 In this video we'll talk about multiplying and dividing real numbers. So let's see if we can follow the pattern. So positive two times positive two is four, two times one is two, two times zero is zero, and then two times negative one, well if we look at the pattern it looks like we're decreasing by two every time so it must be negative two. And then two times negative two if we decrease by two again we're going to be at negative four. If we have a negative two times a positive two it's negative four, just like what we just found. Negative two times one is negative two, we found that one two in the opposite order. Negative two times zero is zero, negative two times negative one, this time we're adding two every time so it should be a positive two, and a negative two times a negative two would be a positive four. If we look at the sign rule it's a product of two numbers of the same sign, that would be like these here and these here. When we have the same sign you'll notice that we always have a positive answer. And if we have a product of two numbers of different sign that's like these then we have a negative answer every time it doesn't waver. So let's see if the same thing is true for division. Four divided by two we know to be two, four divided by one we know to be four, four divided by zero does not exist because you can't divide by zero. And so then four divided by negative one, if you look at this it looks like we are increasing by two every time, so four divided by negative one should be negative four, and four divided by negative two should be negative two, and negative four divided by two is negative two, just like four divided by negative two. Negative four divided by one is negative four. Again you can't divide by zero so it does not exist. And negative four divided by negative one then would be a positive four. And negative four divided by negative two would be a positive two. So are the sign rules same or different? Well when the signs are the same and we are dividing then it looks like we always got a positive answer, so that one works. And if the signs were opposites it looks like we always had a negative answer. The division sign rules are the same as the product rules. So let's try some, remember the rules. We have a negative times a positive, so that means that we are going to have a opposite signs, so when they are opposite signs then our answer is going to be a negative. So we have a negative and then we take three times four and that's twelve. Here we have the same signs and so we have a positive answer and then we take ten times nine to be ninety. How about this one? A negative divided by a positive, the opposite sign, so that's going to mean that our answer is a negative and twenty seven divided by three is nine. We have the same signs here, so we know we are going to have a positive answer and this is tricky. You find this a lot when we are solving equations, so you want to remember this one. Negative divided by negative is a positive and it's going to be a positive twenty one over twenty eight, but we can simplify that because this is seven times three and twenty eight is seven times four, so it's really a positive three over four. Now five divided by zero, remember we are dividing by zero so it does not exist. You can't divide by zero. Finally this problem, we have opposite signs so we know it's going to be a negative answer and then if we multiply we are going to have five times twelve on the top and four times twenty five on the bottom, which will give us sixty over one hundred and if we reduce that, they both can be divisible by ten and that will leave us with six over ten and then we still have a negative here all the way through and then I have a negative and they are both divisible by two so three times two is six and five times two is ten so our answer is negative three fifths.