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.

Note Taking Using Index Cards for Signed Numbers

In this series we will discuss how to prepare for a test using note taking as a strategy. If you are preparing for a math test that involves memorizing rules for the purpose of solving a problem, then index cards would be a helpful tool. On one side of the index card write down the rule. On the other side of the card, work out a problem using the rule. You can make up the numbers yourself or use the textbook that provides the answer key, (that way you know for sure you did the problem correctly). For example, a lot of students may have trouble memorizing the rules for adding and subtracting signed numbers. Write down the rule for how to simplify when the signs are the same. The rule is "add and keep the common sign". On the other side of the card write down an example or two. -25 + -12. Work out the problem using the rule of adding to get 37 and keeping the common sign of both numbers (-) and our solution is -37. The rule for adding signed numbers that have opposite signs is "first subtract, then take the sign of the number that has the larger absolute value". Absolute value is the distance a number is from zero on a number line. We can not have a negative distance so absolute value is always positive. Let's use -25 + 12. The signs are opposite so we subtract to get 13. Then we look at each number, -25 and 12. -25 has the larger absolute value because the absolute value of -25 is 25 and the absolute value of 12 is 12. So we take the sign of -25 and our solution will be -13. So far we looked at addition problems, now we will look at when the problem involves subtraction. If the problem involves subtraction, first change the subtraction sign to an addition sign. Then change the sign of the second number. For example, 12 - 25. Use your pencil to change the subtraction to addition and now make 25, negative 25. So now we have, 12 + -25 which is an addition problem! So, use the rules for addition to finish the problem.  The signs are opposite so subtract and keep the sign of the number with the larger absolute value and we get -13. What if we were subtracting a negative number such as 25 - -12? We will still change the subtraction sign to an addition sign, then change the sign of the second number thus making negative 12, a positive 12. Now the expression is 25 + +12, which we all know is +37. Of course we know that practice makes perfect so memorizing the rules may take some time but being organized with well written rules and and numeric examples will only benefit you in the end.