Hi guys, welcome to my channel! I'm Gis and today we're going to study algebraic expressions. Did you know that mathematics has several branches?
That's it, there's arithmetic that studies numbers and operations, there's geometry that studies space and shapes and there's algebra. What is algebra? You know?
It is the use of letters in mathematics. And this is the subject we are going to cover in this class today, so do you have questions and want to learn more? Come with me.
. . Well guys, so we're going to start studying algebraic expressions.
But what is an algebraic expression? Do you remember what a numerical expression is? A numeric expression is an expression that only has numbers and operations.
That's it, now we're going to study algebraic expressions . What then changes from the numerical expression to the algebraic expression? Now, in algebraic expressions, in addition to numbers and operations, we will find letters, that's right, now we study letters in mathematics, and these letters, they are called variables because they can take on different values.
These letters can be represented by x, by a, by g, by y. . .
by any letter you want to use, right? And telling you a little bit about the story, the French mathematician who lived there in the 16th century was Vietê, speaking very beautiful French, he was the first to write equations and algebraic expressions using letters and signs. Did you know that?
And the algebra he used at that time is very similar to the one we use today. That's it, so let's continue our lesson on algebraic expressions. Guys, so I brought you three examples of applying an algebraic expression, because you then saw that an algebraic expression is what?
It is an expression that has numbers, operations and letters. And these letters are variable. So here let's think with me.
So I brought you a rectangle, whose side now of this rectangle, this side measures x and this side measures y, so automatically your top side measures x, which is equal to this, and this side here measures y, and then I ask you , what is the algebraic expression that represents the perimeter of this rectangle? you know? First, do you remember what a perimeter is?
Perimeter is the sum of all sides of the polygon here in this case, right? So what does this algebraic expression look like ? Shall we think?
So what do I have? I have a letter x here, a letter y here, another letter x here and another letter y here, right? Now here I wrote the algebraic expression that represents the perimeter.
But then I ask you, can I simplify this writing? Can you join someone there? How many letters x do you see there in that algebraic expression?
You must be seeing this letter x and this letter x, so we have two letters x, so when I write two letters x that means I have the letter x twice, right? And what else do I have? Two more times the letter y, right?
So the letter x was twice plus the letter y was twice. So this one is an algebraic expression that represents the perimeter of this rectangle. Now here's the second example, now I have a triangle and then, right, I've already increased the quantity here, I want to know what the perimeter of this triangle is?
Are you already doing it? Do you already know the answer? Shall we do it together with me?
So I'm going to add this side here which is 2x plus 6 to this side here which is y plus 3 and this side here which measures 8, right? And now people? I wrote the algebraic expression, but we will always try to simplify this expression by joining as many terms as possible of this expression.
So who is it here that I can join? I can join two letters with a letter y? Are they in the same category?
I can't add them when I don't know, as I don't know the value of each one, I can't add them, okay? So I can't join these two letters x with this letter y, but what can I do here guys? I can combine this 6 which is 6 units with this 3 which is 3 units with this 8 which is 8 units, okay?
Right? So here the letter x would look like? Let me just arrange it nicely here, it would then be two letter x even though I'm not going to combine it with anyone, but one letter y which is here but now let's combine the units 6 with 3 are 9, 9 with 8 are 17, so here I have 17 Look, what I now have is an algebraic expression that represents the perimeter of the triangle.
Did you see how different they are from each other? Look, here we only have the letters, here I already put the expression that has a letter, there is a letter here, just the unit . It's OK?
Now let's move on to the next situation. So here's the thing, the situation I brought to you and you must have already experienced this situation or seen someone going through it. I went there to ride my bike in the park, right?
Then I got there and went to rent a bike, the charging time, I went there to rent it, then I got there and there was a sign there saying: the fixed price for you to rent a bike is 3 reais, which means I have to pay 3 and reais to rent a bike, but I have to pay a fee of 2 reais per hour that I pedal, is that the right amount? And then I ask you, is it possible to write an algebraic expression that represents this situation here? For a specific amount of hours?
Or any quantity? Or can we write a generalized algebraic expression? Let's do the following so you understand the expression, let's pretend I went to the park and rented the bike for 2 hours, what would the bill be like?
So it would be 3 reais plus 2 reais times per hour. How many hours did I stay? two then you have to multiply this here by 2 so it would be, remember that the order here is multiplication first, 2 times 2 are 4, 4 plus 3 are 7 reais, okay?
So there's a numerical value for that there. Now if someone else went there and rented this bike for 5 hours, how much would they pay? 3 plus 2 reais which is the price of an hour but the person rented it for 5 so I have to multiply by 5, so I would have 2 times 5= 10 with 3= 13.
So 13 reais would be the price of the person who rented the bike for 5 hours and now if I told you what is the amount the person should pay if they rent this bike for x hours? It means it can be for any value, but now we're going to write a generalized algebraic expression because I'm going to put the x, okay, to represent any number of hours. Do you already know how it will look?
So here you must have paid attention that 3 is always fixed, I haven't changed it, right? And here you must have also paid attention that this 2, which is the price for each hour, was also fixed there in the formula, didn't I change it, who kept changing? The number of hours kept changing, that is, the time I rented the bike did change, so that means that my variable in this expression will be time, so here I'm going to put x because then I can generalize that the person can rent at any time it can be 5, 6, 8, 10, 12 for any quantity I change this value of x I will be able to reach the final value for the price of this rental, okay?
So here what I wrote here, I wrote an algebraic expression that represents the rental, the price of renting a bicycle, right? OK? I brought here another example.
Look at the situation now, we are a cafeteria, right? Here we have the prices of the items in the cafeteria, that's all there was, okay? The coxinha was 5 reais a piece, the soda was 3 reais a piece and the ice cream was 7 reais a piece, okay?
I picked random prices here just so we can understand the issue. So now I need you at home to think about what algebraic expression I should write that will indicate the amount spent by a person who bought it. And she bought x drumsticks, she bought y soda and she bought z ice creams.
And now what does this algebraic expression look like? Shall we try to resolve it? So what do I know here guys?
I know that each drumstick costs 5 reais and this person bought x drumsticks, it was x drumsticks so look at our variable because she could have bought 2, 3, 4, 8 drumsticks so I take the number of drumsticks she bought and multiply it by the price for each coxinha here it is 5 reais, right? Then what else? Then the person bought y soda, this y is also a variable that can be 2, 3, 1, 4, okay?
So it is also a variable and each soda costs 3 reais, so what should I do 3 reais multiplied by the amount of sodas he bought, right? And here also z is another variable because it represents the quantity of ice creams he bought, he bought z ice creams, that is, he could have bought 1, 2, 3, 4. So that's why it is a variable, because I can buy any amount.
Each ice cream costs 7 reais, so 7 times the amount of ice cream he bought, which in this case the person bought z ice creams, so here folks, I have the algebraic expression that represents the expenditure made there in this cafeteria by this person in this case I I went to the cafeteria anyway, just so we could relax a little and try to understand the algebraic expression beauty? So guys, I want to make a request for you now. Subscribe to my channel, okay?
And leave a thumbs up for Gis.
