Have you ever forgotten some of the basic algebraic laws and can't find your old high school text to look them up? Want to dazzle your co-workers with math terminology that they know they should remember? Well, this page will be growing as new tables of those basic arithmetic laws are added. There are lot of mathematical rules, so over time, this page will continue to expand.
| Algebraic Laws | ||
|---|---|---|
| Commutative Law | Addition | a + b = b + a |
| Multiplication | ab = ba | |
| Associative Law | Addition | a + (b + c) = (a + b) + c = (a + c) + b |
| Multiplication | a(bc) = (ab)c = (ac)b | |
| Distributive Law | Multiplication | a(b+c) = ab+ac |
| Rules of Signs | ||
| Addition and Subtraction | a + (-b) = a - (+b) = a - b | |
| a + (+b) = a - (-b) = a + b | ||
| Multiplication | (+a)(+b) = (-a)(-b) = +ab | |
| (+a)(-b) = (-a)(+b) = -(+a)(+b) = -ab | ||
| Division | (+a)/(+b) = (-a)/(-b) = -(-a)/(+b) = -(+a)/(-b) = a/b | |
| (+a)/(-b) = (-a)/(+b) = -(-a)/(-b) = -a/b | ||
| Exponents | ||
| Definition | an = a * a * a * a . . . [for n factors of "a"] | |
| Laws of Exponents | Products | xa * xb = xa+b |
| Quotients | xa/xb = xa-b | |
| Powers | (xa)b = xab = (xb)a | |
| Product Raised to a Power | (xy)n = xn * yn | |
| Quotient Raised to a Power | (x/y)n = xn/yn for y not equal to 0. | |
| Zero Exponent | x0 = 1 for all x not equal to 0. | |
| Negative Exponent | x-a = 1/xa for all x not equal to 0. | |