Multiplication how to Determine the Sign of the Result

Have you ever had to multiply positive and negative numbers and wondered whether the result should be positive or negative? Do you struggle to remember whether two negatives equals another negative or a positive? Assuming that you can multiply basic numbers, this article will instruct you on determining the correct sign for the product or answer when multiplying positive and negative numbers. There are only two possibilities: the product will be positive or the product will be negative. Basically you only need to remember one rule for each situation.

Positive products

When will the product be positive? And when will the product be negative? The product or answer will be positive when both numbers being multiplied have the same sign. That means multiplying two positive numbers or multiplying two negative numbers. Either way, the product will be positive. It may seem a little unusual, however it is true that multiplying two negative numbers will leave you with a positive product. So, if both signs are the same your product is positive. Below are some simple examples that show how multiplying numbers with the same sign always results in a positive result.

Examples with a positive result:

3 x 4 = 12
(Positive three times positive four equals positive twelve.)

-3 x -4 = 12
(Negative three times negative four equals positive twelve.)

Negative products

If the signs of the two numbers are mixed, that is, one is negative and one is positive, the product will be negative. That’s it. When multiplying two numbers with mixed signs, the answer will always be negative. Below are some examples to give you an idea of how this type of multiplication looks.

Examples with a negative result 

2 x -5 = -10
(Positive two times negative five equals negative ten.)

-2 x 5 = -10
(Negative two times positive five equals negative ten.)

In summary, there only two possible instances for the signs of the product or answer when multiplying two numbers. If the numbers being multiplied are the same sign the answer will be positive and if the numbers being multiplied have different signs then the answer will be negative. By following the above simple rules when multiplying numbers, you will be well on your way to mastering the art of determining the sign of the product of multiplied numbers. After a while, you will find that the rules will become second nature and you will no longer have to consciously remind yourself of how to determine the sign.