Most new discoveries in physics are based on the search for new relationships between known quantities. A relationship will show how one quantity will affect the other. You might ask yourself how does wind affect the velocity of a golf ball traveling in the air? Or how far will the golf ball travel if hit with a given force? These are examples of the result of one quantity being related to the result of the other.

A given quantity does not necessarily have to be affected by only one other quantity. It may be be affected by two or more quantities. Lets look at this example. The displacement of the golf ball down the fairway (neglecting air resistance) is related to its initial velocity, length of time in motion, and the acceleration of the ball. When two or more quantities are involved, you can determine the relationship between them by changing one of the quantities and keeping the others the same, then measuring the results.

You will note that when dealing with a square when one of the sides of the square is doubled the perimeter is also doubled. This is one type of proportion. There are two types of proportions. The first are direct proportions. You would say "the perimeter of the square is directly proportional to the length of its side" (see table math-01). Ask yourself this, how is the area of a square proportional to the length of its side? In examination you will note that if for example the length of the side of the square is doubled the area of the square is multiplied by 2² or 4. If the length of the square were tripled the area of the square would be multiplied by 3² or 9 (see table math-01). This proportion would be read as "the area of the square is directly proportional to the square of the length of its side."

The second type of proportions are called inverse proportions. The word inverse here implies opposite. In this case it is the inverse of a direct proportion. In a direct proportion as one quantity increases so does the other. In an inverse proportion the opposite occurs; as one quantity increases the other decreases. An example of this would be the time required to go a certain distance decreases as you increase the speed at which you are moving. The equation for distance is distance equals rate times time (D=VT). In the table above you can see some simple examples of direct and inverse proportions.

By definition an equation denotes a relationship between two expressions. You may be saying well what is an expression. An expression is a number, variable, mathematical combination of two or more numbers and or variables. These are all examples of expression:

3 + 2
4 * 9
6n
x / n
8

If you add an equals sign (=) and evaluate the expression you get an equation.

3 + 2 = 5
4 * 9 = 30 + 6
6n = 30
x / n = Z
8 = 4n

Take a look at the second equation, 4 * 9 = 30 + 6. By separating this equation at the equals sign we get two expressions, 4 * 9 & 30 + 6. Both expressions when evaluated work to 36. Hence it is valid to say that the two expressions are equal.

Now lets look at the third bullet, 6n = 30. First you should recognize that "n" is a variable. A variable is a changing quantity that can have different values. Notice that the variable is directly besides the number 6 without any mathematical sign between them. This is a shorter method of writing 6 * n. Anytime you see two variables or a variable and a number besides each other with no sign between them it means multiply the two values. Note: this does not apply to two numbers besides each other (i.e. 66 is not equal to 6 * 6).

At the fourth bullet you will notice that the equation is comprised solely of variables and no numbers. Remember that x, n, & Z can be any assortment of numbers. For example 90 / 3 = 30, 28 / 4 = 7, 20 / .5 = 40 all satisfy the equation.

You will notice that the fifth bullet is similar to the third except that they are reversed. One unique property of an equation is the expression on the left side may be switched with the expression on the right and still be equal. In both the third and fifth bullets you have one number multiplied by a variable to give you another number. Using the principles of algebra you can "solve the equation" for the value of n.