Who has difficulty performing calculations with fractions who sees the statement there that has a fraction and wants to run away? So you are in the right class at Gis, here I am going to summarize a reminder class for you of all the operations that we have addition subtraction multiplication division potentiation and square root and all of them involving fractions because then you will make a comparison of how it is done one kind of does another and remembers all these concepts. But hey, I'm going to give you a tip, oh Gis, I don't know the concept properly, I need to learn it because I can't remember it if I didn't learn it, so you can find all the links to the classes that have separate classes on addition and subtraction of multiplication of the division of the power and the square root, all of them in separate classes and there are other classes too, right, exercises with fractions so you can remember, not remember, learn and then remember combined?
And then you can rock your activities. So let's start: how do I add two fractions with different denominators? Oh, how I want to transform each one into a decimal and add them together, no, no, no, let's go here, pay attention to what I'm going to do.
So in this case we can apply the method, the butterfly technique method, the butterfly technique we can do when we have two fractions adding two fractions. So then it's a butterfly because we do it like this, we make the wing of the butterfly then do it here and multiply these two numbers then multiply 3 x 5 which will be 15 multiply ok. And then I make the other wing of the butterfly, and then in 4 x 2, which will be 8, then we multiply the numbers that are on the wing of each wing of the butterfly .
If you want to do the drawing to make the butterfly like this, then you can do it. So what I'm going to do with these two numbers that I got here is not an addition so you come here you put addition Between these two results 15 plus eight and then adding 15 with eight I get 23 which will be the result of my numerator . Look, people are always clear that when you 're doing it, you don't need to keep drawing, tracing, you'll already get it, you'll become an expert , right?
How you'll do it with your skill and you'll do it straight away, okay? And then to find the denominator I multiply the two here I do four times 5 and 4 x 5 is 20. Then I ask you, can you simplify this fraction, what does it mean to simplify the fraction?
is to find a divisor common to 23 and 20 but I'm going to tell you that there isn't one because here we have 23 being a prime number so it's not possible to find the numerator and a divisor to the numerator and the denominator at the same time, right. Only if here it was a 46 for example then it was double then there was the relationship but in this case there is not so this fraction here is called an irreducible fraction then mark irreducible that when it is no longer possible to simplify it is now the subtraction of fractions with different denominators. Did you notice that I included examples in all the exercises here, except for these two, right ?
Butterfly method, 3 x 5 which we already saw was 15 and 4 x 2 here was 8, but different here from addition where I have a subtraction. So I'm going to subtract and then from 15 I take eight I get 7 What is the result of my numerator and how do I get the denominator? I multiply, so here it will be 20, and 7/20 is also an irreducible fraction because I can't find a divisor common to seven and 20.
Okay, so you saw addition and subtraction in the same way, do the butterfly and if you need to know How do you do it with the MMC, right? The MMC equivalence process, so you can consult that class in which I explained several examples with all the details, here it is a more reminder class. Multiplication Now, in my opinion, multiplication is easier and when multiplying fractions you multiply the numerators together and then the denominators together, so it's quick to do.
Let's go. If, I almost told you the answer, 3 x 2= 6 and here 4 x 5= 20, now take a good look at this fraction, is it irreducible or can it be simplified? Is it possible to find a common divider, right?
to 6 and 20 which is the number 2 so you can divide it by two by dividing six by two we get 3 and 20 by 2 will be 10 and now three tenths is an irreducible fraction because you can't divide 13 and 10 by the same number. You scored well, so check out the three here and we'll sort them out. Now in division I say that in division we do the ping pong process.
What does the ping-pong process look like? Imagine that you have a ping-pong ball in your hand, you throw it on the floor, it will hit the floor and it will go up, then look at the drawing that it will hit the floor and it will go up. I'm here, what did I do, I threw this little ping-pong ball on the floor, this little ball hits the floor here and goes up, so making this drawing is the result of my multiplication because we do a multiplication here so I do three times five 15, but why do I use the ping-pong technique to remember where the numbers go, the results of the multiplications 3 x 5= 15 went up and then here I make the ping pong ball now I'm Down here, what did I do, I threw the ball up and it hits the ceiling, I forgot the name and it goes down and I make 4 x 2 which is 8, okay?
So this is a way that we can divide fractions, you may have already learned that we can keep the first fraction and multiply by the inverse of the second, but then it ends up being more laborious, so I prefer to use the ping-pong method and This fraction that we have here is an irreducible fraction, you cannot divide 15 and 8 by the same number, there is no common divisor there, right, and now 3/4 squared. We arrived at easy potentiation, folks, what is potentiation, if you don't remember, here's the gis tip, I'll leave the link to the class on potentiation with both natural numbers and fractions in the description. And then to do the power, see that here I have an exponent of 2.
So this means that I must perform two factors of the multiplication, right, the power is the multiplication of equal factors, two factors 3/4, which will be 3/4 x 3 /4 and doing here what I have, I have the multiplication of fractions so the power turns into the multiplication of fractions and you already know the multiplication of fractions multiplies the numerators among themselves and the denominators among themselves, then I do three times three. How much will 3 times 3 be 9 and 4 x 4= 16 and here too I got an irreducible fraction can't find a divisor that can be done by 9 and 16, okay? And finally here is the easiest one of all, it's not difficult, people, it's easy, but how easy is it with a square root and even with a fraction, look how easy it is, so I'm going to take the numerator and I'm going to write it separately from the denominator, but you you see that this radical symbol and it is involving the two numbers is the numerator and the denominator, so I'm going to write a Radical for each of them, then I'm going to write a Radical for nine and then a Radical for 16 and doing So from here I can calculate each square root separately.
What is the square root of 9, okay? If you don't remember the square root, take a look at the description that has the link to the square root class, and the square root of 16 here will be 4, look how easy it is to do. square root with fraction you need to know square root otherwise it won't work, right?
And then, you don't need to do this step here that I did, write each number with its separate radical, just look here at the square root of nine 3 square root 16 four and it's very calm and also stops this habit of wanting to transform numbers fractions here, all in decimals to do the operations, you don't need to take a look at the general board, here I did for you with all the operations here that we worked on in the classroom and then you mark them and remember them when doing the exercises and Another observation here is that potentiation and rooting are inverse operations. You saw that here I took three quarters and squared it and got 9/16 and then here I took what, I took this result itself which was 9/16 and I took the square root of it and of course I would get three cuts that are inverse operations. Okay, so check out this tip that I'm giving you.
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