Hi, welcome to Math Antics. In this lesson, we’re gonna learn about negative numbers.
Negative numbers can be a little confusing at first, so don’t get discouraged if it takes you a while to get it.
To learn what negative numbers are, we first need to start with ‘whole numbers’.
You remember what whole numbers are, right?
They’re the set of numbers on the number line, starting with zero, and then counting up one at a time:
1, 2, 3, 4… all the way to infinity.
That’s a LOT of numbers, but it’s only half the story!
And that’s because the number line really goes in BOTH directions.
You’re used to seeing the number line starting at zero and just going to the right, but the number line also goes to the left.
And what numbers are on that part of the number line?
Yep… you guessed it… negative numbers.
The negative numbers are just like a mirror image of the numbers on the right side of the number line that we call the positive numbers.
And zero is the special number that separates the positive numbers from the negative numbers.
By the way, when you combine all these numbers
(1 ,2, 3, and so on up to infinity, and -1, -2, -3, and so on down to negative infinity, and the number zero)
that entire set of numbers gets a special name in math. They’re called ‘the Integers’.
As you can see, the negative numbers look just like the positive numbers.
The only difference is that they have a ‘negative sign’ in front of them.
The negative sign looks just like the minus sign.
In fact, if we wanted to, we could write a positive sign (a plus) in front of all the positive numbers.
But to save time, we just assume that if a number doesn’t have any sign in front of it, then it’s positive.
Positive is the ‘default’ sign.
Okay, now that you know what negative numbers are, we need to learn how to compare them to other integers.
Remember that in math, comparing just means saying which of two numbers is bigger or smaller than the other, or saying that they’re equal.
And to do that, we use the greater than, less than, or equal signs.
You’re probably already pretty good at comparing positive integers.
Like if I ask, “Which is bigger: 2 or 3 ?” You know that 3 is bigger than 2.
But what if I asked you to compare two negative integers? “Which is bigger: -2 or -3 ?”
Ah, this is where negative numbers can be a little tricky, especially if this is your first time learning about them.
That’s because you’re SO used to 3 being bigger than 2 that when you see -2 and -3,
it’s really tempting to think that -3 must be bigger than -2, but it’s NOT!
Negative 3 is actually smaller (or less) than negative 2.
And to help you understand why, let’s look at our number line again.
Have you noticed that if you start at zero on the number line and then you move to the right,
the numbers keep getting bigger and bigger as you go along.
1 is greater than 0, 2 is greater than 1, and 3 is greater than 2, and so on…
But what if we go in the opposite direction instead; to the left?
As we go to the left, the numbers get smaller and smaller.
2 is less than 3, 1 is less than 2, and 0 is less than 1.
Well, those same exact rules apply to negative side of the number line also.
The numbers get bigger as you go to the right and they get smaller as you go to the left.
So, since -3 is on the left side of -2, it’s actually smaller than -2.
I like to think of it like this…
On the positive side of the number line, 3 is more positive than 2 (so it’s bigger).
But on the negative side of the number line, -3 is more negative than -2 (so it’s smaller).
And you can use that idea no matter what the numbers are.
On the positive side, 500 is more positive than 200 (so it’s bigger)
but on the negative side, -500 is more negative than -200 (so it’s smaller)
Keep that in mind if anyone every offers to give you negative 500 dollars.
The ‘500’ part sounds pretty good, but the negative part… not so much!
Alright, so the positive integers are on the right side of zero on the number line, which means they’re all greater than zero.
And the negative integers are all on the left side of zero on the number line, which means they’re all less than zero.
Wait… Hold on a second… “Less than zero!?”
How… How can ANY number be less than zero?
I mean… Doesn’t zero mean ‘nothing’?
Ah, that’s a good question.
At first, it can be hard to see how there could be numbers that are less than zero,
but here’s an example that will help you understand.
Let’s say we want to use integers to measure how many meter above sea level small islands are.
This island is 10 meters above sea level.
This island is only 5 meters above sea level.
And this island here happens to be exactly the same height as sea level.
So we can use the integer zero to show how it’s height compares to sea level.
But what about this island?
It’s not even above sea level at all. It’s 5 meters below the surface.
But our measurement is supposed to tell us how many meters ABOVE sea level it is.
Fortunately, with negative numbers, that’s no problem.
We can just say that its height (compared to sea level) is negative 5 meters.
Or, what about an example with money?…
Suppose there’s three brothers who each have a different amount of money.
The first brother has $20, the next brother has $0, and the last brother actually OWES his dad $20.
What number do we use to represent how much money he has?
Yep… negative 20 dollars!
And temperature is another great example.
We use zero degrees Celsius to describe the temperature for water to freeze, but it can be warmer or colder than that.
The temperature could be negative; like negative 20 degrees!
So negative numbers are very useful in the real world to help describe things that can be above OR below zero.
Okay, now that you know how negative numbers work, let’s see how we can compare any two integers.
If we don’t include zero for a moment, basically there’s just three situations.
You’ll either need to compare two positive integers,
or two negative integers,
or one positive and one negative integer.
And you already know how to compare two positive integers.
The further right on the number line you go, the bigger the numbers get.
7 is greater than 4,
50 is greater than 20,
and 1,000 is greater than 100.
It’s also really easy to compare a positive integer and a negative integer,
because a positive number is ALWAYS bigger than a negative number.
ALL of the positive numbers are on the right side of the number line and ALL the negative numbers on the left.
So -5 is less than 5
and -40 is less than 3
and -100 is less than 1
The only tricky situation is when you have to compare two negative integers.
Then you have to think about which one is further to the left on the number line.
Again, a great way to do that is to identify the number that would normal be more positive on the positive side of the number line
and realize that it’s more negative on the negative side.
-8 is more negative than -4, so it’s smaller.
-15 is more negative than -10, so it’s smaller.
and -100 is more negative than -25, so it’s smaller.
Alright, so in this video we learned what negative numbers are and how they can be used to describe things in the real world.
They’re just like positive numbers, but on the other side of zero on the number line.
And we leaned that the whole numbers, along with their negative counterparts, form the set of numbers we call integers.
We also learned how to compare integers.
As you go to the right on the number line, the integers get bigger, and as you go left, they get smaller.
Comparing integers can be confusing at first, so be sure to practice until you’ve really got it.
As always, thanks for watching Math Antics and I’ll see ya next time.
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