 This video will talk about adding and subtracting real numbers. Let's start with adding and the first way to talk about it is if they have the same sign. We all know how to add 2 plus 4, we know that that would be equal to 6, but let's use a number line to show us that it really is that. So we start at 2 and then it says to add 4, so we go 4 to the right because that's a positive direction, so 1, 2, 3, 4 and there we are at 6. What if that had been negative 2 plus a negative 4? Well, we would have started at negative 2 and we would have gone in the negative direction for units, so to the left. So we will 1, 2, 3, 4 and that gets us to negative 6. So we start here and we go left 4. In this example we started here and we went right 4. Alright, so what happens if we have different signs? Like this example of negative 3 plus 6. So again, you start wherever it is and you start at negative 3 and then it asks us to go 6, so this is a plus so we're going to go right 6 units. So from negative 3 we go 1, 2, 3, 4, 5, 6 and we're at 3. If we look at this one we have 8 plus a negative 9. So we started 8, we started 8 and then we're going to go negative 9 means we're going to go to the left 9. So we go 1, 2, 3, 4, 5, 6, 7, 8, 9 and we get down here at negative 1. So if you look at that, we had 2 plus 4 and it was equal to a positive 6 and we had negative 2 plus negative 4 and it's equal to negative 6. So we could just say when you add signs, if we just wanted to do the arithmetic without a number line, we would say that you just add the numbers and then assign the sign. If you have opposite numbers though we have negative 3 plus 6 so it's really kind of like taking the two numbers and subtracting them. So subtract, they say it's the absolute value of the numbers of each number and then assign the sign on the larger. What does that mean? Well that means here if we had this 3 plus negative 3 plus 6 it means the absolute value of negative 3 plus 6 but we have to subtract them. So it's the minus the absolute value of positive 6. So absolute value of 3 negative 3 would be 3 minus the absolute value of 6 would be 6 and 6 minus 3 if you want to switch them around you could say 6 minus 3 is equal to 3. Now we just have to determine what the sign is and 6 is larger and it's positive so we have a positive 3. If we look at the other example real quick we had 8 the absolute value of 8 minus the absolute value of negative 9. Although let's put the bigger number first so the absolute value of negative 9 minus the absolute value of 8, absolute value of negative 9 is 9 minus the absolute value of 8 which is 8 it's equal to 1 but again we have to go and see which was our bigger number. 9 was our bigger number and it was a negative so this is a negative 1.