Rules for Multiplying and Dividing Signed Numbers

There are different ways to memorize the rules for multiplying and dividing signed numbers. Often times, if we discover why a rule exists, then we will have an easier time not forgetting that rule. Let's being with multiplying numbers. We learned in second grade that 2 x 4 = 8. We also learned that multiplication is "quick addition" and I can use this to help me when it comes to multiplying signed numbers. 2 x 4 = 8, also means that I have added groups of two (2 + 2 + 2 + 2) a total of four times, which will give me 8 or, I can also say that I added four (4 + 4) a total of two times to get 8. I can use the same approach if I wanted to find the product of -2 x 4. Using the same logic that I am adding -2 a total of four times (-2 + -2 + - 2 + -2),and since I know that -2 + -2 = -4. I get -4 + - 4 which is -8. The key here is to make sure you know your rules for adding signed numbers. The same rule will apply if I had to find the product of -4 x 2. I am adding -4 a total of 2 times so I can write -4 + -4 and still get -8. Now, I can write my own set of rules for multiplying numbers with opposite signs, if the signs are opposite, meaning one number is positive and the other is negative, my product will be negative. What happens when the signs are the same? If the signs are the same, our product is positive. Yes, even if both numbers are negative, when multiplied together, we get a positive solution. What about division? Well, division is simply the reverse of multiplication. 16 divided by 8 is 2 (16 / 8 = 2), because 2 x 8 is 16, right? We look at division of signed numbers the same way. -16 / 8 = ? I ask myself,"What must I multiply 8 by to get a negative 16?" If I say "2" that would not be correct because I know that positive 8 times positive 2 is positive 16. But I want negative 16, therefore my answer is negative 2. I check my answer using what I know about multiplying signed numbers. Does 8 x -2 = -16? Yes it does because -8 + -8 = -16 just as -2 + -2 + -2 + -2 + -2 + - 2 + -2 + -2 = -16. What if the signs are the same? Such as -16 / -8. The same rule applies for division as it does for multiplication. A negative divided by a negative is positive. When it comes to multiplying and dividing, we need only remember two things...if the signs are the same, our answer is positive, if the signs are different, our answer is negative.