DIVISÃO COM NÚMEROS DECIMAIS | DIVISÃO COM VÍRGULA | \Prof. Gis/

Hey guys! For those of you who have doubts about division with decimal numbers, I invite you to watch this class because I will explain to you exactly how to proceed to carry out this operation. So welcome to my channel, I'm Gis and I'm going to explain division with decimal numbers today, so let's go?

[Music] Hi guys, to start the class I want to make those two requests to you, shall we? Subscribe to my channel here and give Gis a thumbs up, don't forget, okay? And also for those of you who didn't attend the division class with natural numbers, I'll leave the indication here so that you can watch and remember all the division concepts so that you have a good performance here in division with decimal numbers.

Let's go? So I brought you here, 6 divided by 5, what should I do to perform this division? First we are going to set up the calculation 6 divided by 5, so what am I going to think about?

How many times does this 5 fit into 6? Once, right? Because 1 x 5 is 5, there is 1 left and I subtract it here, right?

And now what should I do? One unit, there is one unit left here, right ? I divide a unit by 5, can I divide it among 5 people?

No, right, what do I have to do then? Then I'm going to do the following: one unit, one unit guys, isn't that the same thing as 10 tenths? Do you remember this here?

One unit is the same thing as 10 tenths, so I'm going to put a 0 here because then that one unit became 10 tenths, now I ask you, 10 tenths do I divide this 5? Now we can divide, but before I continue this division, here in the quotient I have to put the comma because the next digit that will come here will be what? It's going to be our tenth, because I'm dividing 10 tenths by 5, so how many tenths do I multiply by 5 to get 10?

There are 2, okay? So that's why we put a comma and put this 0 here in the number that I'm going to divide here, okay? So this is the explanation why, two times 5 is 10 and then I have a remainder of 0, okay?

So look here in the consciousness that I got this 1 in the quotient of 1. 2, this 1 is representing the unit, right, it is an integer and the 2 is representing the tenth, that's why I told you, I put the decimal point because then I I was going to start working with tenths, okay? Beauty?

Look at the second example, so 125 / 4 and then what do I do? I'm going to get that little arch here at 12, right? Because I know that 12 here I can divide by 4, it will give 3, 3 x 4 are 12 and there is 0 left, so what do I have to do now?

There's a number 5 to download here, right? I lowered 5, this 5 is representing 5 units, right? 5 / 4, right?

How many times? Once, 1 x 4 is 4 and there is 1 left, now what? There's no one else for me to lower and this remainder of mine here is smaller than the divider, we can't do this division like that, so we're going to follow the same reasoning that I did here, remember the tenth?

One unit = 10 tenths? There is one unit left, so one unit is the same as 10 tenths, but what do I do? I'm working with tenths here, what do I really have to do here in the quotient?

I came here to put the comma because the next number that I multiply here now by 4 will be tenth, how many times will it be there then? There are two which is 2 tenths, 2 tenths times 4 gives 8, 8 tenths, so here doing the subtraction is, it will give 2, what now guys? 2, 2 tenths divides 4?

No, right, because it's smaller, what should I do then? Taking this 2 tenths I will put it as 20 hundredths. And now?

Twenty hundredths divides 4, because it is hundredths, because it will be in the second box here, ten hundredths. How many hundredths do I multiply by 4 to give 20 hundredths? There are 5, 5 x4= 20 and here I have a remainder of 0.

So the result of my division was 31 integers and 25 hundredths, just remember, here I have the ten, oh, another thing for us to remember, I explained it in class natural number, here I'm going to put the capital letter, capital D, to differentiate the ten from the tenth, okay? So here I have 3 tenths is 3 tenths 3 tens a unit, here I have 2 tenths and here I have 5 hundredths, so these are the reasons we put these zeros here in these remainders when they are smaller than the number I am dividing Here, is our divider ok? Look at the last one now, 3 / 20.

Can 3 units be divided by 20? It's not possible, but what can I do with these 3 units? 3 units is the same thing as 30 tenths, isn't that so?

So as now this here is tenth I have to come here and put a 0 because then it is 0 unit which is representing that there will be 0 units, because this 30 is in tenth now, so 0 unit and the number here will now be in tenth it is not? How many times does 20 arrive here at 30? Once, 1 x 20 is 20 from 20 to 30 is 10, and now we have 10 tenths left here, can I divide 10 tenths into 20 parts?

No, what do I do? 10 tenths is the same thing as 100 hundredths, isn't that so? o unit, tenth, the next number that goes here the digit that goes here is the hundredth, so that's why I said that here it became the hundredth, so now there will be 5, 5 x20 are 100, so here the remainder is zero so I I solved the three divisions until I got the remainder zero, is that ok?

Let's move on to the next examples, shall we? Guys, look, I brought the other examples now where I put the dividend being the decimal number and the divisor being an integer, decimal dividend and integer divisor, okay? For us to practice in different ways in all possible cases so that you can understand, you know, the division and, oh, ace your studies in the classroom.

So here 56 integers and 4 tenths divided into 6, what's the first thing I have to look at guys? To perform the division here I have to put the two numbers here, both the dividend and the divisor, they are integers, how do I transform them? What do I have to do here?

To make this 56. 4 a whole number, what do I have to do? That's exactly what you said, I have to multiply this number here by 10 and if you missed my class where I explained the division by 10 by 100 by 1000 the multiplication by 10 by 100 by 1000 I will leave the card here so you can return go there and see what the rule is in the practical way that I explained to you, okay?

So here 56. 4 times 10 what do I know? I know it will be 564, right?

Because when I multiply by 10, the decimal point moves one place to the right, okay? And then the 6 I need to multiply by 10 also just copy the 6? Of course you need to, the same as I do in the dividend I have to make a divisor so I multiply it by 10 which will also give 60 and now I do the normal division I proceed normally with the division.

So let's go, 56 starts here, can you divide 60? No, right, so let's take 564 how many times do you take 60? Are you thinking about the multiplication table of 60, or rather, thinking about the multiplication table of 6, how many times does 6 come close to 560 here?

What will you give? That's right, 9, right, because 9 x 6 are 54, so 9 times 60 are 540, so here is 9, 9 x 6 are 54, so as there is 0 here, 540, right? Then there will be a surplus here, I will subtract 420 and there will be 24 left, 24 units, can I divide it into 6?

I can, right? And how much will it give? Not in 6, I'm dividing by 60, I'm looking from below, oops.

. . How much will it give then?

24 units divided by 60 won't work because it's not enough, so what do I have to do? This 24 units will be the same thing as 240 tenths, but how did I transform these 24 units into 240 tenths, what do I have to do consciously? Put the comma because the number that will be multiplied here will be my tenth, the decimal number here which is tenths times 60 will give 240 tenths or close to it.

So how much will it give? Think about the 6 times table, 6 times how close to 24? It's 4, right, so it's going to be 4 tenths, that's why I put the comma, because this number here now I transformed it into tenths, 4 tenths times 60, the 4 x 6 gives 24 but this 0 here I put it here and then I put the subtraction with the remainder is zero, so the quotient of my division was 9 integers and 4 tenths, okay?

Next case, now I have two decimal places, what do I have to do to make this number a whole number? I now have to multiply by 100 so this one here is both the divisor and the divisor when the dividend is multiplied by 100, so it will be 2,904 because even if it was 2,904 people? Because when I multiplied by 100 the decimal point moved two places to the right, okay?

Divided by 12 times 100 just add the two zeros here which gives 1200 now we will proceed normally with the division. So then I have how many times 1,200 fits in the 2,904 are twice, right? Twice 1,200 is two thousand four hundred.

Doing the subtraction here gives 0504. And now guys? There are 504 units left, I can divide it to 1,200, right ?

What do I really have to do? I'm going to transform these 504 units into 5,040 tenths, so if I do this transformation here in tenths I add the comma and the next digit that will be here will be my tenth, right? So how many tenths times 1,200 that comes close to 5,040 or 5,040 will give, that's right, 4 times.

4 times 1,200 will give you 4,800, here it is 0 and 4, here you have to take out that loan, right, here it is 4 and here it is 2, very good. Now I have 240 tenths, tenths, right, because here I transformed it into tenths, can you divide it to 1,200? No, what do I have to do?

Transform 240 tenths into 2400 hundredths, okay? Why do I even make this transformation? Because the next digit that goes here will be what?

unit, tenth, it will be hundredth, okay? So here it will be twice, 2 x 1,200 will be 2,400 and we have zero remainder, okay guys? So here is my quotient.

We move on to the next one then. Now I put it with three decimal places, what does that mean? Now I need to multiply this here by a thousand because when I multiply this here by a thousand it will be a whole number here, the secret is to look at how many decimal places it has, if there are three I multiply it by 1000, if there are two by 100 here it was one I multiplied it by 10, so that number you are going to send us, okay?

In these cases here, here I will also multiply by a thousand, so here it will be, when I multiply by a thousand the decimal point will move three places to the right, one, two, three, so it will be 9,648 divided by 4, 4 x 1000= 4000 and now how many times does 4 thousand fit? Now we have to make that little arc, right? 9,648 is twice the 2 times 4 thousand and it's 1648 thousand and then here I do it and there's one left over, right?

Why didn't I do it for three people? If you make 4 x 4000 thousand out of 12,000, you would pass the dividend here, it cannot pass, it has to be a number first, okay? That's why I multiplied by 2.

And is 1648 units possible to be divided into 4 thousand? It's not right, what do I have to do? So I have to transform these 1648 units into 16,480 tenths and when I transform this into tenths I put that comma because my next number here will be tenths, okay?

How many times, how many tenths times the 4 thousand of 16,480? Or how close is it, right, if it's not exact? There are 4, 4 x 4 thousand are 16,000 and then here is 00480, there are 480 tenths left, is it possible to divide by 4 thousand?

Isn't it still possible what I'm going to do? I'm going to transform this 480 tenths into 4,800 hundredths, so the next number that I put here, the next digit that I put here, will be a hundredth, right, because one place, two places, after the decimal point, how many times will that be now? Once, 1 x 4 thousand will be 4 thousand, so I'll shorten the path here, there's 4 thousand to get to 4,800, there will be 800 left, okay?

800 hundredths but now guys, you can't divide by 4 thousand so I'm going to transform 800 hundredths into 8 thousand thousandths, the next digit that goes here is the unit, tenth, hundredth, thousandth, that's why only here I transformed it into thousandths, okay? good? And then there will be 2 times, 2 times 4 thousand are 8 thousand and the rest here will be zero, it's very colorful, my conscience here, right, each digit of a color, it's to highlight a lot so you can understand why I did it it's OK like that?

So it was 2 integers 412 thousandths, okay guys? Now let's move on to the next cases. Let's go.

. . Guys, so I'm making here several possibilities of what could happen, the dividend being integer here I brought it with a decimal divisor, oh integer dividend and decimal divisor, decimal dividend and decimal divisor.

So I'm offering several possibilities so that you can answer your questions and understand this content well, okay? So let's go. And I have 420 integers and I want to divide it by 1.

2 which is one integer and two tenths, what should I do? What did we do in the previous case? Don't we look at the dividend here and multiply?

And in the case where the dividend is an integer, who will I look at now? I'm going to look at the divisor that here is the decimal. So my divisor has one decimal place so I have to multiply it by 10 very well, by 10 because even if I multiply it by 10?

To turn it into a whole number, right? So that would be 420, is that it? No, right, I'm forgetting to do something, also multiply the dividend by 10 because the same thing I do here I also have to do here, so it will be 4200 divided by 12 because when I multiply by 10 the decimal point moves to the Right a house, okay?

Now let's do the normal division, 42 here, I make the arc to form 42, you can divide by 12, can't you? How many times does 12 reach 42 or equal 42? Think about it, how much is that?

It's 3 times, 3 x 12, how do you figure that out? Those who don't have this skill, do the multiplication math, you can start there, 12 x 2, two x 2 are 4, 2 x 1 are 2, it's 24, which means I have to try a close number. So I do it, 12 x 3, 36 is the closest, why do I know that is it?

Try the next one, 12 x 4= 84. The next one is more than what I have here, that's why I used 3 which gave 36, so 3 x 12 are 36 and then I do the subtraction, here I'm going to have to do it a loan, an exchange, a donation, asking for a donation from your neighbor, right, so here it will be 12 from 6 to 12, let's do it in red so you can see here, added a ten here, there are 6, 3 strips 3 are 0, ok , what do I do now? Then I have 0 to reduce, below 0.

Is 60 possible to divide by 12? It does, doesn't it? Then I would continue these contents here for me to discover.

So 12 x 4 = 48 now if I do 12 x 5 two 2 x 5 are 10 it goes up to 1. 5 x1= 5 with another 1= 6, exactly. 60 so here gives 5, 5 x 12 which are 60 then zero and zero below 0 here, so I ask you, will zero be enough to divide by 12?

How many times does 12 fit inside 0? It's 0 times. 0 x 12 are 0 and then you didn't even need to do that here, right people, I would already put the 0 directly in the quotient there, okay?

So my bill was 350, okay? Let's do the next one, but I have to delete these contents now, don't I? If you think I'm explaining this division here a little too quickly, you can go to the division of natural numbers class where I explained in detail how the division process is done, okay?

I'll leave the card here for you and you'll go back and watch it, okay? So come on, what happens here? 184 integers I want to divide by an integer and 25 hundredths, and now what do I do?

I look at the divisor here since it's integer here, right, the divisor has two decimal places, so it has to be multiplied by 100 which are two decimal places, because when I multiply an integer and 25 hundredths by 100/ what's going on happen with this number people? It will become 125 but here I must also multiply by 100, so it will be 18,400 divided by 125, right? Now let's analyze 184, you can divide it by 125, right?

How many times does it fit? Once the 125, once x 125= 125 let's go to our subtraction, here he will borrow 1 he gets 7, from 5 to 14 there are 9, right? 7 subtracts 2, there are 5 and here 0.

Now what do I need to do? Below this 0 that is here, it has now formed 590. 590 can be divided by 125, how many times is 125?

Let's do it here and then we delete it, 125 I don't know, let's try for how long? Why 3? Come on, 3 x 5 is 15 goes 1, 3 x 2= 6 with 1 = 7.

3x 1= 3, it will be 375. What if I do it for 4? 125 x 4 gave 500 if I try one more time it will give me 125 more it will pass then, so I have to try times 4.

4 x 125 gives me here, oops, confusing 4 in my head. It came to 500 and then I subtracted it, leaving 90. Now what?

I have one more 0 to lower here, 900, how many times can 900 be divided here? How many times does 125 go into 900? Then I would continue with my division calculations, 125 I know that if I do times 5 it gives 625, let's try to look at 8 to see how much it gives?

8 x 5 is 40 goes up 4, 8 x 2 is 16, 16 with four is 20, goes up 2, 8 x 1 = 8, 8 with 2 is 10 oh, it's a thousand gone so it has to be one less, so let's do it 125 x o 7. 7 x5= 35 rises to 3. 7 x 2= 14 with 3 = 17 rises to 1.

7 exchanges here he lent but then he kept 9 and here he got 10 units, right? So here is 5, here is 2, here is 0. And now there are 25 units left, can I divide 25 to 125?

No, but I will transform now this 25 in? That's right, 25 will form 250 tenths, so when I transform this here into tenths I have to put that comma because the next number here is now the tenth. So how many times, how many tenths times 225 is 250 tenths?

There are two times 125, 2 x 125 gives 250. Well, then the remainder is 0, just to shorten the path here, okay guys? So my quotient here is 147 integers and 2 tenths.

Let's do the next one, let's go. . .

but we have to delete it first. . .

what do I have to do here now? See that I mixed now the dividend is decimal and the divisor is also decimal. One decimal place in each one, how do I transform the dividend and divisor into integers?

How much? That's right, I multiply both by 10, right, because each one has a decimal place. So now it will be 143 by 65, right?

And then we're going to do the division. How many times does the 65 fit into the 143? There are 2 because 2 x 65 gives 130, okay, I already did it here, I thought quickly, so here there is 3 left, here there is 1 left and here there is 0 left.

And now 13 units can be divided to 65? No, right, what do I have to do? Transform these 13 units into 130 tenths, then when I transform them into tenths, my next digit here has to be tenths, so I add the comma, then it will be twice 2 x 65, that is, 2 tenths times 65 gives 130 tenths, and then I have remainder 0.

So, are you understanding this content well? So I'm going to do a few more examples so you can see the different possibilities for us to calculate with decimal numbers. Let's go?

Shall we do the next cases I brought then? Now I brought it, the dividend being a number with two decimal places, right, so it is 3 integers and 24 hundredths and the divisor one decimal place and then I have the dividend with three decimal places and the divisor with one decimal place and then here two numbers integers, that you will here will happen here, I will ask the question and you will answer it for me at the end. So let's go.

. . what now guys?

What am I going to do to transform the dividend and divisor into an integer? Because I divide with integers, right? So do you have an idea?

That's right, if I multiply by 10, this will be 18, right? Beauty. But now if I multiply this here by 10, what will I get?

The decimal point moves one place, it will be 32. 4, it will still be a decimal number, so it is not possible to multiply by 10 as I was unable to transform the two integers so I will multiply by 100, I will always look at that number if I divided the dividend and the divisor, whoever has the most decimal places then I multiply by that number, okay? So as there are two decimal places here I multiply them both by 100, because there are 2 zeros in 100.

So when I multiply 3. 24 by 100 it gives 324 and here it gives, it is by 100 here it skips one, two, 180 because when I multiply by 100, the decimal point moves two places to the right, right, she was here, she jumped one, two. And now I have the division of what?

From 324 by 180 let's proceed normally now. Let's make the arc here to form 324. How many times does 180 fit inside 324?

If I do 180 twice, 180 +180= 360 will pass, so it won't be possible to do it twice. So it only has to be 180=180 once, then we will do subtraction 4 here I will change 8 to 12 there are 4 and here 1, there are 144 units. Can I now divide 144 units into 180?

Of course not? What do I do? Then I go there and transform 144 units into 1,440 tenths, then what do I do?

Comma here in the quotient because what I have to multiply here is tenth now, isn't it? How many tenths times 180 will make 1,440? You already know?

What would I really have to do? I would have to do the multiplication, 180 times, I'm going to test a number, here I did it once, I don't know, if I do it 7 times, we'll try it seven times. 7 x 0= 0, 7 x 8= 56, goes up 5, 7 x 1= 7 with 5= 12.

1260 is close, will the next one be enough? 180 x 8. 8 I know here that my remainder will be zero.

So my quotient here is 1 whole and 8 tenths, okay? Here's the next one, oh I have here now one, two, three, and here I have one, how much do I Will I multiply to make the divisor and dividend whole numbers? If I multiply both, in red, by 10 what will happen?

This one stays in one piece, beauty. But this one will be 28. 08, it still won't be integer, so if I multiply it by 100, this one will be 280, it's still not enough, so I have to multiply it by a thousand because, oh, one, two, three.

I always look at the one that has more places after the decimal point, okay? So here it will be 2808 and here, how do I do it? I'm going to advance three places, the decimal point is here, it jumped one, two, three and I add 10 more, one, two , three for 1200, okay, and let's do the normal division now.

2880 can be divided by 1200, so how many times will it be here? Twice, very well, 2 x 1,200 will give 2400 and that leaves 0408 and then guys, can 408 units be divided by 1200? No, right, but you've already learned, I transform this here 408 units into 4080 tenths, then I add the decimal point to find who is the tenth here.

How many tenths times 1,200 is 4,080 or is it close to 4,080? It will be, let's do the math here so we can check this, 1200 x 3. 3 x 0=0, 3 x 0=0, 3 x 2= 6, 3 x 1= 3.

3,600 oh, because if I put 4 times 3600 + 1,200 will pass so I know it's 3 tenths here which will give 3,600 now that's 0. 8 and here I make that exchange with the neighbor and here it is 4 because out of 10 I take 6, 4 remains 0, and then people? Can you divide the 480 tenths that remained here into 1,200?

It's not possible then, I'm going to transform 480 tenths into 4,800 hundredths, the next number that I'm going to multiply here now in the quotient will be hundredths, how many hundredths times 1,200 from 4,800? You already know, right? Because if 3 times are 36, four times 1,200 will give 4,800 and here I will have a remainder of 0.

So my quotient is 2 integers and 34 hundredths, okay? And now that the last one, this one is different, it's a whole number with a whole number, which means I don't need to multiply by anyone there, right, not by 10, not by 100, not by 1000. Let's continue normally.

How many times is 3 from 25 or close to 25? There are 8 because 8 x 3 are 24, 24 leaves 1 and here 0. It gives one unit, can I divide one unit into 3?

No, what do I really do? Here, I transform this unit into 10 tenths and then there is the decimal point here, right, because the number will be tenths. How many tenths x 3 gives 10, is it close?

It's 3, 3 x 3 is 9, then I make the loans, oops, because I cut the 0, and there was 10 here from 1 and 0, I didn't even need to do it, right, again there's a tenth left now, so it's not possible to divide so I'm going to transform this one-tenth into 10 hundredths so now here are 3 again, 3 x 3 are 9 from 9 to 10 is 1, again I'm going to have to transform, so again from 3, 3 x3 gives 9. There we go Just by repeating this all the time, you could see that it is repeating here in the quotient in the decimal part 3333, which means that this number here will be infinitely repeating 3333, which means that this number here is one, you know the name, right? Okay, it's a recurring decimal, okay?

Why is it a recurring decimal? Because we have a repetition in the decimal part, a period formed here of 3333, so you can learn better about decimals there in the class where I explained about sets, not about sets, about periodic decimals, there's a class there, I'll leave it the card here for you so you can see more about recurring decimals. So when I have a recurring decimal, look instead of writing 3333 all the time, what can I do?

I put 8. 3 as the 3 is that digit that is repeating, I go there and put a dash over the three to indicate that there is a repetition, that is, the period is there. Because we call the number that is repeated there in the decimal period, so the period in this case here is 3, okay?

So here I brought one more curiosity for you to know what a periodic decimal means and that this type of result can also happen here in division with decimal numbers, okay guys? So I close the class with these several examples, several possibilities that I made to show you how to divide with decimal numbers and I hope you understood and enjoyed the class, okay? So don't forget to subscribe to the channel and give Gis a thumbs up and also watch the multiplication, addition and subtraction classes with decimal numbers in which I explained in detail to you the procedures for solving these operations, so until next time.

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