Mental division of two fractions? I've got a non-calc paper coming up, and when going through a test, this fraction came up:
$$
\frac{8}{-0.4} \equiv  \frac{8}{\big(\frac{-2}{5}\big)}
$$
Going through the answers he says: $$8/2=4$$ I then assume he did -(4*5)
so: $$\frac{8}{\big(\frac{-2}{5}\big)} = -20$$
I can see what he's done, but I don't see what's happening mathematically?
$$\frac{a}{\frac{b}{c}} \equiv \frac{a}{b}\cdot c$$

What he is using is that $\frac{a}{\frac{1}{b}} = a*b$. That way he could transform a division involving decimals into simple integer multiplication.
