Algebra is a very powerful form of mathematics. It is based in and requires the use of arithmetic knowledge and principles. Normally, algebra is taught to children after they have been trained in the many aspects of arithmetic for years. Algebra, like mathematics is a form of math which millions of people use on a daily basis. Which parts of it, and how it is applied varies with the situation. Obviously, people in math oriented careers such as mechanical engineering or aeronautics or accountants are using a great deal more of it than theatre professionals or English teachers. Many jobs require little use of algebra, but most people’s lives, at least for adults, involves at least some.
There are a few fundamental principles of algebra, and some basic differences between it and arithmetic. For the first time, symbols are introduced that are, by comparison more complex and that require a higher level of mental organization to achieve. Right now we’ll just name them: The Communicative Law of Addition, 2. The Associative Law of Addition, 3. The Commutative Law of Multiplication, 4. The Associative Law of Multiplication, and 5. The Distributive Law of Multiplication over Addition.
One of the best uses for algebra is that people can make a different type of calculation using it. The best examples may come from the marketplace since we all buy items and a small shop is fairly easy to understand. For example, let’s say you go to take inventory at the end of a shift at a retail store. You see where the shelves are normally stocked and you can tell that there is now space for 5 more to be brought from the back to stock the shelf. You know that the shelf holds 15 of this kind of item- let’s say it’s bath towels. What you are wondering is: once you re-stock the shelf, how many will you have in stock since you have to place your next order before you go below 55 bath towels in stock. At the beginning of the week, when you unloaded the truck, there were 103 of these bath towels. A normal algebra problem is: How many bath towels must be sold before you re-order? 103-X=55 is the math sentence that you can create to express this.
If you see a subtraction problem ‘buried’ in this sentence, you are seeing that correctly. Remember, the power of algebra is to make you able to do more with arithmetic than you had previously realized was possible. Math consists of facts. That is, when you add 2+2 you ALWAYS get 4 if you do it correctly. It doesn’t matter what you’re adding up. It’s just true. Also, you know very well that once you are aware that 2+2=4, if you are getting any other kind of result then you have made a mistake and are wrong. This is what makes math as great as logic; you can always tell right from wrong when you do it right, once you know what you are doing. In this straightforward problem above there is only one answer. The way to solve it is to rearrange the equation and isolate the variable.
The definition of a variable is that it indicates an unknown quantity that we are going to solve for in an equation. 103-X=55. Luckily, another rule of algebra is that this kind of equation is always balanced, just like a set of scales. So, since the difference between 103 and 55 can be expressed through subtraction to get just one other number; then we can ‘rephrase’ the above equation to read: 103-55=X, and now we are back to arithmetic.
That problem shows you perfectly the way simple algebra and arithmetic go together and yet are different. In the next lessons we will go more into depth about different kinds of equations and about working with the numbers.
