RAZÃO E PROPORÇÃO | igualdade entre duas razões \Prof. Gis/ #02

Hi guys, welcome to my channel, I'm Gis and in this class we're going to study proportion. So you have doubts and want to learn, come with me. Guys, what is this proportion thing?

For you to study proportion first you have to go there and attend the ratio class which was class one which I will leave an indication here for you ok this is class 2 so the focus here is on proportion. So a proportion is what it is an equality between two reasons look here an equality between two reasons there to generalize so you can try to understand what this means an equality here I have equality here I have a reason here I have reason and this it means what does a stand for b, just like the equality symbol here in the proportion it represents as well as o, as well as, so a stands for b as well as c stands for d, okay, I can say it like this or I can say that the numbers a and b they are proportional to the numbers c and d, so could you say an example like this o 3/4 is proportional to 15/20 I can say this I can because o and 3 to become 15 I multiplied by 5 and 4 to become 20 I also multiplied by 5, okay, so there I put an example so you can understand numbers a little better. Now I 'm going to explain to you the property of proportion and then we're going to do examples, shall we?

Guys, so the fundamental property of proportions tells us like this, remember the proportion I just wrote a is to b just like c is to d, so I also instead of writing like this I can write horizontally like this a is to b just like c is for hence when I work with the proportions I have the so-called means and the extremes, right the terms are called means and extremes, so oaeod are called extremes and obeoc are called means they are close to each other another, is in the middle there, let's remember it like this, so you don't forget who is the middle and the extreme. And it's the same thing here, isn't it? The aeod are the extremes and the beoc are the means.

But what does all this mean, what is the point of knowing this property of proportion? That's where the secret comes, so if you multiply the extremes you already know what extremes are and you already know what half beauty is now we're going to see if you multiply the extremes which is a times b, what will happen will having to give the result of this multiplication here will have to be the same result of the multiplication of the means of b to c, that's why I wrote here for you so that you know what is extreme and what is half, okay, you will find a statement that says the multiplication of means and extremes, so you have to know who each term is, okay? So look here, the multiplication of a by d has to be equal to the multiplication of b by c, so this is our property, okay, now we're going to apply it.

Do you remember the example I just did, it gives the proportion that was 3/4 is equal to 15/20, right, that's the example I put up just a little while ago, wasn't it, so let's test to see if these numbers really are proportional, let's multiply, then extremes 3 times 20, you don't even need to put it together like that, okay, people, I just did it here to indicate for you, three times 20 is 60 and when I multiply four by 15 four by 15 is also 60 so this multiplication has to have the same result when this happens we have numbers that are proportional we have a proportion ok look what that I brought now for us to do together 6 and 10 are proportional to 15 and 25, how am I going to put this together from here, let's make our proportion 6/10 cute, so 6 is to 10 as well as 15 is to 25 ok now we are going to apply so the property of proportions here multiplying then extremes 6 x 25 if you do the math there it gives 150 and 10 times 15 also gives 150 so we saw that these numbers are proportional now we are going to do an example applied to everyday life, shall we? Guys, I brought an example, right? Now for us to apply the concept of the proportion not being there in that a with b, for us to see an example from everyday life, I brought a beautiful, wonderful photo of me with a unicorn, for those who don't know, I love unicorns, okay?

and I also love stars ok it's not just a joke so I brought well then here she has a 10 by 15 photo so what does that mean there we have a photo so be careful with my photo what happens in this photo what does this 10 by 15 mean than the same thing as that 3 by 4 photo which means that I have, photo for here, that I have 10 centimeters here in width and I have 15 cm in height so that's what 10 by 15 means, okay, I want to enlarge it so that it is 45 at the height, so I want to enlarge and when I enlarge a photo I have to enlarge it using proportion because otherwise everything will be distorted, the body will be distorted, the head will finally have to work on a proportion, that's why when we do an enlargement we can't clicking on the plus on the side we have to click on the bottom and then it comes out proportional but then let's do the math so we can find out which photo of me doesn't want to stop here, so I want to enlarge this photo, of course I'm not going to do it here in the real size it will be, which is 45, I'm just going to do the sketch, okay, so I want to enlarge this photo of mine, okay, what do I want? I want it to be 45 cm in height, so how much does it have to be? here in the width for this expansion to occur, right to be proportional, you have two ways to do one, from 15 to 45, from here to get to 45, what counts?

What I'm looking for is x 3, 10 times three or 10 x 3 is 30 so my photo will be 30 centimeters wide then the other way you could have done it didn't even need to draw anything here was to put together my photo like this it's not 10 by 15 so it's 10 by 15 as well as what happens this 10 in width this one is height this is 45 is height so where do I put 45 put it at the top or at the bottom I put it at the bottom o height with the height 45 here and here Since I don't know who it is, I can put a question like I put here or if you've already attended Gis's equation class, then you can go and put the x as the unknown, so the unknown term, so you can come here and put an x, okay, and what which we studied in the property of proportions that if I multiply the means, the multiplication of these means has to be equal to the multiplication of the extremes, so if I multiply here crosswise, right, let's say like this, it works out better if I multiply crosswise, if I multiply these two it has to be equal to the multiplication of these two, it is multiplied crossed, so 15 times x, 15 times 15 by 15 will give 1X, 450 by 15 will give 30 so I have here what is the width of my photos ok guys so here is an example applying the context the concept of proportion the property of proportion in a real example, let's do another example ? Let's go? So another example, 5 and 10 are proportional to 7 and 16?

It's a question, I need to check if these numbers are proportional, so let's use the fundamental property of proportions, let's set 5 to 10, so what, what is it? 7 is to 16, how do I check if they are proportional? Remember the multiplication of means and extremes?

So, cross-multiply, actually, right ? This here is a statement, right, a false relationship, right? So what happens if it is false, then it means that 5 and 10 are not proportional to 7 and 16, so here I just answer, just answer: they are not proportional.

This was a question that is a type of exercise that could appear on your exam in your competition, okay? Look at another example now the numbers 4 and 10 are proportional to 10 ex note that here, unlike this exercise above, he is stating that they are proportional in the exercise above he is asking if they are proportional, ok so there is the difference so he stated that they are proportional let's set up this relationship so I have that four is to 10 just as 10 is to 10 is to x right now he asks what the value of x is, well we know so in proportion I do that application of multiplication 4 times x, I'm going to do it here on the side it is four times x has to be equal to multiplication of 10 times 10, 10 times ten is 100 and now what I do here as this four is being multiplied by x I divide by four and from the concept of equation that I do on the other side I do on the other side four by four, four by four gives one x and 100 by 4 will give 25 so let's put the answer here so x = 25 as the statement stated that they were proportional I was already able to find the value of x now let's do the last example of this class, shall we? So people, observe that the example I brought here is a little more difficult and the other one is not impossible to do, remember that I tell you about mathematics, nothing is impossible, we just need to train, right?

You have to understand, watch Gis's class to understand , look here the numbers x and x + 3 are proportional to 6 and 7 so he is stating that it is proportional, he is not asking are they proportional so calculate the value of x how do I set up the proportion let's go putting it in the fundamental property of the proportion x is for x + 3 and just as 6 is to 7, 6 is to 7 and now I don't have that fundamental property of proportion I multiply the means and the extremes, cross multiply so I will multiply x by 7, x by 7 will be 7 times _ multiply all of them by two here so you have to put a parentheses here, okay then I'm going to do the distributive property of multiplication so here it will be 7 times x gives 7 x equal to here applying the distributive property I'm going to multiply this six with this x which will be 6 x and these six times 3, 6 times 3= 18 well what do I do now to solve this equation I'm going to have to take these 6x from here so I'm going to subtract 6x from here and I subtract from this side too because the scale reminds me of what I do with one side, I do it on the other side so that it keeps it in balance, okay, let's continue the exercise here, so now I'm left with 7 take away 6, 7 take away 6 from 1 x is worth 18, do you want to take the real test, come on, let's get that there again so I have 18 is to 18 plus three as well as six is ​​to 7, so here it is 18 is to 21 and six is ​​to 7, a quick way to doing 18 to 6 didn't divide by three 21 divided to 3= 7 I tested it but if you want to go there cross multiplying 18 x7 will give 126 and if you multiply 21 by six it will also give 126, so it is a multiplication of the means by extremes have the same result. So you saw that there are two ways to do this real test, I can see the simplification there or I do the cross multiplication, ok guys, so I'm going to end the class here in proportion, which was our class 2, don't forget to sign up here On Gis's channel, give me a thumbs up and watch class 1 and also be sure to watch class 3 where I'll explain about magnitudes. So until next class.

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