts. Why?

If you wanted to calculate the area of a square or rectangle, how would you do it?
 

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