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

Question

Insert the appropriate sign for the following expression:

$-12:-8:?>0$

00:00 Complete the missing value

00:06 Negative divided by negative is always positive

00:18 Let's assume the missing value is positive

00:24 Positive divided by positive is always positive

00:28 Positive is greater than 0, therefore the missing value must be positive

00:31 And this is the solution to the question

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 $+\frac{1}{90}$

$+\frac{1}{90}$