Hi all!
This serves as a review to those of you that have already learned about negative numbers in school, and as a guide to beginners. Let’s get started!
So.. what are negative numbers?
Imagine a number line. In the middle of that line is the number 0. To the right of 0 are the positive whole numbers (1,2,3,….). But have you ever wondered what lies on the left of the number line? The exact same positive whole numbers, but with little hyphens in front of them (-1,-2,-3..) and so on. These are the negative numbers.
But, they work a little differently compared to positive numbers. Whereas 1<2, -1>-2. Shocking, isn’t it? Intuitively, though, it makes sense. You would rather be 1 dollar in debt than 2 dollars in debt, because in order to get 2 dollars into debt, someone would have to take 1 more dollar from your already 1 dollar in debt. Thus, your net worth is less compared to before, isn’t it?
It could also help to look at the number line.
If you didn’t memorize that negative numbers with higher magnitudes(absolute value of the number: |-2|=2) are actually lower compared to negative numbers with lesser magnitudes, no worries! Just quickly imagine a number line.
A good rule of thumb to follow is that when you go from right to left, you are actually following the pattern of decreasing numbers. So(1<2, 0<1, , -1<0, -2<-1), and so on. Pretty easy to remember, right?
Now let’s move on to operations with negative numbers.
Addition and subtraction basically work the same way as positive numbers, but there are a few changes to multiplication and division.
What do you get when you multiply two negative numbers, for example -1*-3? There is a useful way to think about this.
The total of these groups of numbers is 0, as there are 3 yellow circles and 3 red ones. Think of this as the number 0 on the number line. Now, the negative symbol means that we must subtract or take off 1 group of the 3 of the negative red circles, indicated by the multiplication of -1 and -3. If we do so, we get:
3 positive circles! So, -1*-3=+3. Wow, that’s cool! Two negative numbers actually multiply to become one positive number.
To a similar analogy, -1*3, or 1*-3 gives a negative result, -3. And it is basically the same rules for division, where two negatives such as -2 and -1 divided by each other gives a +2, and one positive such as +1 and one negative such as -2 divided together gives -2.
That’s it for our lesson on negative numbers! Please let us know if you have any questions.