Name: Algebra Basics: What Is Algebra? - Math Antics
Uploaded: 2016-07-22T17:03:51.000Z
Duration: 12 min 7 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Adverbs of degree

In this lesson, we're going to learn some really important things

about a whole branch of math called Algebra.

The first thing you need to know is that Algebra is a lot like arithmetic.

and it uses the same four main operations that arithmetic is built on:

addition, subtraction, multiplication and division.

the only thing that was ever unknown was the answer to the problem.

For example, you might have the problem 1 + 2 = what?

The answer isn't known until you go ahead and do the arithmetic.

Now the important thing about Algebra is that when we don't know what a number is yet,

that symbol is usually just any letter of the alphabet.

A really popular letter to choose is the letter 'x'.

So in arithmetic, we would just leave the problem like this: 1 + 2 = "blank"

and we'd write in the answer when we did the addition.

But in Algebra, we'd write it like this:  1 + 2 = x

The 'x' is a place holder that stands for the number that we don't know yet.

What we have here is a very basic algebraic equation.

An equation is just a mathematical statement that two things are equal.

An equation says, "the things on this side of the equal sign

have the same value as the things on the other side of the equal sign."

In this case, our equation is telling us that the known values on this side (1+2)

which happens to be the unknown value that we are calling 'x'.

is to figure out what the unknown values in equations are.

And when you do that, it's called "solving the equations".

In this equation, it's pretty easy to see that the unknown value is just 3.

All you have to do is actually add the 1 and 2 together on this side of the equation

and it turns into 3 = x, which is the same as x = 3.

So now we know what 'x' is!  It's just 3.

That almost seems too easy, doesn’t it?

And that's why in Algebra, you are usually given an equation in a more complicated form

This is exactly the same equation as 1 + 2 = x,

but it has been rearranged so that it's not quite as easy to tell what 'x' is.

So in Algebra, solving equations is a lot like a game

where you are given mixed-up, complicated equations,

and it's your job to simplify them and rearrange them

until it is a nice simple equation (like x = 3)

where it's easy to tell what the unknown values are.

how you actually do that (how you solve equations)

but for now, let's learn some important rules about

how symbols can and can't be used in algebraic equations.

The first rule you need to know is that the same symbol (or letter)

can be used in different algebra problems to stand for different unknown values.

For example, in the problem we just solved,

the letter 'x' was used to stand for the number 3, right?

But 'x' could stand for a different number in a different problem.

Like, if someone asks us to solve the equation, 5 + x = 10.

In order for the two sides of this equation to be equal,

'x' must have the value '5' in this problem, because 5 + 5 = 10.

So 'x' (or any other symbol) can stand for different values in different problems.

to stand for different values in the same problem at the same time!

For example, what if you had the equation: x + x = 10?

This equation says that if we add 'x' to 'x' we will get 10.

And there are a lot of different numbers we could add together to get 10, like 6 and 4.

But, if we had the first 'x' stand for 6 and the second 'x' stand for 4,

then 'x' would stand for two different value at the same time

If you wanted symbols to stand for two different numbers at the same time,

you would need to use two different symbols, like 'x' and 'y'.

So in Algebra, whenever you see the same symbol repeated more than once in an equation,

it's representing the same unknown value.

Like if you see a really complicated Algebraic equation (like this),

where 'x' is repeated a lot of different times,

all of those 'x's stand for the same value,

and it will be your job to figure out what that value is.

we can't use the same letter to represent two different numbers at the same time,

Could we use two different letters to represent the same number?

Let's say you have the equation: a + b = 2

What could 'a' and 'b' stand for so that the equation is true?

Well, If 'a' was 0 and 'b' was 2, then the equation would be true.

If 'a' was 2 and 'b' was 0, the equation would also be true.

If 'a' was 1 and 'b' was also 1, that would make the equation true, right?

So, even though 'a' and 'b' are different symbols,

and would usually be used to represent different numbers,

there are times when they might happen to represent the same number.

Oh, and this problem can help us understand something

very important about how symbols are used in Algebra.

Did you notice that there were different possible solution for this equation?

In other words, 'b' could have the value 0, 1, or 2 depending on what the value of 'a' was.

'b' can't have two different values at the same time,

but it's value can change over time if the value of 'a' changes.

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Algebra Basics: What Is Algebra? - Math Antics

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