Math - As Easy As It Gets: The Basics of Algebra

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Algebrese for Beginners

7 students enrolled

What Will I Learn?

- use different types of numbers, like natural numbers, whole numbers, rational numbers, prime numbers, negative numbers and more
- perform basic operations on different types of numbers
- add, subtract, multiply and divide positive and negative numbers
- calculate the absolute value of a number
- use the commutative and associative properties of addition and multiplication
- use different types of fractions, like common fractions, decimals and percentages
- expand and reduce fractions
- add, subtract, multiply and divide fractions
- find common denominators
- divide numbers with remainders
- use improper fractions and mixed numbers
- change common fractions to decimals and the other way around
- use percentages to calculate increase and decrease
- compound percentages
- use powers and roots
- use the exponential notation
- use negative and fractional exponents
- use the scientific notation
- raise powers to powers
- perform operations in the right order
- work with variables
- simplify algebraic expressions
- use prime factorization
- use divisibility rules to check whether a numbers is divisible by another number
- find the greatest common factor
- factor by grouping
- distribute terms, signs and polynomials
- balance equations and inequalities
- use proportions
- solve for variables in formulas
- solve linear, quadratic, quadratic-like, cubic, polynomial, radical, rational and absolute-value equations and inequalities
- use sign diagrams
- use the quadratic formula to solve quadratic equations

Requirements

- This is a course for beginners, so no special knowledge is required

Description

Math is a very, very broad area of science. It’s the essence of science. It rules the world of science. Each branch of science is rooted in math. In this course we’re going to talk about the basics of algebra. Whether you have never used algebra or it’s been so long since you last did, in this course you’ll have the opportunity to start anew and go through all the important topics from easiest to more advanced. The purpose of this course is to show you how to cope with the most typical problems you may come across.

**Discover The Fascinating World of Mathematics.**

- Types of numbers
- Mathematical symbols
- Binary and unary operations
- Absolute value
- Signed numbers
- Common fractions and mixed numbers
- Decimals
- Percentages
- Powers
- Roots
- Variables
- Factoring
- Distribution
- Linear, quadratic, polynomial and other equations
- Inequalities
- ... and much more

**Don’t Wait Any Longer. Don’t Be Afraid Any Longer. Go For Math. Fall in Love with it.**

Math is everywhere. Not just at colleges and universities. It’s omnipresent. You can solve a lot of problems if you know math. So, let’s learn how to cope with the most typical basic math problems you can come across.

**Contents and Overview**

This course is targeted at school-age students who feel like polishing up their math skills as well as adult students who want to recapitulate on the basics of math. Each lecture is brief and concise, focused on one topic. Each lecture consists of two parts. The first part is theoretical. It introduces the topic, explains how things work. There are also examples to show how theory works in practice. The second part contains an exercise for you to do along with the solution.

The language is simple and you should have no problems understanding what I’m talking about. As we proceed you’ll get familiar with new, more advanced concepts.

This course is divided into 10 sections, each of them covering a broader topic subdivided into lectures. The pace is up to you, you can go through the easier parts faster and then take more time to study the more sophisticated ones.

After you finish each section, there’s a quiz for you that covers the material discussed in that section.

**This course contains:**

- 90 lectures in 10 sections
- 6 hours of video content

After you finish this course you will be able to move around the fascinating world of algebra and apply your knowledge to everyday life problems. You will be able to use quite a lot of tools and techniques. This will make a good starting point for more advanced study.

Who is the target audience?

- This course is best suited for students who want or need to recap on their basic mathematical knowledge, the basics of algebra.
- This course is for students who want to know how numbers work.
- This is also for students of all ages who want to revise for school.
- This course is NOT suitable for kids who have just started their education in elementary schools.

Compare to Other Algebra Courses

Curriculum For This Course

90 Lectures

06:01:30
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Introduction to the Course
2 Lectures
03:20

In the first lecture I will tell you what this course is about and who it is for. I will tell you what I expect from you at the beginning of the course and what you will be able to do after finishing this course.

Preview
01:55

In this lecture I will give you some hints as to how to use this course most effectively. I will tell you what a typical lecture looks like and what kind of exercises you can find in the course.

Preview
01:25

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Some Algebrese
12 Lectures
53:40

Let’s see what we’ll learn in this section.

Introduction to Section 2

02:22

Numbers is a huge topic. In this lecture we’ll have a look at the different types of number, like natural numbers, integers, rational numbers, etc.

Numbers

06:09

As this is a course for beginners, I decided to introduce some basic terminology that you should get familiar with before you move on so that we can understand each other better.

Basic Terminology

10:08

Math is full of symbols. One reason is that they are more concise than words. Another is that they are understood worldwide whereas languages vary from location to location. In this lecture we’ll have a look at some basic symbols math uses.

Symbols

05:41

In this lecture we’ll discuss the basic operations like addition, subtraction, multiplication and division. We’ll also have a look at some terminology each of them uses.

Basic Operations

06:14

Some operations, like addition or multiplication, require two numbers (at least) to operate on. That’s why we call them binary operations. There are also operations performed on one number, the so-called unary operations. In this lecture we’ll have a look at the former and the latter.

Binary and Unary Operations

02:44

Positive numbers are quite intuitive. Negative ones – not that much so. Let’s talk for a while about both positive and negative numbers.

Positive and Negative Numbers

02:47

In this lecture we’ll be talking about absolute value. We’ll see what it is and how to calculate it.

Absolute Value

02:30

Operations on signed numbers may seem tricky on occasions. If we take a negative number and a positive one, multiply them together, will the result be positive or negative? Problems like this are the subject of this lecture.

Preview
07:13

There are a few interesting numbers called identities. What’s so special about them is that when used in operations with other numbers they behave as though they were not there at all, by which I mean the result is the same whether they are there or not. Sounds complicated? You’d better find out yourself.

Identities

02:58

Commuting and associating are two very important properties of addition and multiplication. In this lecture we’ll see what they are and what they consist in.

Commuting and Associating

04:01

Let’s summarize what we’ve learned in this section.

Conclusion to Section 2

00:53

Test your knowledge. How much can you remember from section 2?

Some Algebrese

20 questions

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Fractions
15 Lectures
01:07:39

Let’s see what we’ll learn in this section.

Introduction to Section 3

02:59

In this introductory lecture to fractions I will just give you some idea about different types of fractions we’re going to discuss in more detail in this section. You will also get familiar with some basic terminology.

Fractions Terminology

03:40

Whenever possible, we should reduce fractions so that they are easier to handle. In this lecture we’ll see how. There are also occasions when we need expanded fractions. This is also discussed in this lecture.

Expanding and Reducing Fractions

03:43

Some operations require the elements they operate on to be compatible. Two fractions are compatible if they have the same denominators. And if they don’t, you can always transform them in such a way that they will have a common denominator. How to do it? This is the subject of this lecture.

Common Denominators

05:33

Fractions are operations of division. As an introduction to improper fractions and mixed numbers, let’s revise division with remainders. This will come in handy in the next lecture.

Division with Remainders

02:27

Improper fractions are used much less frequently than proper ones. Still, there are occasions where they make sense. In this lecture we’ll see what they look like and how they can be rewritten as mixed numbers.

Preview
04:15

In this lecture we’ll compare fractions. At first we’ll compare fractions with the same denominators, then ones with different denominators.

Comparing Fractions

03:24

Multiplying and dividing fractions is way easier than adding and subtracting them. Maybe not so much easier, but usually much faster. That’s why we’ll start with these two operations and only later see in more detail to the other two.

Multiplying and Dividing Fractions

09:24

In this lecture we’ll see how to add and subtract fractions. It’s not difficult because you already have all the tools you need. It’s just a bit more time-consuming than multiplication and division.

Adding and Subtracting Fractions

04:15

Decimals are just a special case of fractions where the denominator is a power of ten. In this lecture we’ll learn the basics of decimals.

Special Case: Decimals

05:19

Decimal and common fractions can be easily converted between each other. In this lecture we’ll see how to change decimals to common fractions. This conversion is pretty straightforward.

Changing Decimals to Common Fractions

09:30

Changing common fractions to decimals can sometimes turn out a bit tricky, especially when we have repeating decimals. In this lecture we’ll deal with that.

Changing Common Fractions to Decimals

02:49

Another special case of fractions are percentages. In this lecture we’ll just talk about the basics of percentages.

Special Case: Percentages

04:45

In this lecture we’ll go a bit deeper into percentages. We’ll see how percentages may be used to calculate increase and decrease. We’ll also touch upon compounding percentages.

Percentages: Increase, Decrease, Compounding

04:36

Let’s summarize what we’ve learned in this section.

Conclusion to Section 3

01:00

Test your knowledge. How much can you remember from section 3?

Fractions

15 questions

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Powers and Roots
12 Lectures
41:54

Let’s see what we’ll learn in this section.

Introduction to Section 4

02:32

Let’s start with some basic terminology that will make it easier for us to move around the realm of powers and roots.

Powers and Roots Terminology

04:27

Writing large numbers can be tedious, especially if we don’t need very precise values. Using exponential notation can simplify things dramatically. In this lecture we’ll explore exponential notation.

Exponential Notation

04:37

Multiplying and dividing powers is easy. These two operations can significantly simplify things. In this lecture we’ll see how to multiply and divide powers.

Multiplying and Dividing Powers

02:53

As mentioned before, exponents may be negative as well. What does it mean and how to interpret such powers? In this lecture we’ll see where negative exponents come from and what they mean.

Preview
04:33

Very large numbers and very small numbers, with tens or hundreds of zeros, are rather difficult to handle. They’re hard to imagine and it’s pretty easy to ‘lose’ one or more zeros while using them. That’s where scientific notation, the subject of this lecture, comes in handy.

Scientific Notation

04:17

Zero has a special meaning in math. It’s the same in powers. If the exponent equals zero, there’s so much less work to do. We’ll see how to handle zeros as exponents in this lecture. We’ll also see why it is that way.

Zero as Exponent

02:34

Sometimes we need to raise a power to another power. We can do it in two separate steps or use some properties that facilitate it. In this lecture we’ll see how this can be done.

Raising Powers to Powers

03:36

In this lecture we’ll have a closer look at roots. We’ll see how to make calculations with roots and we’ll explore some of their main properties.

Roots

04:49

Common fractions may be used as exponents. Then they can be used in all the calculations we’ve seen before where we add or multiply exponents. In this lecture we’ll see how.

Common Fractions as Exponents

03:15

We already talked about the order of operations but now that we know powers and roots, let’s see how they fit in. In this lecture we’ll see how nested grouping works and how powers and negative numbers work together.

Order of Operations

03:26

Let’s summarize what we’ve learned in this section.

Conclusion to Section 4

00:55

Test your knowledge. How much can you remember from section 4?

Powers and Roots

12 questions

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Variables
6 Lectures
13:46

Let’s see what we’ll learn in this section.

Introduction to Section 5

01:32

As usual, we’ll start the discussion of variables by introducing some basic terminology. This lecture is really short and simple.

Variables Terminology

01:39

In this lecture we’ll see how to add and subtract terms containing variables. This technique is commonly used in algebra to simplify complex expressions.

Adding and Subtracting Variables

04:30

In this lecture we’ll see how two perform the other two operations on variables: multiplication and division. These two are really easy.

Multiplying and Dividing Variables

02:48

Finally let’s see how we can reduce powers and employ the other techniques we covered before to simplify algebraic expressions.

Simplifying Algebraic Expressions

02:22

Let’s summarize what we’ve learned in this section.

Conclusion to Section 5

00:55

Test your knowledge. How much can you remember from section 5?

Variables

5 questions

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Factoring
10 Lectures
47:45

Let’s see what we’ll learn in this section.

Introduction to Section 6

02:21

We already discussed prime and composite numbers in Section 2, but, as we’re going to need them desperately here, in this lecture we’ll recapitulate them shortly.

Prime and Composite Numbers Recap

01:31

Prime factorization is the thing that simplifies calculations dramatically. In this lecture we’ll see what methods can be used to factorize numbers.

Preview
08:44

To make life easier, we can use some rules to check if a given number is divisible by some other number. In this lecture we’ll discuss the most common rules of divisibility.

Preview
11:03

Now that we know so much about prime factorization, we can use this knowledge to reduce fractions. This way you can easily reduce a fraction to its simplest form.

Reducing Fractions Revisited

05:55

In this lecture we’ll learn how to find and pull out the greatest common factor.

The Greatest Common Factor

05:12

Prime factorization is the ideal way of factoring expressions but sometimes it’s easier to recognize other factors than the prime ones and factorize repeatedly until it’s possible. In this lecture we’ll see how we factorize in a practical way.

Factoring – The Practical Approach

04:19

Some expressions seem prime but are not. In this lecture we’ll learn how to get at the factors by grouping terms.

Factoring by Grouping

02:30

There are a couple of cases when you can use ready-made formulas to factorize expressions. In this lecture we’ll talk about the most common ones.

Special Factoring Cases

05:13

Let’s summarize what we’ve learned in this section.

Conclusion to Section 6

00:57

Test your knowledge. How much can you remember from section 6?

Factoring

7 questions

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Distribution
6 Lectures
19:48

Let’s see what we’ll learn in this section.

Introduction to Section 7

01:16

In the previous section we talked about factorization. In this section we’ll be doing quite the contrary. In this lecture we’ll see how to distribute single terms.

Distributing a Single Term

04:10

In this lecture we’ll be talking about distributing signs and in particular we’ll concentrate on the negative sign which may cause some problems as opposed to the positive one.

Preview
05:29

In this lecture we’ll talk about polynomials in general and about distributing polynomials in particular. We’ll also learn about the different types of polynomials.

Distributing Polynomials

03:35

Sometimes distributing polynomials can be simplified, provided you notice some patterns. In this lecture we’ll discuss the basic patterns you will probably most frequently come across.

Special Distributions

04:26

Let’s summarize what we’ve learned in this section.

Conclusion to Section 7

00:52

Test your knowledge. How much can you remember from section 7?

Distribution

6 questions

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Equations
15 Lectures
01:14:20

Let’s see what we’ll learn in this section.

Introduction to Section 8

03:17

Equations consist of expressions with an equal sign (=) somewhere between them. In this lecture we’ll see what they look like, what it means to solve an equation and what types of equations there are.

Basics of Equations

03:29

Before we start solving equations, let’s talk about balancing them, which will come in very handy in the next lectures. We’ll learn how to transform equations in such a way that they are easier to handle and still give the same solutions.

Balancing Equations

10:49

In this lecture we’ll talk about the simplest type of equations, linear equations. We’ll learn how to handle them step by step and how to check whether the solution is correct.

Linear Equations

04:12

Proportions, which are discussed in this lecture, are a special type of equations. Proportions can simplify solving fractional equations.

Proportions

03:56

In mathematics, physics, but also in other areas, we use lots of formulas with multiple variables. They are usually meant to be solved for a particular variable, but what if we wanted to solve for another variable? In this lecture we’ll see how.

Solving for Variables in Formulas

04:20

In this lecture we’ll have a look at the simplest examples of quadratic equations – those with one or two of the terms equal to zero. We’ll see what approaches we can take to solve them.

Simple Quadratic Equations

07:02

You can solve quadratic equations by factorization but sometimes it’s easier to use the quadratic formula. In this lecture we’ll learn how to use it and how to use the discriminant of the equation to sort out how many solutions there are.

The Quadratic Formula

05:05

Using the same techniques as before we can solve some polynomial equations provided the powers fulfill some conditions. In this lecture we’ll be talking about such quadratic-like equations.

Preview
05:47

In this lecture we’ll talk about simple cubic equations. By simple I mean those that lack some of the terms or can be easily factorized. We’ll talk about other cubic equations as well as other polynomial equations in general in the next lecture.

Simple Cubic Equations

05:06

Polynomial equations may take quite a while to solve. In this lecture we’ll see how we can do it. This method can also be applied to quadratic and cubic equations as we’ll see.

Polynomial Equations

11:22

Radical equations are equations with radicals. In order to solve them, we should first get rid of the radical sign, which can be done by raising both sides of an equation to a power. In this lecture we’ll see how it works.

Radical Equations

03:31

Rational equations, which are the subject of this lecture, can be solved using techniques you already know. In this lecture we’ll have a look at a simple and a more complex example.

Rational Equations

03:36

Finally, in this lecture we’ll discuss yet another type of equations, the absolute-value equations.

Absolute-Value Equations

01:57

Let’s summarize what we’ve learned in this section.

Conclusion to Section 8

00:51

Test your knowledge. How much can you remember from section 8?

Equations

10 questions

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Inequalities
11 Lectures
37:24

Let’s see what we’ll learn in this section.

Introduction to Section 9

02:17

Now that we know equations, it’s time to have a look at inequalities. They have quite a lot in common, so you shouldn’t have any problems figuring them out.

Basics of Inequalities

05:03

In this lecture we’ll see how inequalities can be balanced. Again, we can add, subtract, multiply and divide, but there are a few things that must be taken into consideration while doing this.

Balancing Inequalities

07:56

Linear inequalities are the simplest ones. In this lecture we’ll see how to handle them.

Linear Inequalities

02:17

Inequalities may be chained into long strings as long as the direction of the inequality symbols is maintained. In this lecture we’ll see how this can be done and how to perform operations on such inequalities.

Inequalities with Multiple Expressions

04:38

Quadratic inequalities are slightly more difficult to solve because the solutions may belong to separate intervals. In this lecture we’ll see how to cope with such cases.

Quadratic Inequalities

03:46

Polynomial inequalities are pretty easy to solve, especially if you have the factorized form. In this lecture we’ll see how to do it.

Preview
03:11

Sign diagrams are a tool to accelerate your work on polynomial inequalities. They’re a sort of shortcut enabling you to quickly see what signs there should be in all the particular intervals.

Sign Diagrams

03:10

Rational inequalities, which are the subject of this lecture, are solved pretty much the same way as polynomial inequalities, so you should have no problems with them.

Rational Inequalities

02:11

The last type of inequalities we’re going to have a look at are absolute-value inequalities. In this lecture we’ll learn how to solve them depending on the direction of the inequality.

Absolute-Value Inequalities

02:08

Let’s summarize what we’ve learned in this section.

Conclusion to Section 9

00:47

Test your knowledge. How much can you remember from section 9?

Inequalities

6 questions

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Course Summary
1 Lecture
01:55

Let’s summarize what we’ve learned in the entire course.

Course Summary

01:55

About the Instructor