this is lesson number 10 multiplying and dividing real numbers before we actually dive into the rules for multiplying and dividing real numbers I need to run through three different types of fractions that you need to know about and commit to memory if you can keep these straight positives and negatives mixed with fractions will become a little bit easier for you so let me tell you what they are if I write out 1 15 you know that the one is positive and the five is positive but what if I write it like this it's a comma there what if I write the negative I put a negative out in front who's negative is the one negative is the five negative are both the one and five negative is nobody negative well here's the answer this number negative one5 means this it means either the one is negative or the five is negative but not both so there are three fractions that mean the same thing the negative out in front negative 1 is the same thing as negative 1 over5 or 1 over neg5 those three mean the same thing do another one let's say I do uh -2/3 okay the negative is with the two right now well it would also mean I could write that as put a comma there I can put that negative out in front and I could put it out down with a three and it would mean the same thing let's do one more let's go uh -2 that was bad that was bad let's go two over this pencil is about ready to drive me nuts two over7 the negative as we see is downstairs I can write it upstairs or I can write it out in front you need to know that all three of those mean the same thing all right now let's multiply and divide real numbers and uh there's a couple rules with this that we got to be aware of so let's do some easy stuff first so let's do um let's do 2 * -6 so we're doing 2 * 6 actually let me put a couple down together Let's do let's do -2 * 6 and then let's do -2 * -6 so there's basically basically three combinations you need to worry about all right and let's look at them real quick um notice notice that I have one negative here I have one negative here and I have two negatives here another way of thinking about it this guy's positive and this guy's negative this guy's negative this guy's positive negative and negative if the signs are different this is one way of thinking about it if the signs are different your answer will be negative different signs negative if the signs are the same the answer is going to be positive so different different and the same if the signs are different the answer is negative the signs are different the answer is negative the signs are the same the answer is positive actually that kind of makes sense because you know if I asked you what is 2 * 6 you're going to say 12 do you ever sayga -2 no it's positive 12 look the signs are actually signs are the same so the rule actually does work with any case so this is going to be -12 this will be -12 this will be positive2 let's do a couple more let's do -4 times let's get away from six let's do4 * 5 let's do uh -4 * 5 let's do 5 * -4 and let's do four time five mix them up a little bit negative positive they're different different signs means negative answer negative negative same positive answer positive and negative positive and negative are different so it's a negative answer positive and positive they're the same if they're the same it's a positive answer what's four * 5 20 let's do another set let's go negative uh 2 * 7 let's do 7 * -2 let's do um -7 * 2 let's do -7 * -2 let's kind of mix it up I'm just looking through I'm just going to compare I'm looking for are they the same or are they different they're different so it's negative different so it's negative different so it's negative same so the answer will be positive so if they're different they're negative if they're the same it's positive 14 14 14 14 so what happens if we kind of put some of this together um we'll get something that looks like this let's say I did -2 * 6 * -3 let's do two at a time negative times positive they're different so the answer is going to be negative it's 12 multiplying negative time negative positive because they're the same that's 36 all right let's run through a couple other things um if I have a negative sitting in front of a um a parentheses something like this you need to understand that this negative is really a negative one and that this problem and this problem are the same thing we can call those a coefficient almost so the signs are same so it's going to be positive and that's four let doing a couple if I did uh negative five this is really a negative one signs are the same answer is positive 1 * 5 is five sometimes you might see something like this remember this you can think of it this way this is one way of thinking about it two negatives give you a positive that would be like a negative one signs are different so the answer is negative 1 * 6 is 6 let's do a couple others let's do negative * 1 * 1 * 5 two negatives right here I'm going to give you a positive signs are different ansers negative 1 * 1 is 1 signs are different again so that'll be negative as well 1 * 5 is five and there it is I got to sneeze in just a [Music] moment all right I'm back all right I'm gonna do number 30 with you on your homework so here's number 30 or something similar to number 30 so we're going to do negative um Negative X Plus let's say 16.4 and we're going to say x is equal to 2.6 all right this one's a little bit it's no different than what we've been doing but it's got a little bit of a Different Twist um and I put these in here for a certain reason to help you start recognizing how to add decimals together easily for example let's just plug in the -2.6 into here so we get Negative there's the -2.6 six make sure and use parenthesis when you do it I can't write a six there it is plus 16.4 remember two negatives give you a positive now let's look at this instead of reaching for your calculator let's just think this through real quick what's six and four isn't that 10 so when I add 2 + 16 and I get 18 this point this 6 and point4 really adds up to an extra one and so it becomes 19 um so I guess I'm trying to get you to recognize that 6 and 04 you're going to add one to whatever your answer is so 2 + 16 gives you 18 so add one that gives you 19 another example if I had 7 um let's say 7.2 Plus uh 5 5.8 7 and five is 12 but look 0 2 and8 is really a full one so that becomes 13 do one more let's do uh I'm thinking let's do 4.3 plus 12 7 notice that three and seven gives you 10 so that's a full one so 4 + 2 is 16 but I'm going to add one to that and it'll be 17 so as you're working through those just notice that uh sometimes those will work out for you if not you just do them in the calculator and get the answer but I'm looking for I'm trying to encourage you to do some of them in your head good luck on lesson number 10