# Decreasing a variable by a factor

I have this problem: 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?

• 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. Aug 2 '17 at 22:36
• ell.stackexchange.com/q/52706 Aug 2 '17 at 22:44
• 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 $I$.