Intro to negative numbers

in this video I want to familiarize ourselves with negative numbers and also learn a bit of how do we add and subtract them and when you first encounter them they look like this deep and mysterious thing when we first count things we're counting positive numbers what does a negative number even mean but when we think about it you probably have encountered negative numbers in your everyday life and let me just give you a few examples so before actually I give the example the general idea is a negative number is any number less than a zero less than less than zero and if that sounds strange and abstract to you let's just think about in a couple of different context if I have if I have a if we're measuring the temperature and it could be in Celsius or Fahrenheit let's just we're measuring it in Celsius and so let me draw a little scale that we can measure the temperature on and so let's say that this is zero degrees Celsius that is one degree Celsius two degrees Celsius three degrees Celsius now let's say that it's a it's a pretty chilly day and it's currently it's currently three degrees Celsius and someone who predicts the future tells you that it is going to get four degrees colder the next day so how cold will it be how can you represent that coldness well if it only got one degree colder we would be at two degrees but we know we have to go four degrees colder if we got two degrees colder if we got two degrees colder we would be at one degree if we got three degrees colder we would be at zero but three isn't enough we have to get four degrees colder so we actually have to go one more below zero we have to go one more below zero and that one below zero we call that negative one we call that negative one and so you can kind of see that the number line as you go to the right of zero on the number line increases in positive values as you go to the left of the number line you're going to have negative one then you're going to have negative two you're going to have negative three and you're going to have depending on how you think about it you're going to have larger negative numbers but I want to make it very clear negative three is less than negative 1 negative 3 there is less heat in the air than negative 1 it is colder there's there's less temperature there so a large so let me just make it very clear nate- 100 is much smaller much smaller smaller then much smaller than 1 or sorry much smarter than negative 1 you might look at 100 and you might look at 1 and your gut reaction to say wow hundreds a much larger number than 1 but when you think about it negative 100 means there's a lack of something negative hundred if it's negative 100 degrees there's a lack of heat so there's much less heat here than if we had negative 1 let me give you another example let's say in my bank account today I have 10 dollars let me do this in a new color so let's say today today I have I have $10 $10 now let's say I go out there because I feel good about my $10 and let's say I go and spend let's say I go out there and I spend $30 and for the sake of argument let's say I have a very flexible Bank one that lets me spend more money than I have and these actually exist so I spend $30 so what's my bank account going to look like so let me draw a number line here and you might already have an intuitive response I will owe the bank I will owe the bank some money so let's let me write this over here so tomorrow tomorrow what is my bank account so you might immediately say look if I have $10 and I spend $30 there's $20 that had to come from someplace and that $20 is coming from the bank so I'm going to owe the bank $20 and so in my bank account to show how much I have I could say 10 minus 30 is actually negative $20 so in my bank account tomorrow I am going to have negative negative $20 so if I say I have negative $20 that means that I owe the bank I don't even have it not only that have nothing I owe something it's going in reverse here I have something to spend no one knows if to some degree if my 10 dollars in my bank means the bank owes me $10 I have $10 that I can use to go spend now it's an I owe the bank I've gone in the other direction and if we use a number line here it should hopefully make a little bit of sense so that is zero I'm starting off with $10 I'm starting off with $10 and spending $30 means I'm moving 30 spaces to the left so if I move 10 spaces to the left if I only spend $10 I'll be back at zero if I spend another $10 I'll be at negative 10 if I spend another $10 after that I will be at negative I will be at negative 20 so each of these distances I spent $10 I'd be at 0 another $10 I'd be at negative 10 another $10 I would be at negative 24 in this whole distance right here is how much I spent I spent I spent $30 so the general idea when you spend or if you subtract or we're getting colder you would move to the left of the number line the numbers would get smaller and we now know they can get smaller than 0 they can go to negative 1 negative 2 they can even go to negative 1 point 5 negative 1.6 you're getting more and more negative the more you lose if you're adding if I go and get my paycheck I will move to the right of the number line to the right of the number line now with that out of the way let's just do a couple of more pure math problems and just think about what it means if we were to say if we were to say let's say 3 3 minus 4 so once again this is exactly the situation that we did here with the temperature we starting at 3 and we're subtracting 4 so we're gonna move forward to the left we go 1 2 3 4 so that gets us to that gets us to negative 1 and when you're starting to do this so you really understand what a negative number means I really encourage you to visualize the number line and really move along it depending on whether you're adding and subtracting now let's do a couple of more let's say I have let's say I have 2 minus 8 2 minus 8 and we'll think about more ways to do this in future videos but once again you just want to do the number line you have a 0 here we're at we're at let me draw the spacing a little bit so we have 0 here we're at 1 - if we're subtracting eight that means we're going to move to eight to the left so we're going to go one to the left two to the left so we've gone two to the left to get to zero we have to move how many more to the left well we've already moved two to the left to get to eight we have to move six more to the left so we're gonna have to move one two three four five six more to the left well where is that going to put us well we were at zero this is negative 1 negative 2 negative 3 negative 4 negative 5 negative 6 so 2 minus 8 is negative is negative 6 you have to move to minus 2 would be 0 when you're subtracting 8 you're subtracting another 6 so we go to negative 6 we go 6 below zero let me do one more example and this will be a little less conventional for you but hopefully it will make sense let us let us take and I'll do this in a new color hmm let me take negative 4 minus 2 so we're starting at a negative number and then we're subtracting from that and if it de seems confusing just remember the number line just remember the number line so this is zero right here this is negative 1 negative 2 negative 3 negative 4 so that's where we're starting now we're gonna subtract 2 from negative 4 so we're gonna move to to the left so we're gonna go if we subtract 1 we will be at negative 5 if we subtract another one we are going to be at negative 6 we are going to be at negative 6 so this is negative 6 let's do another interesting thing let's start let's start at negative 3 let's say we have negative 3 instead of subtracting something from that let's add let's add 2 to it so where would this put us on the number line so we're starting at negative 3 and we're adding 2 so we're going to move to the right so you add 1 you become negative 2 but if you add another one which we have to do you become negative 1 you move 2 to the right so negative 3 plus negative 2 is it is negative one and you can see for yourself that this all fits our traditional notion of adding and subtracting if we start at negative one and we subtract two we should get negative three kind of reverses this thing up here negative three plus two gets us there then if we start then we subtract two we should get back to negative three and we see that happens if you start at negative one if you start at negative one right over here and you subtract two you move two to the left you get back to negative three so hopefully this starts to give you a sense of what it means to deal with or add and subtract negative numbers but we're gonna give a lot more examples in the next video we're actually going to see what it means to subtract a negative number