law of math

You probably know that the basic operations of arithmetic are:
addition
subtraction
multiplication
division
Each of these (and the higher operations as well) have certain "properties." That means that each has certain ways that it deal with particular "laws" of mathematics.
What is nice about these "laws" is that most of them are simply descriptions of things that you know happen.
For example, with addition, you know that if you have 5 things, and you get another 3 of them, you will end up with 8 things. You also know that if you started out with 3 things, and you added 5, you would still end up with 8 things.
This kind of law is simply a description of reality. I like to call it a "descriptive" law.* Don't let that somewhat big word throw you. You know what "describe" means, so you can easily see that a "descriptive law" is something that describes what happens. It doesn't happen because we "want" it to, or because "the teacher said so" or because some idiot behind a desk at the state capitol decided that he wanted to test you on it. I happens regardless of what we "think" about it, or what we want. We can all see that it happens. It is a "shared reality" which we can use.
You can also consider descriptive laws laws of nature. They happen naturally. We didn't have to invent them, they just "showed up."
A good example of a descriptive law is the Law of Gravity. Simply taken, that law states "If you drop it, it's gonna fall." You can't really argue with that. (Yes, sure, you can if you are in space, etc. but let's not get silly here, ok?) It's not like there was no gravity, and one day Isaac Newton said, "Hey, you know what would be fun? If things fell when you dropped them," and then all of a sudden everything started dropping from the sky. In other words, Newton didn't decree the law, he described it.
Just to be a little more complete on this, let me say that noticing something happens often does not mean that it will happen always. These things have to be proven by rational proof to become what we call a "law." Newton was not great because he noticed "things fell." (Heck, even I notice that!) His greatness lie in his proofs, among other things.
OK, so why am I going into such detail about descriptive laws? Because there is another kind, which is a little harder to understand, and I don't want you to confuse the two.
The other kind of law is called "prescriptive." Before I come right out and tell you what that means, can you guess what that might mean? If a doctor "prescribes" something for you, s/he more or less tells you what to take. S/he is not describing what you are doing, s/ he is telling you what you must do. We hope that s/he has a good reason (and s/he usually does.) In other words, prescriptive laws don't describe laws, they decree them.
Examples of prescriptive laws would be the laws of a country, state, city, etc. Take the law that you are not allowed to rob a bank, for instance. Of course, in reality, you can rob a bank, but because it is best for society, they decreed that you shouldn't. On the other hand, when we go back to the law of gravity, that law isn't concerned with what you should or shouldn't do, it is concerned with what you can or cannot do. I think you get it by now.
In the case of prescriptive laws of math, they have been created to make the whole system of mathematics work, and be easier to understand. For example, there is the prescriptive law called "The Order of Operations" (you may know it as PEMDAS, or "Please Excuse My Dear Aunt Sally." There is no natural reason we have to do the operations in this order. It is simply a law agreed upon, so that everyone will get the same results as everyone else for certain equations. It keeps order.
One of the things that prescriptive laws MUST take into account is that they may not break any descriptive laws. That is because descriptive laws are not something which you can debate. They are not about what should happen, they are about what happens no matter what you think should happen. You cannot change descriptive laws. For example, you cannot make a law that "anytime you add two odd numbers you must get an odd number." It just wouldn't work. Try it. 9 + 5 = 14, 3 + 1 = 4, 5 + 7 = 12, and so on. You can say you made a law that "anytime you add two odd numbers you must get an odd number," but it will not be valid. It will be nonsense. It would be like making a law that said, "From now on everything will fall up when I drop it." It would sound cute and silly, but then you would have to grow up (about that, anyway.)
By the way, your math teacher probably never heard of these kinds of laws. They aren't in any of your textbooks. The reason for that is that neither teachers nor textbook authors tend to be philosophical about how you learn. The good part about that is that it means you don't need to learn the terms "descriptive" and "prescriptive" laws for any tests.
The reason I am telling you about them here, is because once you understand the deeper Ideas about laws, and why they exist, you will understand how to use them better, and not be intimidated by them.
* It has been pointed out to me that the terms "descriptive" and "prescriptive" already exist in the philosophy of science. My uses of these words is not necessarily based upon any existing uses and should not be confused with them. I simply use them to make it clear to the reader that some things are more or less inevitable, and others are convention.