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Multiplying and Dividing Positive and Negative Numbers

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Today we're going to talk about multiplying and dividing positive and negative numbers. As you can see behind me, I started by creating a chart with rules for multiplying and dividing positive and negative numbers. We're going to put some examples right alongside it, so you can either go through the table and write it down as I go through it, or you can wait until the end and copy down in your notes. But either way you're going to want to make sure that you get this in your notes so that you can use it. You can refer to it as you're doing your own examples.

All right, so let's look at our rules. When we are multiplying or dividing by a negative number, the sign of our answer is going to change. So we're actually going to start with something that rule does not apply to, something that we already know. If we're multiplying or dividing by a positive number, our answer is going to be positive. So positive times a positive equals positive. Positive divided by a positive equals a positive. You already know this. But here's an example. Positive 3 times positive 4 equals positive 12. And a positive 8 divided by a positive 2 is going to give me positive 4.

Again the general rule doesn't apply, because I'm multiplying or dividing by a positive number. So my answer is going to stay positive, the same sign as the number I started with.

All right, now let's look at an example where the rule does apply. Let's say I start with a positive number, and I multiply or divide by a negative. Then my answer is going to be negative. It's going to have the opposite sign of what I started with. Instead of positive, it changes to a negative. So an example of that would be positive 3 times negative 4. It's going to give me negative 12. Instead of positive, my answer is negative. Similarly, a positive 8 divided by a negative 2 is going to give me negative 4. Instead of positive, my answer is negative.

Let's look at another example where again the rule does not apply, because we are not multiplying or dividing by a negative. If I start with a negative number, multiply or divide by a positive, my answer's going to stay negative. So a negative 3 times a positive 4 is going to give me negative 12. And a negative 8 divided by a positive 2 is going to give me negative 4.

My problem started with a negative number, and my answer is going to be negative. The sign doesn't change because, again, we only multiplied or divided by a positive number.

So one last case. A negative multiplied or divided by another negative is going to become positive. Since I multiply or divide it by a negative number, my answer is going to be positive instead of negative. So a negative 3 multiplied by a negative 4 is going to give me positive 12. Instead of negative, we have positive. The sign of our answer changes.

Same thing here. A negative 8 divided by a negative 2 is going to give me a positive 4. Instead of negative, my answer is positive.

So I hope that by using this table, and these examples, you'll be able to remember the rules for multiplying and dividing by a positive and negative number. Thanks for watching.