hello everyone so in this lesson we're gonna start looking at integers so kevin what are integers okay guys so integers are numbers like these that you can see on your screen so they are complete numbers you see they don't have any funny decimals like 3 comma 2 1 4. that is not an integer they are all the complete numbers they include negatives they include 0 and they include 1 so it's all the numbers like minus 20 minus 18. so it's any negative and any positive number and also zero it just mustn't be any weird things with decimals and things like that like three comma eight to none of those so to define it i'm just gonna say that it's numbers like minus five minus four minus three minus two minus one zero one two and three and so on and so forth now we're going to do some integer calculations but to help you out in the beginning i'm going to draw a number line and the first calculation is going to be minus 3 plus 4. so if you are at -3 now whenever you plus you must go to the right so if you add four you would end up over here at one so minus three plus four is equal to one next minus two minus six so if we start at minus two now when you minus you must go backwards so it's one two three four five six so it gives you minus eight minus eight plus four so you start at minus eight and when you plus you always go to the right and that gives you minus four minus six plus three so minus six is over here and if you plus three you go to the right and so you end up at minus three for the next ones why not try pause the lesson or pause the video and try them yourself so here we're gonna do minus seven plus three so you start at minus seven and you add three and that will give you minus four ten minus twelve so technically i don't have a ten over here so 10 should be there and if you minus 12 well then you have to go 12 places back and so you'd end up at minus 2. 8 minus 10 so you start at 8 and you go 10 back why 10 back because it said minus and so you end up at minus two minus seven minus three so you start at minus seven and then do we go to the right or to the left well because we're minusing we go left one two three and so you end up at minus ten minus six minus two so we start at minus six and because that's a minus we're going to go two places to the left and that's minus eight minus three minus two so you start at minus three and you go two back and so that's minus five minus three minus two plus four so now we do three steps so we start at minus three and we minus two so that means one two backwards then you plus four so now we go four four it's one two three four and so you end up at minus one so can you see what i did there i went backwards first two places then i started here and i went four places forward and i ended up at minus one here's minus eight so we start at minus eight and we plus two so we go two to the right and then we plus four so we carry on going to the right three four until we end up with minus two minus three plus seven one two three four five six seven and then you plus two one two and so we end up with six all right guys but now this isn't grade three we need to know how to do this without a number line so let's start challenging ourselves okay so think about this three minus eight so imagine the number line in front of you if you have three and someone takes away eight well that would give you minus five then if you have minus five and you plus two then you would end up at minus three and then the last one is minus three minus five minus one so minus three minus five so minus three is over here and if you minus you go to the left and so three and five gives you eight so this would be minus eight then you're going another one backwards because it's minus and so after minus eight you would get minus nine all right guys so there we go you guys need to practice your integers and as you practice they become easier to work with