REGRA DE TRÊS SIMPLES - GRANDEZAS DIRETA E INVERSAMENTE PROPORCIONAIS - Matemática básica

In this class, you will learn very important content. But why did I speak so happily? Very important, why are you going to learn?

Simple rule of 3 that is used like this, too much in our daily lives, if you don't use it yet, let you become an adult and you will see how much it will be used. Let's go? When I said very important, then you should look at this example that I'm going to read now, and then you think, wow, it really is used.

I don't use it yet, but I've seen someone in my family using it or I will one day use it too. So an example says the following. A mother used the leaflet to check the dosage of a medicine she needed to give her son.

In it, the following dosage was recommended. 5 drops for every 2 kg of body weight every 8 hours. If the mother correctly administered 30 drops of the medicine to her child every 8 hours, then the body mass is?

So, guys, how am I going to carry out the strategy, how am I going to develop the strategy to resolve this issue? So see that I already brought it here separately for you. What are the quantities involved in this exercise?

And another thing that is very important when reading the statement and this is a 2012 Enem question. So, when reading the statement, what should you do? You must already be highlighting, right?

Highlighting the important information that will help in developing a strategy. So, as you can see, the quantities involved in this exercise are body mass and number of drops, the dosage of the medicine that is administered. The first thing I advise students to do when carrying out a rule of 3 exercise is to identify the relationship between these quantities.

If these quantities are directly proportional or if they are inversely proportional, and how do I do that? I do it using arrows, right? The arrows, oh, so let's think about it like this, the greater the person's body mass, what happens to the amount of medication they have to take?

Number of drops will increase. O. So see that I like working with arrows today, Gis, but if I say it like this, the smaller the body mass, what happens to the number of drops?

The number of drops a person will take is smaller. So you were able to see that in my speech either the 2 arrows went up because my question, the more mass, the more drops of medicine or the less mass, the fewer drops of medicine, regardless of the way I asked, they are both in the same direction. And therefore, when they are in the same direction, I have quantities that are directly proportional quantities, which I say GDP, okay, for short, directly proportional quantities.

Then, after I have identified whether these quantities are directly or inversely proportional, then I go there and put the number, but say, why do you put the number, only then should you ask why it is better for us to analyze what the quantities are? ? Because from the moment I put the number here, the student may start to get confused.

Wow, but that's the number. Then it turned into this. So that's why I don't put the number.

Firstly, I identify how these quantities are related. Now let's get to the numbers, so, body mass, guys, what is body mass? body mass is how much does a person weigh?

But we don't say the weight, right people? It's body mass, who hasn't been to the pharmacy and stood on the scales to weigh, weighing is to see the body mass we have, let's talk straight, okay? So, the recommendation written on the leaflet was that you should administer 5 drops of a certain medication for every 2 kg of body weight, right?

Imagine if you don't read the leaflet and then take the wrong dosage of the medicine? It's not possible, right, guys? You have to pay close attention.

So, what do I want to discover there? The statement says that if the mother then correctly administered 30 drops, where do I put 30 here, or here? Here, right, guys?

So, she administered correctly, 30 drops. How many kilograms does the child weigh then? That's not what you're asking, Ah, but Gis, there's a time every 8 hours, but the time won't change, right people, because it's an indication of how often you can take the medicine, so leave it he for there.

And now what do I do? I've already included the magnitudes. I have already identified the relationship between the quantities, I have put the respective values ​​ready and now we will see when we have the quantities they are.

Directly proportional, I do cross multiplication. Multiplication in x, so you won't have to solve all the rule exercises and multiply the cross, which isn't, okay? In this case I will do it, because it is directly proportional, so I multiply 2 by 30, 2 by 30, is equal to 60, right?

And then I divide it by what's left, because then I would multiply the 5 by the unknown value, but then I like to explain it directly. So I always multiply the 2 values ​​here and then I divide by what's left. So that means I divide by 5, 60 ÷ 5, I can take 6 which gives 1, 1 × 5, 5, one remains, then I reduce the zero to 10, then I do 2, 2 × 5= 10, zero remainder , let's cut the last one here, right?

So what does it mean? This means that this child whose mother gave 30 drops had 12 kg of body mass. Gis is what I learned, my teacher said, look, I should multiply then, 2 by 30, look how you must have learned, so I'm going to write it here in the corner, look, pay close attention, look, it's like this , 2 to 5 there, here is 30 and then generally you must have learned with x here, right ?

So, how do you do it? Multiply x times 5 which gives 5 x equal to 2 × 30 which is 60, and then do X= 60 divided because here you are multiplying then divide by 5, which will end up in 12. But I prefer to do it first without the Put the question mark, which is the unknown value and without putting together a little equation I like to do it straight, I always multiply the values ​​that exist here diagonally, as the students say, ok and divide by what is left, it will always work out like this right when they are directly proportional quantities, it will always multiply diagonally, so that's good and another way wow, how many ways you could do it too, look here, look.

From 5 to 30. What happened here from 5 to 30? It wasn't multiplied by 6.

So, as the magnitudes are directly proportional here I could do it quickly, look, I multiplied it by 6, 2 × 6 which gave 12. That's how quick people can do it. When they are directly proportional, it's a breeze.

But what if it were, conversely, you would multiply on one side and do the inverse operation on the other and divide, it would also work like this, without calculating all this, okay? So, mark the techniques that we did to solve this little rule, when it is directly proportional and now let's move on to another exercise, shall we? The director of a school hired a team of 6 people for 40 days to fix the roof of the school where she works.

However, worried about possible delays, she decided to hire 2 more people, considering that all professionals have the same efficiency. So, what was the deadline for completing this work? So see, in this question, what are the great things that I have already written here to make your life easier.

The magnitudes in this situation, then, are quantity of people and time, right? To work, then time like I'm going to start doing this exercise the way I told you, which is very easy. We are going to identify what the relationship is between the quantities, so let's think, if I increase the number of people there carrying out the work, in this case by changing the school's roof, what happens over time?

time decreases, remembering that the statement said that people have the same efficiency, right? That will maintain this efficiency. So, the more people working, the less time they will spend.

So, the greater the number of people, the shorter the time. Just like if you asked like this, because sometimes students get confused. I ask, starting with bigger or smaller, it doesn't matter, now let's ask the question, how many fewer people work there on my site?

What will happen longer will take longer, will take longer, so it will be bigger. So you saw the less people, oops, the more time on the opposite side of me, the less people, the more time or more people, the less time. How did you manage to notice that the arrows are in opposite directions?

another and, for this reason, we are working with inversely proportional quantities. The jeep and then we remember the jeep and that car, right? And that little jeep, it goes straight, right?

Nothing, right? Let's think like this, so it goes straight, so in this case I won't do the cross multiplication like in the previous example. And yes, I'm going to do a straight multiplication remembering the Jeep, okay?

And then we go to our next step, which is to put the numbers here in their respective magnitudes, what is the number of people so we had 6 people who were working and they would carry out this work for 40 days. Remembering that time is given in days here, okay? So, what happened?

The director was worried and decided to hire 2 more people. So I'm not going to come here and put the number 2, because it's not just 2, she added 2. So we have a total of 8 people, 8 people will carry out this work in how many days?

And now we can analyze, Ah, if the number of people increased, the number of days will decrease, right? So let's think about the answer and then, as I told you, when quantities are inversely proportional, we will multiply straight. Who do I multiply with who now, the 2 straight numbers here, oh 6 times 40, remember in the other example, I didn't multiply diagonally because that was cross multiplication.

Here it is straight, so it will be 6 × 40. I do 6 × 4 = 24 so 24 and then add the zero, so it becomes 6 × 40 = 240 and then I divide this result by the number left here, which in this case will be 8, okay? So always like this, multiply the rectum and divide by what is left.

If there were 8 here, I would divide it by the number that was here, that depends, no problem, where is it? You will always divide and 240 ÷ 8. I take 24, which is 3, 3 × 8= 24 then there is 0 and 0 below this zero here goes zero in the key.

So it means that these 8 people will do it, they will complete this work in 30 days oh, okay, do it like this, I think it's the quickest way possible, Gis, but I want to do the one that does it with the X the same you did in the other example, so let's go, we'll take 6 times 40 which will be equal to 240 equals 8 times the X that you would put here, right? And 8 times X is going to be 8 x now, what am I going to do? This 8 is not multiplying, so it will be divided on the other side, so it will be 240 ÷ 8, which will be the value of x, which we already discovered that this value is 30.

There is also another way that you should have learned, because I learned this way, which is to do what? Which is to keep the first here and invert the second, and then cross-multiply, but as I'm here to make your life easier and not harder, right? It's not that difficult, guys, but let's do it a quicker way, right?

And doing this way here, which I think is the simplest of all, not even this way with x, and then the student sees x and will start thinking about it, Gis, I don't know, do it directly, people, put a question there and it's the same X thing and do it straight and that's it. Look how fast it is, and then you're asking because production was the first thing that asked when I started doing the exercise. Is it possible to do it like the little arrow from here to here, what did I do from 6 to 8 from 6 to 8?

If we analyze it, it was multiplied by 4/3, so it ends up being more difficult in this case to do because you saw that other one there? It was a whole number, wasn't it? So it was quick, here it was 4/3 and how I identified that it was 4/3 because I did 8 ÷ 6 oh, 8 ÷ 6 if we simplify it gives 4/3.

So I know it was 4/3, so now, if I multiply, oops, multiply not here I multiplied, right? By 4/3. And then, as we are working, with inversely proportional quantities here, I don't multiply by 4/3, but rather, I divide by 4/3, so it will be 40 ÷ 4/3, then I apply the Ping pong method, it will be 40 times 3 which is 120, and here in the case where there is no one, I put 1, 1 × 4= 4 and 120 ÷ 4 gives us 30.

So you can see how many possibilities I am giving you to solve in the exercise, but I still say this one, which I did first of all, is the simplest possible, real people. After I learned how to do it, I never did it again, but then it's up to you, okay? I'm Showing here a way for you to rock.

In your activities and if you enjoyed today's class. Ah, give Gis a thumbs up in today's class, it's a really nice thumbs up. And subscribe to the channel, because I think you are not subscribed to Gis' channel and by subscribing to the channel, activate the bell to receive notifications of the classes I publish.

And then you will ace all your activities and exams, because I will help you, people do it, recommending the videos. And speaking of recommending videos, see that here I only did 2 examples, there are more classes on the channel about the simple rule of 3. There are also classes, in case you are confused about magnitudes, about ratio and proportion, and also about the compound rule of 3, because here it is simple, but we also have about compound and how you will find these classes so you can ask more questions, Go to the description of this video below.

And there are all these classes, I will leave all the links clearly so you can go there and watch all these classes, so don't forget to share this class here, look. Summary class, let's put it that way, but I said so much, didn't I? But it was a summary, okay guys, so time to say goodbye, enough talking Gis, goodbye and see you next class.

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