OPERAÇÕES COM NÚMEROS RACIONAIS | OPERAÇŌES COM FRAÇÃO \Prof. Gis/

You look at this expression here and you start to think, Gis is difficult, you're scared to solve this expression and I'm going to tell you that it's not difficult because as long as you know the concepts related to operations with rational numbers you will Resolving this from here is easy. Take the opportunity to subscribe to Gis' channel and give it a thumbs up, you help Gis and Gis helps you! And then let's analyze first by looking at this expression that you are afraid to solve, right, let's analyze what operations I have, so I have a division, an addition and a multiplication.

But in this case I have the parentheses so of course I must first proceed by solving inside the parentheses, okay and inside the parentheses if we analyze I have an addition and a multiplication who comes first between the addition and the multiplication? Very good for you who are saying that multiplication attended Gis do pacocha's class, right? Oh yes, then everyone will know everything.

So let's go, what I don't use, I copy 7/2 divided, right, making it very detailed so you can understand, okay. Here it will be 1 integer + now I will multiply these two fractions and to multiply fractions I multiply the numerators with each other and then the denominators with each other, so here there will be two 2 x 15 which are 30 and 5 x 4= 20 and For those of you who still have doubts about how to multiply fractions between rational numbers, go to the description and you will find all the classes you need. And now guys, I have to solve here inside the parentheses, I have 1 integer plus 30/20ths.

And you can see that here I can simplify these 0 with this 0, so I only have 3/2 left. Look how easy it is to do it with 3/2 then it will be 7/6 divided by open parentheses, guys now I have an addition so you can see that this one has no denominator I come here and put the 1 underneath it just to stay there right for us to do it and then I remove the MMC between one and two or you can do it using the butterfly method. Whichever one you prefer is here, in this case I'm going to give you a reminder of the MMC, the LMC between one and two will be two, ok then I do the equivalence of 1 to 2, it was multiplied by 2, then I also multiply this guy by two which is 2, 2/2 which was an integer, right now from two to two was times one, so that three remains and if you had made a butterfly you would have achieved the same result and sometimes even faster.

Continuing, let's go here because I can't write on the studio wall, right people, otherwise the production will fight me, I will now have 7/6 divided by, finally I can perform its addition, addition inside the parentheses, so denominators are equal I keep the denominator and add the numerators 2 + 3= 5 and here I have what I have is a division between two fractions and then I will apply the ping pong method, ping pong is what we do like this, multiply I said it well So, with emphasis, multiply 7 x 2=14, and even do it correctly, 7 x 2= 14, go up there and then 2 x 5= 10, bring the result down and 14/10 is a fraction that can be simplified and we can simplify this fraction here by two since the numerator is the denominator they are even, so it will be 7, 7/5 oh, so 7/15 is the result of our expression and just one detail that production is asking people if here oh here I If you wanted to apply the butterfly method, what would it look like? Take a look here and it would be 1/1 + 3/2, wouldn't that be it? Oh, doing it here for you gives you a reminder, I'm going to do here 1 x 2 which is 2 and 3 x 1 which is 3, I would add it by adding 2 +3= 5 and the denominator, how do I get the denominator, I multiply the two, 1 x 2= 2, 5/2 look here, 5/6, you see how I say it, sometimes the butterfly, after you get the hang of it, is much quicker to do than here, removing the MMC and doing the process of equivalence, so here's the same result as I signed up here, but I did it in a different way and then you can see which one you understand best, Ok?

Shall we do more examples? Now in this example here you already get it out of the way, right? First of all, we analyze what operations we have, you see that here I have the number in parentheses, right?

It's here because it's a negative number, that's why I put the parentheses, here and here, so if we analyze I have a multiplication, an addition and another multiplication, which operation should I start with? Well done to you who spoke about multiplication, are you paying attention in Gis class? Heh, yes.

So here I'm going to multiply these two fractions, then I'm going to multiply the numerators with each other and then the denominators so I should do it here - 3 x 2, that's 3 x 2, 3 x 2 are 6 but this one is negative and this is positive which will give minus, ok and 5 x 3 which are 15 but I can take this minus here and put it on the side, I know, people can put it, but mathematically it is wrong to write it like this, that's why I put it right in the middle of the fraction, right there, continuing + now I'm going to perform this other multiplication so I multiply numerators with each other, denominators with each other, then the result that I 'm going to get here I'm going to put in parentheses because I already know that the result is going to be the one that's going to be negative, right, because here it's minus, here it is more negative, let's even put negative here so we don't forget and then I'll make 3 x 5 which are 15 and 5 x 4 which are 20 perfect. Oh, the equals sign was missing here, folks, in the first case I didn't put the equals sign and no one said anything to me, did you notice that I didn't put it? Now, when you go to your notebook, I'll put the equal sign and then what I'll do now, I'll do the sign rule to remove the parentheses.

Look, I wrote it wrong here, minus 6/15ths, this minus isn't here, right Gis, this minus is right here. And here folks, you can see that between the parentheses here I have the + and - sign and then I apply the plus and minus sign rule, plus and minus will be minus so I don't need to write parentheses anymore because I've already done the rule of sign, 15/20ths, 15/20ths and now how am I going to proceed here now we can do either MMC between the two denominators or I do the butterfly method. Which MMC do you prefer in this case?

So let's do MMC here, I'm going to pull it here, to do it at the top here, MMC between 15 and 20 and if you want, before removing the MMC between 15 and 20, perform a simplification in the fractions. You can, do you prefer? So let's make a simplification between the fractions here, the 6 and the 15 can be divided by 3, dividing by 3 each of them I will get minus two because 6 divided by 3 is 2, 15 by 3 are 5 oh, I did so a simplification and here this 15/20ths I can divide by 5 which when divided by 5 will be 3 because 15 divided by 5 is 3 and 20 by 5 is 4.

So see that they are equivalent fractions but a number is smaller so we can think MMC Who can tell me between five and four between five and four will be 20 and then I do that process of 5 to become 20 was multiplied by 4, so I also multiply the numerator by four which will be eight, the minus sign is following here from four to have become 20 I did x 5 I multiplied three by five which will be equal to 15 now what do I do the equals sign is missing so I keep the denominator which is 20 and I think here I owe 8 and I I owe 15 when I have two debts I combine them, right, so it will be 23, but it will be positive 23, right people, if I am combining two debts, it will be negative 23, so the fraction will be equal to minus 23/20ths, which is called a fraction irreducible. And why is it called an irreducible fraction because it cannot be simplified, so I managed to find the result of our expression here, and you, did it another way? When you got here, you applied the little butterfly to train and tell Gis later how you did it.

And let's go to the last example for those of you who took a look at this account here, you won't leave Gis' video, you can stay until the end and I'll solve it from here and I'll explain how it will be solved in another way because looking there It's scary, right people, so what does it mean that I have a fraction here, a fraction here. And this risk here in the middle, which is also representing a fraction, all of this here would be the numerator and all of this here is the denominator, but do you know how I'm going to do it? First I'm going to calculate the numerator, I'm going to forget that the rest exists, then I come here and I calculate the denominator and there's no secret.

So let's start, I'm going to calculate what 1/2 minus 1/3 will be, forget about that rest here, let it go, you can apply butterfly production said that he likes to do it using the butterfly method people, so let's go, I'm going to multiply these two here and then multiply these two here, oh 1 x 3 will be 3, 2 x 1 will being 2, it is not less in the middle 3 - 2 will be equal to 1 and to find the denominator I multiply 1/6 then it was difficult so it means that the entire result of the numerator I will exchange for 1/6, it was not difficult, right people. Now we're going to do the denominator - 19/6 - 17/3 then we're going to do it using the butterfly method, I'm going to do it here, 19 x 3 which will be 57, why do I know it's 57? Because I did it like this, 3 x 20 will be 60, but then I take three units from 57, it's minus here, put the minus sign, now I'm going to do 2 x 17, which will be 34, oh minus here, and then here I multiply the two denominators.

Let's put the answer here so I owe 57 and I owe 34 I have two debts so I'm going to add these two debts and if I owe 57 and I owe 34 I'm going to owe, I'm going to owe how many people 57 with 34 = 91 I'm doing the calculation mental in and 2 x 3= 6 oh then I arrived at the result of the so-called. So this count here in the numerator was 1/6 and this count in the denominator was - 91/6 and what do I do now we're going to write so here again the numerator was 1/6 I'm going to put it here, but guys now what What I'm going to do instead of writing this fraction line down here so you don't get scared to death and find it difficult, I 'm going to do it here, divided, ok, because this fraction line here, this little line, it means division, doesn't it, so here? I wrote divided by the result given here which was minus 91/6.

And now what I do is I have a division of two fractions and then I can apply the ping-pong method. Remembering that the ping-pong method is a specific method that I explained here on the channel, maybe you could have learned it another way, but you can do it normally and it will give the same result. So here I do a ping-pong method, I do 1 x 6, it's the name ping-pong, which Gis put it, it's not the way to do the math, which is the same for everyone, it will be 6 and 6 x 91 which will be 6 x 1= 6, 6 x 9= 54.

Then 6 x - 91 will give - 546 and now this numerator did not give positive positive with negative plus and minus will be equal to minus I know the negative result. And now you can simplify this fraction, I'll tell you that you could simplify it at the beginning Now, here at the beginning you could simplify it, you can simplify it by six then I'll get that here it will be 1 o, minus one, 546 divided by 6 it will be equal to 91, so the result of our expression that you were scared to death of dividing into that one at the beginning of the class will be -1/ 91 avenths. So what did you think, leave it in the comments so Gis found this one more difficult or the others more difficult?

Did you manage to remember the methods such as addition, division and multiplication between rational numbers, which in this case we not only work here with fractions, leave it in the comments for Gis, enjoy and leave a thumbs up for today's class, subscribe to the channel and share this video with your colleagues for everyone, right, remove this doubt, remove this fear of carrying out operations with rational numbers, agreed? And I'll see you in the next class. .

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