I have this problem:

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So at first I was having some problems with the wording. The part of "reducing by a factor of 2/3" made me think this way: So reducing by a factor of 66.7% means that they want 33.3%.

So I solved like this:

$$R = \frac{9}{\frac{1}{3}I}=\frac{9(3)}{I}$$ $$\frac{1}{3}R = \frac{9}{I}$$

So I chose that the resistance would reduce by a factor of 1/3

However, that is incorrect. They explain that "reducing by a factor of 2/3" means multiplying I by 2/3, not by 1/3. Can someone explain why?

  • 1
    $\begingroup$ This is just a nomenclature issue; I agree that it is quite confusing at times (e.g. price reduced by 25%). I think the word "factor" implies multiplication here, but it's just generally kind of unclear. $\endgroup$
    – platty
    Aug 2 '17 at 22:36
  • $\begingroup$ ell.stackexchange.com/q/52706 $\endgroup$
    – hjpotter92
    Aug 2 '17 at 22:44
  • $\begingroup$ Also, math.stackexchange.com/q/64448 $\endgroup$
    – hjpotter92
    Aug 2 '17 at 22:45

Admittedly, the wording isn't the best, but because the factor is $<1$, it is generalized as a decrease in the size when you multiply $\frac{2}{3}$ by $I$.

  • $\begingroup$ Agree. And confusingly "reduce by a factor of 2" would likely mean "divide by two" because it is greater than one $\endgroup$
    – Χpẘ
    Aug 2 '17 at 23:07

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