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Rules Help You Out

Sometimes you might become frustrated with all the rules in your life. Do this. Do that. Don't do this. We agree, sometimes it can be too much. However, the rules that help you do math make life so much easier. They provide a framework where everyone gets the same answer to the same problems. 2+2 will always be four because of specific rules. 2+2*3 will always be 8 because of the order of operations you already know about. The big guidelines in arithmetic happen for addition and multiplication. You can move numbers around, switch sides, add nothing, and you can totally change a problem. Many of the difficult problems you find on a test can be shuffled around to create easier problems. The rules in math are your friends.

Identities

An identity is an equation. It's got some terms and an equals sign. The key to an identity is that it is true for any values that you use in the place of the variable. As a reminder, a variable is a letter that can be used to represent any number. X, y, and z are variables you will often find in math. Easy examples of identities include the concept that a+0=a or a*1=a. As you move forward in math and learn geometry and trigonometry, you will learn about many more identities. You can also make your own identities. They don't have to be famous ones. x/5=0.2(x) will always be true no matter what real number you choose for x. The whole thing is called an identity equation. Whatever identity you make up, it MUST be true all of the time for every real number.

Axioms and Laws

Axioms are true statements in math. They set up a general idea that you can use in a variety of problems. They cannot be shown through mathematical proofs. They are just starting point statements. You might also hear the term postulate instead of axiom. For example, if a+b is a real number, a*b is also a real number. There's no mathematical proof that will show you this is true, it just is. When you add two real numbers and get a real number, you will also get a real number if you multiply them. You'll be learning about commutativity in the next section. You'll understand the axiom that states a+b=b+a. This is just a statement or rule that is always true.

You'll also hear about laws in mathematics. They are very close to axioms. There are associative laws, commutative laws, and distributive laws in addition and multiplication. Use the term your teacher wants you to use. Remember that laws in science are different from laws in math. Mathematical laws describe situations in abstract environments. Scientific laws have evidence and observation to support them. The laws in math are starting points while the laws in science are proven over time. Sir Isaac Newton didn't sit down and say "This is a law of motion." He observed the world, used calculus, and showed that the law worked through hundreds of experiments.

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