## 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:**

bq.

**A. Addition:** for example,

bq.

**B.
Multiplication:**for example,

There are other minor variations of these operations:

bq.

**C. Subtraction, adding a negative:** bq.

**D. Division, multiplying by an inverse:** .

Cool.

Now, let's put it all together:

Sounds like a joke, right? Ok, here goes: . Wait… now what?

This is a mathematical expression. Expressions that involve one or
more variables and some constants are called
**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!**

**Click
Here for Algebra-part-i**

**Click
Here for Algebra-part-iii**

**Click
Here for Algebra-part-iv**

**Click
Here for Algebra-part-v**

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