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we need to come up with some rules how to add sine numbers for example if I gave you four plus and negative three and I say what's the answer by the way I have a habit just me I have a habit I put all the negative numbers and parentheses doesn't matter if you put them or not but that's just my habit what's negative five plus a negative seven what is negative fifteen plus ten what's eight plus seven we can answer one question right now eight plus seven we should know the answer that that's what 15 because the numbers we've done that but we never dealt with it with positive and negative numbers so how do we add when you have positive and negative numbers and the rule is straightforward how do we go if the numbers have the same sign if the two numbers have the same sign what do you want to do add the absolute value of the number add the absolute values and keep the sign notice these two numbers were the same we add them without the sign 8 + 7 15 these numbers have the same sign if we add the 5 + 7 which is what 12 when we keep the sign so the two numbers have the same sign just add the numbers without the signs and leave the sign alone what about the numbers have different signs subtract the smaller we think about the absolute value the smaller absolute value from the larger one and take the sign of the number with the larger absolute value the larger absolute value so let's look at these guys these two have different signs subtract the smaller absolute value from the larger one what's the absolute value for negative 3 3 what's the absolute value for 4 subtract 3 from 4 what's 3 from 4 1 and take the sign of the number with the larger absolute value this one has the larger absolute value what's the sign of that positive so basically don't pay attention to the sign in translation don't pay attention to the sign subtract the smaller number from the larger number and take the sign of the larger that's what this one is telling you here's two numbers with different signs don't pay attention to the signs first subtract the smaller number from the larger number 10 from 15 5 what's the sign of the larger negative that's a negative 5 when the two numbers have the same sign don't pay attention to the sign add them and keep the sign much easier than all this definition and what I'm gonna do and now just give you problems and practice on these I'm not gonna take absolute value and do all the gibberish stuff we can do them in our head - three plus or minus one look at the two numbers same sign or different signs same so what do you do add them one in three four and keep the sign let me keep the sign what is negative two plus nine same sign or different signs subtract the smaller from the larger two from nine and what's the sign of the larger positive we never put the plus sign just write seven negative 35 plus 35 yep well different signs subtract them well 35 from 3500 does not have a sign you try it negative two point one plus zero point eight same sign or different signs so go ahead see if you can figure the rule you subtract the smaller from the larger right so what's 2.1 take away 0.88 from one we can't write this becomes one that's 11 8 from 11 3 & 0 from 1 which is 1 so it's 1 point 3 and what is the sign of the larger positive or negative negative you try this one negative 3 plus 1 plus 8 plus a negative 6 do two at a time what is negative three plus one yep you subtract the smaller from the larger which is two and what's the sign commonness let me copy the rest of the problem I have enough paper don't worry about it now the next one minus two plus eight same sign her up as a sign opposite subtract the smaller from the larger six and what's a sign of the larger positive and the last one is what different signs subtract them six from six and what's the sign zero now some of you probably learn a different way when you have numbers like these you probably learn to take the negative numbers and make one number out of them so add this to this because they're both negative what's -3 plus a minus 6 when they're the same sign what do you do add them and keep the sign what's 3 & 6 9 with the sign minus take the positive numbers add them make one number out of them these are the positive numbers what's 1 plus 8 9 now you subtract these numbers to the different signs 9 from 9 zero so when you have a lot of numbers a chain of them that's a common practice you'll take all the positive numbers make one number out of them add them take all the negative numbers make one number by adding them then do whatever you need to do let's give you another one like this and you can do it any way you want to now when I do this I'm going to do it both ways I'm gonna grab the first two numbers and I look at them as a three plus and negative one these are opposite signs so what happens when you add the opposite signs subtract the smaller from the larger one from three two and what's the sign of the larger positive let me write the rest of the problem now we take the next tool notice they are what opposite signs subtract the smaller from the larger two from eight six and what's the sign of the larger the absolute value minus a larger than negative six right now again opposite signs subtract the smaller from the larger absolute value wise to from 6 4 and what's the sign of the larger absolute value negative and finally these two have the same sign you add them and you keep the sign which is what negative 15 again you the other way of doing it is a lot faster and probably easier we take all the negative numbers we make one number out of them we add them into one number what's one in eight nine and eleven 20 right that's a negative 20 there's the plus sign take all the positive numbers and add them two and three five now notice these numbers are what opposite and signs subtract the smaller from the larger five from 2015 what's the sign here negatives are the same answer two steps now I'm going to continue with the video so if you understood the multiplication I mean the addition well the subtraction is really nothing but continuation of this so I'm going to the next section on this so this video will have both sections on it how do we subtract that's section seven three subtractions of sign number and the rule I'm going to use is this one we have a rule methods if you want to subtract two numbers a minus B that is really the same as a plus the opposite of B notice what I did let's pay attention slowly I changed that minus sign to a plus so the first value did not change so the first one didn't change the second one I won't change the minus to a plus and what happened to a third piece I took the opposite of that so if I said to you what is five minus three and we could have given you some set of rules for that but we decided not to because this equation says you can use the same rule just learn for addition if you do one extra step and that is leave the first number alone change this one to addition no longer subtraction and take the opposite of that number this is the same as this do we know how to add that we just finish that two numbers different signs subtract the smaller from the larger which is what - and what's the sign positive so instead of giving you another set of rules we're saying no no no let's use the same rules that we have learn them and just make that extra step seven minus a negative four correct leave the first one alone change this one to a plus and take the opposite of that what's the opposite of negative 4 4 7 plus 4 the same sign you add them which is what 11 signs positive minus 2 minus 4 leave the first one alone change the subtraction to addition and change the 4 to it negative 4 you adding two numbers of the same sign so what's the result negative 6 so let's give you a few to try do we have an answer to that let's see leave the first one alone this becomes a plus and what's the opposite - negative - two opposite signs subtract the smaller from the larger - from four which is what - and what's the sign of the larger absolute value larger negative nine minus a negative nine try that what do we have 18 yep leave the first one alone change that to a plus and the opposite of negative nine which is what nine nine plus nine eighteen negative nine minus twelve point one this will be leave the first one alone negative 9 this becomes plus and this number becomes what negative 12.1 the two numbers have the same sign you add them is that 21.1 and the sign will be the same keep the sign negative twenty one point one couple more then this section is done five plus negative six minus negative eleven if you remember once plus wouldn't touch anything so the first two are gonna stay the same till we get to that one we're gonna change it to a plus or the first to no change because these are addition here is a subtraction change the minus to addition and do what the opposite of that number which is what eleven let's do the first two different signs subtract the smaller from the larger five from six negative one very good it's one with the sign - add to add a 11 notice different signs subtract the smaller from the larger which is what 10 and the sign is positive okay you try this I did something on purpose here intentionally and there's the - - here I don't put in parentheses because a lot of times your book doesn't put them in parenthesis does that mean to change that to a plus no because that's not subtraction what is that then that's really a negative number I just didn't put it there so that number is a negative number stays the same I always put them around in parenthesis but the book doesn't this is a subtractions see that - that's subtraction make it a plus and what's the opposite of 3 negative 3 that's addition we don't touch it and they're number one touch we only switch the sign when it's subtractions so the first number was a negative number notice all the numbers are negative if you want you can just add them and stick the sign in two and three five five and five ten what's the sign negative ten four minus two minus a negative three now if you remember the order of operation you're going to do what what's inside the parentheses first remember that so let's not pay attention to that four in the front this becomes what - and what are we going to do with that minus sign change it to addition and that number becomes what what's two plus three five let's bring the rest of the problem there is the - and there's the four now we have subtractions what do we do change it to addition and change that number to it negative five for plus and negative five different signs subtract the smaller from the larger for from five which is what one the sign is minus one one more of these problems do what's inside the parentheses where is 3 3 plus negative 2 what is that equal to 1 subtract the smaller from the larger the side of the larger as one now that becomes the new problem how do we subtract leave the first one change it to addition take the opposite of their number 1 from 7 6