Algebra, part I- Numbers, Variables, Operations, Expressions, Relations
This series of lessons is designed to help you learn, or review, the fundamentals of algebra. We start off with the very basics- numbers, variables, and operations.
Algebra is one of the main branches of mathematics. It concerns studying number structures and relations.
Let's start with the very first thing that math involves- numbers.
Numbers- these are the symbols we use to do math. For example, 3, -289, 0, five.
There are actually various types of numbers around. They include:
A. Real numbers -This group, denoted by a lareg R, represents the large portion of numbers you've ever seen. Every numberyou can place on a number line is real.
B. Natural numbers - This group, generally denoted by an N, is the group of all positive integers, like 7, 18, or 219499234.
C. Integers - This group is denoted by a Z, and it represents all integers, including the natural numbers, 0, and negative multiples of all natural numbers like -5 and -2439.
D.
Rationals - This group is Q, and it
represents all nice numbers that can be expressed as a ratio of two
integers. 1, 1/3, 0.4 and -6/7 are all rational numbers, while
or
are irrational numbers.
Numbers are cool. You may ask yourself, why do I need all of these different types of numbers? Are there unreal numbers floating around, and if so, what are they used for? Why do we need irrationals, can't all numbers just be nice?
Questions such as this will be answered in a future part of the series.
For
now, let's introduce the next big step-
variables:
Variables are non-numerical representations of numbers. They're usually letters, like X or Y. They can also be Greek letters like alpha, or crazy stuff like @. In actuality, variables can be anything you can think of, like a pickle or a shoe.
So what are variables useful for? We use variables to represent unknown numbers in mathematical expressions. Before we can move on to mathematical expressions, however, we have to take a look at one major thing first.
Introducing- operations:
Operations are basic actions you can perform with your numbers and variables.
The basic operations are:
A. Addition: for example,
B. Multiplication: for example,
There are other minor variations of these operations:
C. Subtraction, adding a negative:
D. Division, multiplying by an inverse:
.
Cool.
Now, let's put it all together:
Sounds like a joke, right? Ok, here goes:This is a mathematical
expression. Expressions that involve one or more variables and some
constants are called
%{color:#a81e1e}polynomials. is another polynomial.
There are lots of polynomials around, but what are they good
for?
On their own, polynomials aren't good for much. But they become a whole lot more useful when we add this:
Relations between mathematical variables
Relations in math, you may be surprised to know, have nothing to do with my various ex-girlfriends. These mathematical symbols include "=", ">", "<", etc. They allow us to compare mathematical expressions.
Here's a super easy
example: . Here's a slightly more
complicated example:
. You may already realize
these are equivalent, i.e. they mean the same thing. How do I know
that? Simple, because mathematical expressions can be simplified.
For example, say
. We can subtract
3 from both sides to get
, then divide by 5 to
get
.
This process is called Solving mathematical
equations (with 1 unknown).
Next time, we'll talk about solving inequalities, equations with 2 unknowns, and other techniques to simplify expressions.
Thanks
for reading this Welcome to Algebra Lesson!
Post Comments
vikky123 said – Fri, 01 Aug 2008 09:29:00 -0000 ( Flag Edit Link )
very good .continue more…........