Multiplication in school is generally begun with memorizing times tables. It isn’t until quite a bit further into schooling that negative numbers are introduced. Most students have a hard time grasping the very concept of negative numbers, so adding and subtracting with them is already difficult enough. Multiplying with them is simpler because determining the product’s (absolute) value is fairly easy. However, the new dilemma of figuring out whether the product will be negative or positive tends to give many kids trouble.
Although the reason behind what sign the product has may be difficult to understand, figuring out what the sign will be is actually simple. There are just two (yes, only TWO!) rules that you have to remember.
1. If the multipliers’ signs are the same, the product will be positive. This is to say: positive times positive equals positive, and negative times negative equals positive.
2. Simple enough, right? And- you guessed it- if the numbers to be multiplied have different signs, the product will be negative. In other words, negative times positive equals negative, and positive times negative equals negative.
As mentioned, the two rules are extremely simple. Most students get caught up on the second half of the first rule, and the entirety of the second. Their confusion is quite rational, however. If two positive numbers multiplied together make a positive product, then why wouldn’t two negative numbers multiplied together produce a negative product?
The idea that must be grasped is that negatives cancel each other out. In the first rule, we have negative times negative equals positive. Just imagine that the two negatives cancel each other, and a positive product remains. In the second rule, students tend to get caught up in the order of the signs, and forget the general rule of multiplication: A times B results in the same product as B times A.
The second rule has essentially the same equation listed twice. You’ll notice that only one of the numbers to be multiplied is negative, so there is no other negative to cancel them out. It’s as if the negatives get to run all over the positives, until they come across another negative, if you think about it. It doesn’t matter if the negative number or the positive number comes first, because the order of the numbers to be multiplied does not change the equation in any way.
The two rules listed are the only things you truly need to remember, and they are easily memorable anyway. Same sign: positive. Different signs: negative. There really isn’t much to it.