# Interactions in Multiple Linear Regression (Divide Vs Multiply)

My question is about the difference (in general) between the interaction terms $$x_1x_2$$ and $$x_1/x_2$$ in multiple linear regression.

Suppose you are performing multiple linear regression and you have interactions present i.e. an independent variable has a different effect on the outcome depending on the values of another independent variable. Therefore you decide to model as follows:

$$Y = \beta_0 + \beta_1x_1 + \beta_2 x_2 + \beta_3x_1x_2$$

For example where $$Y$$could represent Impurity after a chemical reaction, $$x_1$$represents Reaction Temperature, $$x_2$$ represents Reaction Time.

Adding an interaction term between Reaction Temperature and Reaction Time $$x_1x_2$$ would effectively change the gradient for Reaction Time as we change the value of Reaction Temperature from low to high (and vice-versa for Reaction Temperature).

My questions are:

1. What impact does the interaction term $$x_1/x_2$$ have when compared to $$x_1x_2$$ ?
2. In what circumstances might you include an interaction term of $$x_1/x_2$$ as opposed to $$x_1x_2$$ ?