Hi! This is Rob. Welcome to Math Antics. 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. It follows all the rules of arithmetic and it uses the same four main operations that arithmetic is built on: addition, subtraction, multiplication and division. But Algebra introduces a new element… the element of the unknown. When you were learning arithmetic, 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, we use a symbol in its place. 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) are equal to what’s on the other side, which happens to be the unknown value that we are calling ‘x’. One of the main goals in Algebra 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 like this: x – 2=1. 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. We’re going to learn a lot more about how you actually do that (how you solve equations) in the next several videos, 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. That’s okay, but what’s NOT okay is for a symbol 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 and things could get really confusing! 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. Okay, so for any particular equation, we can’t use the same letter to represent two different numbers at the same time, but what about the other way around? Could we use two different letters to represent the same number? Yes! – Here’s an example of that. 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. Or, we could switch them around. If ‘a’ was 2 and ‘b’ was 0, the equation would also be true. But there’s another possibility: 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. If ‘a’ is 0 then ‘b’ must be 2 If ‘a’ is 1 then ‘b’ must be 1 If ‘a’ is 2 then ‘b’ must be 0 ‘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. In Algebra, ‘b’ is what’s called a “variable” because it’s value can ‘vary’ or change. In fact, in this equation, both ‘a’ and ‘b’ are variables because their values will change depending on the value of each other. Actually, it’s really common in Algebra to refer to any letter as a variable, since letters can stand for different values in different problems. But at Math Antics, we’ll usually just use the word “variable” when we’re talking about values that can change or vary in the same problem. Alright, so far we’ve learned that Algebra is a lot like arithmetic, but that in includes unknown values and variables that we can solve for in equations. There’s one other really important thing that I want to teach you that will help you understand what’s going on in a lot of Algebra problems, and it has to do with multiplication. Here are the four basic arithmetic operations: addition, subtraction, multiplication and division. Although in Algebra, you’ll usually see division written in fraction form, like this. In Arithmetic, all four operations have the same status, but in Algebra, multiplication get’s some special treatment. In Algebra, multiplication is the ‘default’ operation. That means, if no other arithmetic operation is shown between two symbols, then you can just assume they’re being multiplied. The multiplication is ‘implied’. For example, instead of writing ‘a’ times ‘b’, you can leave out the times symbol and just write ‘ab’. Since no operation is shown between these two symbols, you know that you’re supposed to multiply ‘a’ and ‘b’. Of course, you can’t actually multiply ‘a’ and ‘b’ until you figure out what numbers they stand for. The advantage of this rule about multiplication is that it makes many algebraic equations less cluttered and easier to write down. For example, instead of this: a * b + c * d=10 You could just write: ab + cd=10. You can also use this shorthand when you are multiplying a variable and a known number… like 2x, which means the same thing as 2 times ‘x’ or 3y which means the same thing as 3 times ‘y’ Since the symbol and the number are right next to each other, the multiplication is implied. You don’t have to write it down. Finally some good news! Now I never have to write down that pesky multiplication symbol again! Oh yeah!! Ah, not so fast… there are some cases in Algebra where still need to use a multiplication symbol. For example, what if you want to show 2 x 5? If you just get rid of the times symbol and put the ‘2’ right next to the ‘5’, it’s going to look like the two-digit number twenty-five, which is NOT the same as 2 x 5. So, whenever you need to show multiplication between two known numbers, you still have to use the times symbol, unless… you use parentheses instead. But aren’t parentheses used to show grouping in math? How can you use that to show multiplication? Ah, that’s a good question. Parentheses are used to group things, but whenever you put two groups right next to each other, with no operation between them, guess what operation is implied. Yep! Multiplication! For example, if you see the this, it means that the group (a+b) is being multiplied by the group (x+y). We could put a times symbol between the groups, but we don’t have to because it’s the default operation in Algebra. The multiplication is just implied. So, going back to our problem: 2 x 5 If you wanted to, you could put each of the numbers inside parentheses like this, and then you could get rid of the multiplication sign. Now this can’t be confused with the number twenty-five, and since the groups are right next to each other, you know that you need to multiply them. Of course, it might seem strange to have just one thing inside ‘group’ symbols like this, but it’s okay to do that in math. An alternate way that you could do the same thing would be to put just one of the numbers in parentheses, like this. Again, you won’t confuse this with a two-digit number and you know that multiplication is implied. Okay, so we’ve learned that Algebra is a lot like arithmetic, but it involves unknown values or variables that we need to solve for. And we learned that in Algebra, the multiplication sign is usually not shown, because it’s the default operation. You can just assume that two things right next to each other are being multiplied. But why do we even care about Algebra? Is it good for anything in the ‘real world’? or is it just a bunch of tricky problems that keep students busy in school? Actually, Algebra is very useful for describing or “modeling” things in the real world. It’s a little hard to see that when you are just looking at all these numbers and symbols on the page of a math book. But, it’s a lot easier to see when you start taking algebraic equations and graphing their solutions. Graphing an equation is like using its different solutions to draw simple lines and curves that can be used to describe and predict things in real life. For example, there’s a whole class of equations in Algebra called “linear” equations because they form straight lines when you graph them. Those sorts of equations could help you describe the slope of a roof or tell you how long it will take to get somewhere. Another class of algebraic equations, called “quadratic” equations can be used to design telescope lenses, or describe how a ball flies through the air, or predict the growth of a population. So Algebra is used all the time in fields like science, engineering, economics and computer programming. And even though you might not need Algebra to get by in your day to day life,… …so divide both sides by 3. That means x=42. So… in three… two… one… YES!! Alright… now to see how much butter I need. It’s still a very useful part of math. Thanks for watching Math Antics,

and I’ll see ya next time! Learn more at www.mathantics.com

I hate all the guys that disliked

2030 anyone?

Hey algebra,

Stop telling me to find your x-girlfruend she aint comin back

I’m 10 and I’m learning Algebra-

Help

Im 10. Y am i watching this?

3

What the hell is a beyblade

Man now im struggling in YEAR 7 maths and it’s super hard and annoying

your legit my new teacher

Thank you now i know agabra

I found him the MATH GOD

Gracias viejo!!! Te felicito!!!

No rob, algebra is hell

Thanks, I use this to study. Algebra is tough

I HATE math so much

I wish I had you as my math teacher. Our teacher can't explain anything. Almost entire class is confused.

With this I understand everything

Oh my gosh you is Soo smart!!I have algebra and you help to me know how to do it thanks allot!⊂((・▽・))⊃

I have a doubt that why there are 1.2k dislikers of such a superb teaching?

YOU Are great sir😻😻😻

I called my teacher stupid

Because of this man

dang 2015 geez were in 2019 NOW

The 1.3k is from those how want a job as a teacher

Edit: dislikes

You enjoy your sound effects don't you

I'm learning a lot ,thx mathematics

When ur learning this with a teacher and can’t get it but goes home and watches someone u don’t know

I'm in grade 4 and i don't know why I'm watching this

but I understand itThank you bro!Love it😍

thanks man its so good.

Thank you

This made me reassess my love and passion for mathematics after a difficult time of self exploration, transitioning to an adult, and taking a break before diving into the deep end of mathematics such as calculus. I finished high school a few months ago.

Teacher: do this problem

Me: ……..

After he explains it:

Me again: done

In the class i was joking around with my friend calling Algebra, Algebruh because i didn't understand the teacher. I can finally call it Algebra again.

I just switched over to learning in English because I use it more often and I should probably start learning the terms..

I have a 6th grade math mosl test tomorrow thanks for helping! I understand this more than how much I understand this in class

Me:

watches videoTen seconds later…H a c k e r m a nI think he means the x in roman numarals i use algebra with a star

like

Most of the people in these comments should be taking English classes, not Math classes…

X(X+3) = 130

X^2 + 3X = 130

X^2 = 100

X = 10

i took algebra 1 in 3rd grade and algebra 2 in 4th grade. i took geometry in 6th grade and i’m in 8th grade taking advanced calculus

lol jk

I LEARN EVERYTHING ABOUT IT

Goal:Teach under 20min

Hi Rob. Could you do a video on clearing fractions-linear equations? Thanks, I would be so grateful. I have one that is giving me a hard time. Something with two fractions on one side and a fraction and a whole number in the other would be really helpful. And different signs.

I’m in 7th grade and this year they’re doing an algebra class for 8th grade so this year we have 4 tests and our first one is next week and I really need to study

78+x =112 X=32👍🏼

I am 6 and 5/6 years old and I know algebra

math is hard for me

ugh my teacher shouted at me and tried to embarrass

me for getting a question wrong because he didn't explain it properly but now i can show to him i can do it because of this video thank you!

this dude took my maths teaches carrear

you know… if you look at him very clear you can see an older version of Tom holland?

Ahhhhh we meet again my old friend bless your soul for getting me this far

Thank you,sir you made maths a lot easier for me and other viewer's your an amazing ex plainer even better than A LOT teachers. Thank you,you made me understand something i thought i would never understand in a thousand years im in year 6 preparing for my sat's and i just want to recap this so thank you again,sir.

f u man

You said that 2 variables can equal the same number but according to https://www.theproblemsite.com/ask/2016/02/can-x-and-y-have-the-same-value, "this is not algebraically correct, as in algebra, X & Y cannot both be equal to one." But is also said that "there is no algebraic reason why two variables can't have the same value." So can it be the same value or not?

This is very good for me so i can good better at it

Mr matthews

So this mean a plus b has alot of solutions

I need to whatch this for homework I am so bored enyone elts

"I didn't know my 6 grade self would already learning ALGEBRA"

4:31

x=1.125

Thanks, my little brother needed this!

Isaac Newton was pretty good at this algebra stuff.

This is excellent! The analogy of playing computer games to solve algebra equations is marvelous!

Algebra dont say x she ain't gonna come back

This is amazing 🤤

Pooooooooo

👏👏👏👏 didn't know math was this easy

4:28 x=1 I solved it. Most people will not understand this but I want to show I could do it.

(30x+6x)/2x=(3x+15)/x

multiply 2x on both sides

(2x)((30x+6x)/(2x))=(2x)((3x+15)/x)

30x+6x=2x(3x+15)

combine link terms

30x+6x=36x so you get

36x=2x(3x+15)

distribute the 2x in 3x+15

36x=2x(3x)+2x(15) that will equal

36x=(6x^2)+30x

pull out a factor of 6x in (6x^2)+30x

36x=6x(x+5)

then divide both sides by 6x

(36x/6x)=(6x(x+5))/6x)

you get

6=x+5

subtract 5 from both sides

6-5=x+5-5

1=x

then check by replacing x with 1

(30(1)+6(1))/2(1)=(3(1)+15)/1

then you get

(30+6)/2=3+15

then add 3+5=18

and 30+6=30

so we get

36/2=18

devide then

18=18 ✔

3019 anyone ?

Thanks guy your way is easy to understand

Thanks guy your way is easy to understand

I LOVE MATHSNTICS😘

don't question me when I say 3:18

I wish he was my teacher he's so smart!

This guy makes learning math fun. My instructors were boring as hell.

you make algebra so easy to look/answer

One of the best of best who can simplify basic and yet to bigger goal teaching trick

very helpful

4:19

thanks for the help

U awsome rob I in 2019

2019 October???

can you please make advance algebra video

You revise such rudimentary concepts of mathematics, while revitalizing it into this unique explanation I can really follow, subbed !

In math class children are getting sleepy but in watching this video is amazing

Love you

Very good job done by Rob. It really improved my mathematic skills. Note: Better than my boring math teacher.

This man called every math teacher dumb in 400 languages

My brain farted ._.

This is algebra 😭

1 like equals 1. 🥊🎽🔪

Helper to find his x. ⛸

Good old comedy with a side of math

when I saw this video I didn't understand a thing after a few weeks I knew everything :>

Who doesn't get that teachers don't make sense while this guy does 🤔

Watching since 2013

Teachers: I’m the best

Math antics: I’m about to ruin this mans whole life career

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Woah this is why your my favorite

Best MATH TEACHER EVER

Does this mean no one is too dumb to know math just that some teachers are too dumb to impact knowledge? How can he make maths feel so easy? It's like it's magic. I still can't believe this. It's a trick, maths hard.

does Rob have merch?

you are funny at the end

that guy is the same guy