Adding & subtracting negative numbers

let's have some practice adding and subtracting negative numbers so the first example I want to look at is two minus three so right now I'm just subtracting a positive number from another positive number but you might already see that I'm subtracting a larger number from a smaller number so I'm probably or I will definitely end up with a negative number let's just think about this a little bit and I'm gonna do it with the number line so there's my number line right over there now this is 0 this is 1 this is 2 this is negative 1 this is negative 2 we could view this as starting at 2 so this is 2 right over here and then we're gonna subtract 3 from that 2 so we're gonna move 3 to the left on the number line so we're gonna move 3 to the left 1 2 3 and that gets us to negative 1 this is equal to negative 1 now let's mix it up a little bit more let's imagine what we would what would happen if we had negative 2 negative 2 minus 3 so this was positive 2 minus 3 now think about negative 2 minus 3 so once again let's draw our number line and I'll put 0 over here so this is 0 this is 1 this is negative 1 negative 2 negative 3 negative 4 negative 5 negative 6 and I could keep going but we're starting at negative 2 starting at negative 2 and then we're subtracting 3 again so once again we're gonna move 3 to the left of negative 2 so we go 1 2 3 we end up at negative 5 so this is negative 5 so notice in both situations we subtracted 3 we moved 3 to the left on the number line it's just here we started 2 to the right of 0 here we started 2 to the left two to the left of 0 this is negative 2 let's do another example with these same with these same numbers let's imagine negative 2 negative 2 plus 2 I'm sorry plus 3 I encourage you to pause this video and try to think about this on your own so will you draw the number line again I could draw a straighter number line than that so draw the number line again now let's say that this is negative 2 negative 1 0 1 & 2 again we're starting at negative 2 we're starting to to the left of 0 so we're starting at negative 2 and we're gonna add 3 so we're gonna go 3 to the right now 1 2 3 and we end up at positive end up at positive 1 now let's think about now let's think about 2 so positive 2 and we're going to subtract a negative 3 so we're gonna subtract negative 3 and other videos we've already talked about this in fact there's a video explaining why this actually makes sense but when you subtract a negative this is same this is the same thing as adding the positive so 2 minus negative 3 is the exact same thing as 2 plus 2 plus positive 3 these two statements are equivalent and this is just boils down to this right over here is just going to be 5 now let's mix it up a little bit more let's imagine negative 2 let's imagine negative 2 minus negative 3 minus negative 3 now this might seem really intimidating I have all of these negatives in place here but you just have to remember subtracting a negative like this is going to get you a positive so this is the exact same thing as negative 2 plus 3 and negative 2 plus 3 we've already seen it right over here you start at negative 2 you start to to the left of 0 and then we're going to go 3 to the right we're adding 3 1 2 3