Basic arithmetic is the study of the fundamental operations of mathematics: addition, subtraction, multiplication and division of numbers. Before taking an algebra course, you should have an understanding of how to solve problems that use each of those four operations and should be familiar with basic multiplication tables (for example, knowing the answer to "what's six times seven?").
Basic algebra introduces the concept of variables and constants. A "constant" is simply a number. A "variable" is a letter (traditionally "x") that represents a number, but we don't initially know which number it represents. The goal of most algebra problems is to figure out what number the variable is equal to.
One of the first things you'll learn in basic algebra is how to solve linear equations. An example of a simple linear equation is as follows:
3x + 5 = 20
In the example, x is the variable, 3, 5, and 20 are the constants, so your job is to figure out what number x represents. (When the variable is right next to another number, that's a way of representing multiplication; so the example above can be read as "three times 'x' plus five equals twenty.")
It's best to think of equations as consisting of two sides, split up by the equal sign. Using arithmetic, you can effectively move all the constants over to one side, leaving x by itself and thus solving the equation.
The first step to solving an equation is understanding that both sides will still be equal if you do the same thing to each side. So if you subtracted five from both sides of the equation, you would get:
3x + 5 - 5 = 20 - 5
That simplifies to:
3x = 15
Suddenly the equation is a lot simpler. Since division is the opposite of multiplication (just like subtraction is the opposite of addition), we can get the x by itself by dividing 3 from both sides:
3x/3 = 15/3
3x divided by 3 cancels out each 3 and simplifies to just x. 15 divided by 3 is 5. So we're left with:
x = 5
And now that x is by itself on one side, you're finished.
Algebra takes the basic task of "find the variable" and keeps adding layers of complexity on top of it. Beyond the four arithmetic functions, some equations will involve exponents, square roots or more than one variable. Often, your answers won't look like traditional answers at all; instead of "x = 5," you could end up with "x = (5y - a)/z." You'll also most likely learn concepts such as absolute value (the distance of a number from zero), factoring, the Quadratic Formula and imaginary numbers.
After basic algebra is mastered, the normal course progression involves taking geometry, trigonometry, and eventually calculus, while nonrequired supplementary courses commonly include statistics and probability. Geometry uses algebraic equations to find the size, shape and position of points, lines and shapes. Trigonometry (often incorporated into pre-calculus classes) is an extension of geometry dealing largely in right triangles and the application of the functions sine, cosine and tangent. Finally, calculus is the study of limits, derivatives and integrals.