Introduction to basic math

Basic Introduction of Basic Math​

By David493

For all you little ten year-old kids entering middle school, this stuff is necessary to be known if you even think about doing well in math​

Table of Contents

1. Introduction

2. The Numbers

3. Symbols and Signs

4. The Formula

5. Fundamental Operations

Introduction​

Mathematics is a branch of knowledge which involves a great many topics. In the elementary stages of the subject, the topics fall into a logical sequence of development. We are about to study the topics of introductory modern algebra and we must presume a certain amount of mathematical background. In this guide, we shall consider the material with which the reader should already be familiar. Consequently, this guide is in the nature of a review and the material is presented only for easy reference. Should the reader desire more detailed explanations of these concepts, he might want to consult other more in depth guides. In short, this is just an introduction to Algebra.

The Numbers ​

One of the first objects of study in mathematics is the numbers. In my study of arithmetic we were introduced to the integers, fractions, and decimals. We should consequently be familiar with

We should also be familiar with some of the names and concepts concerning numbers.

An even number is an integer that is exactly divisible by 2.

Examples: 2,4,6,8,24,256

An Odd number is an integer that is not exactly divisible by 2.

Example:1,3,5,7,33,51,1143

A Factor of a number is an integer that divides it exactly.

Example: 3 and 5 are factors for 15;2,4,5, and 10 are factors of 20.

A Prime number is an integer which has no factors except 1 and itself.

Examples: 2,7,11,13

A Composite number is a number that is not prime.

Examples: 4,22,35,1028

A common divisor of two or more numbers is a factor that will exactly divide each of them.

Example: 3 is a common divisor of 9 and 27

The Greatest common divisor (G.C.D) is the largest factor of two or more numbers.

Example: 9 is the GCD of 27 and 45.

The absolute or numerical value of a number is the magnitude of the number and is denoted by two vertical bars, InI

Example: I 5 I = 5 and I -5 I =5

Symbols and Signs​

Do i really have to put this?

A part of mathematics is a shorthand of symbols and signs which we must learn as a part of the language. The basic ones are


I. The signs of operation

a) Addition: +; e.g, 3 + 2
b) Subtraction: - ; e.g., 5 - 3
c) Multiplication; X or *;e.g., 7 X 3 or 7 * 3
d) Division: ÷ ; e.g, 4 ÷ 3

II The signs of order

a) Is less than: < : e.g., 4 < 9
b) Is greater than: > : e.g., 7>5
c) Is equal to: = ; e.g, 7 = (14 ÷ 2)

III The signs of grouping

a) The parentheses: () ; e.g., (3 + 2) + (4 + 7)
b) The brackets: [] ; e.g., [(3 + 2) + 5] - 6
c) The braces: {} ; e.g., {[8 + (3-1)] - (6 + 2)}

In the common fraction, the line denotes a division ; for example, 2/3 means 2 divided by 3. The parenthesis is also used to denote a multiplication; for example, (2 + 3) (7 - 4) means (2 + 3) X (7 - 4).

We use a minus sign, "-" to indicate that a number is negative and sometimes a plus sign, "+" to indicate that a number is positive. Thus bothe have a double meaning; i.e., a plus sign may

a) indicate an operation (to add)
b) indicate a positive numver;

a minus sign may

a) indicate an operation (to subtract)
b) indicate a negative number.

The discussion in which these symbols are used invariable makes it clear which of the two meaning is intended.

The Formula​

The area of a rectangle is obtained by multiplying the length by the width. In the notion of mathematics, this fact is written A = ab where A represents the area, a represents the length, b represents the width, and ab means a times b. This is a simple introduction to the algebraic formula, which expresses a fact. Letters are used to represent numbers. The letters have different values depending upon the problem under discussion and their meanings must be clearly defined. They are frequently referred to as general numbers or more commonly Variables. The study of algebra is essentially concerned with the operations of, establishing laws for, and understanding the meaning of such general numbers.

Fundamental Operations​

It is necessary that we establish some ground rules in order that we may proceed in an orderly manner. We start with the four fundamental operations of addition, subtraction, multiplication, and division. First we have the three important laws:

I The Commutative Law

The result of addition or multiplication is the same in whatever order the terms are added or multiplied

II The Associative Law

The sum of three or more terms, or the product of three or more factors, is the same in whatever manner they are grouped.

III The Distributive Law

The product of an expression of two or more terms by a single factor is equal to the sum of the products of each term of the expression by the single factor

Next we have some laws of signs:

I To add two numbers having like signs, add their absolute values and prefix the common sign

II To add two numbers having unlike signs, take the difference of their absolute values and prefix to it the sign of the number having the larger absolute value.

III The product, or quotient, of two numbers has the following rule of signs:

Symbols of grouping preceded by a plus sign may be removed by rewriting each of the inclosed terms with its original sign.

Symbols of grouping preceded by a minus sign may be removed by rewriting or changing the sign of each of the inclosed terms.

If a coefficient precedes a symbol of grouping, it is to be multiplied into each included term when the symbol is removed.

To simplify expressions involving several symols of grouping we work from the inside out by first removing the innermost pair of symbols, next the innermost pair of the remaining ones, and so on. If like terms appear they are combined at each step as in the following example.

Vote for David493 for UE next guide will probably be on another advanced math (functions most likely) or some program. 'Till then thanks for reading my guide and feedback is appreciated.

 

You learn all of this in school, pretty pointless guide IMO

 

True, but I am going to add to this later. It will include

Fundamental Operations
Powers, Exponents, and Radicals
Multiplication and Division
Factoring
Fractions
Simplification of Fractions
Operations of Radicals
Imaginary Numbers
Comparison
Mistakes
A few practice problems.

 

-yawn- School away from school not bad, thanks for that -

 

Finally. An Educational guide. Very good.

 

thank you The Dark, what are my chances in getting into the U E?

 

Y = Your Chance
O = Other person's chance who hasn't applied

Y=O

 

Well looking at it mathematically, the variable Y represents my chances, and the variable O represents other people's chances who haven't applied yet. So with the equation Y=O, I can conclude that I have the same chance as people who didn't apply.

 

Distributive commutative grrr... I got a D on that test with those on it, could never remember them. =P Good guide though.

 

Wow, i was expecting something 100% different. Bravo, Kudos to you sir. 10/10. Honestly i was expecting.. "2+2=FISH! Now go ****ing learn math yourself noobs"

 

Complex although I knew exactly what you're talking about (even though its been nearly 8 years since I was in the 5th grade LOL)

please add color to your guides tho, it makes them nicer to read.

9/10

 

Lul. But also true.

 

Are you serious? Kids come to the internetz to escape school. -.-

But otherwise, a good guide. Add more color.

 

Thanks for feedback so far guys, currently working on another guide.

 

Could you change the color of it? I realize that I, along with many others, wanted to see color, but it is way too hard to see now because a lot of it blends in with the background. Either eliminate the color all together, or use bright ones that will stand out against the dark blue background. Please and Thank You

 

Some things could be explained with a less text book definition... and what about the difference between real and imaginary numbers?

 

Forgetting one HUGE thing.

P = Parenthesis
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction

Thats how you solve ALL equations from left to right from that order.

 

An easy way to remember that acronym, assuming you don't know it already is,

Please
Excuse
My
Dear
Aunt
Sally

 

Yea, well my guide covers more than what most guides you see, I'm satisfied with what I wrote.

 

Just trying to help buddy.