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Basics of Algebra: Part I

by Oren Lahav

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 \sqrt{2} or \pi 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, 1+2=3 bq. B. Multiplication:for example, 2 * 3=6

There are other minor variations of these operations:

bq. C. Subtraction, adding a negative: 5+(-2)=5-2=3 bq. D. Division, multiplying by an inverse: 4 * (\frac{1}{2})=\frac{4}{2}=2.

Cool.

Now, let's put it all together:

Sounds like a joke, right? Ok, here goes: 5x+2. Wait… now what?
This is a mathematical expression. Expressions that involve one or more variables and some constants are called polynomials%. \frac{6a ^ 7}{11}+\frac{4a}{3}+326 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: x=4. Here's a slightly more complicated example: 2x=8. 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 5x+3=23. We can subtract 3 from both sides to get 5x=20, then divide by 5 to get x=4. 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

48 Comments
    veerendrab
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    veerendrabFri, 22 Aug 2008 09:52:11 -0000

    For a starter, it is best place to lean more.

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    manasa
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    manasaTue, 19 Aug 2008 08:25:05 -0000

    best place to learn math

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    bhola
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    bholaWed, 13 Aug 2008 19:29:50 -0000

    well very good refresher lesson

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    BUMBA
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    BUMBASat, 09 Aug 2008 12:20:57 -0000

    I am astudent of class XI ,Iwant to prepare for MATH OLYMPIAD.

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    oLahav
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    Oren LahavMon, 11 Aug 2008 14:06:13 -0000

    At the moment, LearnHub does not offer practice questions for the International Math Olympiad. This may be a future project for us to work on.

    However, you should feel free to make use of the SAT and GMAT Question Banks, which are full of math (and English) questions. Also, if you have any questions regarding specific problems, you can start a community or discussion about them, and the math-oriented LearnHubbers can attempt to help you solve them.

    Good luck on the Olympiad.

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    pratik agarwal
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    pratik agarwalFri, 08 Aug 2008 12:42:34 -0000

    I am class II student and I want to prepare for maths olympiad

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    alphavictor
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    Pravin SharmaMon, 11 Aug 2008 19:04:47 -0000

    wow.. what has this world come to?

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    kajal
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    kajalSat, 02 Aug 2008 14:34:45 -0000

    very good continue

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    mlmprasad
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    mlmprasadFri, 01 Aug 2008 08:43:45 -0000

    nice presentation

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    christieouseph
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    christieousephTue, 29 Jul 2008 17:17:50 -0000

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    DK Arya
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    DK ARYASun, 27 Jul 2008 19:48:41 -0000

    very good! presentation.

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    shriya93
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    shriya93Sun, 27 Jul 2008 11:14:02 -0000

    good stuff.makes us revise the previous class studies which is useful

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    boopathi
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    boopathiSat, 26 Jul 2008 12:03:53 -0000

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    sushil
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    sushilTue, 22 Jul 2008 12:24:06 -0000

    very good effort. i like it

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    Karancha
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    Karan ChaudharyTue, 15 Jul 2008 04:21:29 -0000

    Keep Up the Good Work!

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    vipin
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    vipinWed, 09 Jul 2008 01:59:52 -0000

    good job dudes…..you people are really doing the nice job…

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    winner
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    winnerFri, 04 Jul 2008 05:43:53 -0000

    very gud for understanding basic math

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    Ashwin
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    Ashwin RazdanSun, 29 Jun 2008 09:04:04 -0000

    Good to start with. Liked your clear expression of thought.

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    partha_mylearnhub
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    PARTHATue, 10 Jun 2008 04:41:51 -0000

    this is a good preliminary lession

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    babai
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    babaiSat, 31 May 2008 08:56:34 -0000

    very well…

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    vikky123
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    vikas kumar Adi Fri, 01 Aug 2008 09:29:00 -0000

    very good .continue more………..

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Last Updated At Jan 08, 2013
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48 Comments Basics Algebra algebra Numbers variables Operations expressions Relations

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