Sequential Division Problem: Finding the Sign in -12:-8 for Positive Result

Let's begin by observing the exercise on the left side whilst paying particular attention to the plus and minus signs.

The exercise looks like this:

$-:-:?=$

If we solve the equation from left to right, we can see that we first divide a negative number by a negative number, therefore:

$-:-=+$

The resulting exercise is as follows:

$+:\text{?=}$

Our result needs to be greater than zero, and therefore we need a positive number, in order for the number to be positive.

Hence:

$+:+=+$

$+ > 0$

Therefore the answer is $+\frac{1}{90}$