RAZÃO E PROPORÇÃO \Prof. Gis/ #01

Hi guys, have you ever stopped to observe how much we make comparisons of quantities in our daily lives? If you haven't stopped to observe, I invite you to attend my class and after it you'll stop and think, wow, Gis was right, we really do use this comparison. of quantities and in mathematics we call this a ratio.

So welcome to my channel I'm Gis and in this class we're going to study the content of ratio and proportion so let's go [Music] Well then in this class we're going to talk about ratio, in class 2 I invite you to watch and we'll talk about proportion, so be sure to watch class 2. But then what is the reason, the reason is when I make the comparison between quantities, okay, so look what I brought here for you today, let's generalize the subject first right, so you can understand what can, what can't, what is what isn't and then I'll explain it using other methods, okay, so two numbers a and b which are any numbers but what has to happen here people b is different from zero, b can never be zero then, okay? The ratio then between this a and this b is the quotient obtained in the division of a to b, so the conscious of the division of a to b, then I will explain better how this is and what else you should know because when I work with reason, the order in which I say the quantities will interfere a lot with the result, it won't interfere, okay, and then it will give another result, it will give an inverse result, okay, so it's not interesting if you write it wrong, it has to be in accordance with the statement so if you need to know a reason look here a ratio from a to b you must be thinking, oh Gis, ratio is a fraction so yes the ratio comes from a rational number, okay, it means in Latin apportionment okay good?

So that's why it's division. So here from a to b this is a reason, it's the indication of a reason, in fact, this a is our antecedent and ob is the so-called consequent, so that's why I said that time of order, that's the order I'm talking about it matters. First I talk about the antecedent which would be the number up here and then I talk about what comes after the consequence, ok?

So look at what I brought an example of a reason for you to understand better, so the ratio of 3 to 4 what this means is that if I have three green dots here for every three green dots I have four orange dots so here I So I have a ratio of three to four, okay? And now if I were to say the opposite of talking about the orange ball to the green ball, would the reason be the same? How do I indicate this reason people?

How do I indicate the ratio of 3 to 4? so I have three ways of indicating a ratio, so the first way for me to indicate a ratio, so it could be the same as you have here, right, from a to ba divided by b, so it would be 3 / 4, okay, because I 'm in the order of 3 to 4 , and I could say speak like this to write like this three to four and then I used the fraction, right or I could put it so if I divide three by four I will get 075 so here I have the three ways of representing the ratio, okay? So what happens guys, so if I have three green balls and 4 orange ones I have a ratio of 3 to 4 but what if I doubled the number of green balls instead of three I would have six, and now what happens if I I have now it was three to four then I doubled it I went from 6 to how much now?

What will be the number of orange balls now? they will be eight because I am doubling, I would have a ratio of six to eight but then look here in the first one I would have a ratio of 3 to 4 and in the second one I wrote a ratio of six to eight, what does that mean? that for every 6 green balls I have eight orange ones, what happened here with my reasons?

From here to here I doubled, I didn't double, so from here to here I also have to double and then I end up having what here people I end up having here are fractions that are equivalent, okay so from here to here I doubled automatically I have to double this quantity. Another way for you to understand better is when you are going to prepare, for example, a juice in those concentrated ones that we buy in the market there, so I'm going to buy the juice and I'm going to read it from that instruction, you know, no one does it, we do it all by eye, right, we put a little in there and try it out, but if I follow the instructions in the recipe, it will say, for example: for every one liter of concentrated juice I should use two liters of water so what would the ratio be for each liter of concentrated juice? I'm putting the unit of measurement here, I should use two liters of water, so here I would have the ratio of one to two, I could write it like this in the form of a fraction or I Could you write one for two, okay?

So those concepts there are about reason, I think this is the best way for you to understand what reason is. Think about the recipe, when you're going to make your chocolate milk in the morning, you add a little milk and a little chocolate milk, right, nescau or toddy, let's think about it here, right, but we won't go into details, so you can add, for example, every 200 ml of milk you would put two spoons of chocolate milk, so I said milk for the chocolate milk, and if I said the opposite, then I would say two spoons of chocolate milk for every 200ml of milk. I'm working with reason because I'm comparing the quantities so that My chocolate milk will be good, okay?

or because here my juice will be tasty, right, because if I don't follow this recipe, I don't work, for a reason here it will be bad and the same happens with my balls, if I don't work in the same quantity here, if I have six here I put seven here I'm not going to have a correct proportion, I'm going to have a disproportion, wow, what a strange name, but a disproportion, okay guys? Let's do other examples, let's go guys, so look at the example I brought: in a classroom 25 students are boys and 15 are girls, okay, what's the reason, so I'm going to represent the ratio between the number of girls and boys, do you remember that Did I talk at the beginning of the class about the antecedent and a consequent, the importance of writing in the correct order? because registering in the incorrect order will be in reverse, so it's not right, so who is my antecedent in this case here the antecedent the number of girls ok so girls do one here so we can remember and my consequent will be the number of boys, okay, so what will the representation look like?

so I have how many girls do I have in this class? I have 15 girls, right? And how many boys do I have?

25 students are boys so there are 25 boys, and what does this ratio here mean? does this mean that for every 15 girls I have I have a total of 25 boys and how do I find the result of this ratio? Do you remember what the ratio was, it's the quotient obtained, isn't it, from the numbers a to b, remember that I spoke in general terms so it would be the division of 15 to 25, let's see what happens.

So if I divide 15 by 25 then division you remember, if you don't remember division or I invite you to watch my division class, then you will understand well. So let's divide, we can't divide, I put a 0 here, it will be 6 times 6 x 25 are 150, well then there is zero remainder. So it means that the quotient obtained here, right in the division, was 0.

6, which means 0. 6 for those of you who have already studied percentage, you know that 0. 6 is the same thing as sixty percent and what would be sixty percent people?

? sixty percent is who's number of girls or boys? sixty percent is the largest number, therefore the number of boys, so that means that in that classroom, right, I have 25 boys, these 25 boys are representing sixty percent of the class while the girls are representing 40, but then you must be Wondering, Gis, can't you simplify this fraction instead of writing 15 to 25?

Of course I can, how can I simplify it then? 15 to 25 I can come here and simplify by 5, right, because it divides 15 and divides 25, 15 by 5 is three, 25 by 5 is five, look how much easier it is to understand here, what does that mean? every three girls, right, I have five boys, so let's see the dots so you understand, I'm going to put them, guys, look at my representation, how it turned out so you can better understand this concept of reason, every three girls, I have five boys, so he is representing sixty percent and the number of girls 40%, but we are not working with percentages here We'll talk more about percentages in another class, okay?

So then you watch another percentage class, ok? Shall we do another example? let's go?

Guys, look at the other question that I brought up, I try to bring up questions, right, that are easy for you to visualize because these types of questions are part of your daily life, right? In a test with 20 questions, so the total number of questions was 20, mark this, the ratio between the number that the student got right and the total number of questions is two to five, so look, I'm going to highlight here, which is the reason, it has already been given For you in the statement what is the reason, and what does this reason mean? let's interpret, remember the antecedent and the consequent who I have to put in order the number of questions that the student got right which would be two so it would be two for the total number of questions, and this would be our consequent, so it would be two for five so this one here It is our ratio that represents the number of things the student got right in relation to the total number of questions, okay?

So look, I've already brought you the marbles, for every two orange marbles I have five green ones, what does this marble business really mean? Let's start by saying that for every five questions he had on the test out of 5 in total, let's think of five in total he got only two right, out of five he got it right. .

. look here at the little ball. .

. out of five he got two right, that's not what it happened, but if it had been a student who had been attending Gis's class, and had paid attention, what would this ratio be like ? Here I have the reason that for every five questions he had on his test he got two right so we can use another reasoning to answer but we didn't even read the question, what is the question?

What is the total number of questions he got right, so the test didn't have five questions, only here is the ratio that represents the number of questions answered correctly out of every five, so look here, he got two out of five right, didn't he, so he would get 4 out of 10 right? what I did here look what I did here from 2 to get to the board I doubled it, so here I also doubled it, so from five questions it became 10 so if this test has 10 questions he doesn't get two more correct, he now get four right and now the test will be, he will get six right, but he will get six right, how much now out of a total of 15 observe from 5 to 15 I did times three and here also o times three ok, and now how much that he will get it right now he will get eight out of a total of 20 so I managed to do it and here it was times four and here it was times four, you see so you didn't need to do another type of reasoning here you already managed to find what the total number of questions he got right within this test of 20 questions so he got it right, the answer: he got all eight questions right so you go there and ask. .

. well then the answer he got eight questions right, right, is that ok? Now I'm going to tell you about some reasons that we have in mathematics that are called special reasons.

Have you ever heard of any? So let's see what they are. Look guys, the reasons I brought here now that I'm sure you must have heard of one of them, okay, you may not know the meaning but you've heard average speed who there was no average speed what is average speed is it a reason, you knew that it is a ratio between the distance covered, right, and the time taken to cover that distance, so look at an example that I brought: pretend that I covered a distance of 80 km and for that I spent an hour, so here I would have a average speed of 80 km per hour, you see that notation that I made here is an average speed notation, you may have also seen it on traffic signs on the roads, right?

What is the speed limit? 80 km per hour, so remember that speed is a reason. Look at another case where the reason is demographic density, that's what we use a lot, oh you use demographic density, you study this in geography to calculate what the demographic density of each city is, so you use a ratio and what which is demographic density is the ratio between the number of inhabitants by the area of ​​the region from the place you are going to calculate, then you will do the following calculation, in your home you will research the number of inhabitants in your city and what is the area of ​​your city, the area occupied by your city, then you will divide the number of inhabitants per area and you will get the demographic density, okay, and then you will get inhabitants per square kilometer is a ratio.

And then look at the other example that I also brought, we also use it a lot in scale, what is scale? It's the ratio between the length of a drawing or the miniature, right, I can talk about the miniature of a model of a building when the architects are going to design a building what the architects architects, engineers and now, who does what, right? , they first don't design a model, then they use they work with scale you can observe pretend that there on the model every 5cm he drew there on the model corresponds to 200 cm in the original project in the original building or you could write this here Also, for every 5 cm of the drawing there would be 2 meters of the original, because 200 centimeters is two meters, so here's another example of ratio, now do you remember at the beginning of the class that I said how much we use reason in our daily lives?

? And then you concluded at the end of this class how much we really use it and maybe you didn't realize its usefulness. So, if you liked this class, I'm going to ask you to subscribe to the Giz channel and leave me a thumbs up, and be sure to watch the next classes where I'll explain about ratio, it's proportion, ratio is here about proportion about greatness about little rules that you must be curious to know little rules that I know.

So until next class, bye. . .