I've recently gone back to uni and after a 10 year gap I'm finding basic working a challenge to remember. In a lecture slide there is a derivation of the non-inverting op-amp formula and it skips through rearranging $$\frac{Vin}{R1}\centerdot R2$$ to $$Vin\centerdot \frac{R2}{R1}$$ It's in the slides and I have cross checked the formula so I know it to be true, but I can't remember or figure out what steps are used to rearrange it.

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    $\begingroup$ This question is so basic that you have to ask yourself: what is a fraction? Because the answer to your question will change depending on what $\frac ab$ and multiplication of fractions mean to you. You could also ask a very related question: why is $a-b+c$ the same as $a+c-b$? To me, this question is almost identical to your question, but I know that there are other people out there who might feel differently. $\endgroup$ – Arthur Oct 31 '16 at 12:09

Order of multiplication doesn't matter

$$ \begin{align} Vin \cdot \frac{1}{R1} \cdot R2 &= \left( Vin \cdot \frac{1}{R1}\right) \cdot R2 = \frac{Vin}{R1} \cdot {R2} \\ &= Vin \cdot \left( \frac{1}{R1} \cdot R2 \right) = Vin \cdot \frac{R2}{R1} \end{align} $$

The parentheses just note which operation I do first. So the 'fraction' part can be under any term in the multiplication.


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