Hi guys, welcome to my channel! I'm Gis and today I'm going to teach you division with natural numbers! Do you have questions and want to learn?
So come with me! Hi guys, so today we're going to study division with natural numbers, but before starting the class I'm going to make that request for you, you already know, subscribe to my channel and give Gis a thumbs up? Now let's go to class.
So, people, when you are going to perform a division calculation, it is very important for you to know the names of the terms. That's right, look, when I have a division that I set up the division account, we should know then that the number I put here is called the dividend, the number I put here is called the divisor. Now pay close attention, this is called a divisor, the result of my division is called a quotient, so this one would be our result.
Good and what's left is called the remainder, it can be zero or different from zero. So look here, for example, if I give you the division of 84 / 4, what do you know? You know that this 84 is not our dividend, and this four is our divisor, the value that the result of this division will give here is the quotient, for you to remember, and the amount that will be left over is called rest, okay!
And another thing is also very important that after you finish your division account you do the following analysis, you are going to do a real test to validate your answer. So look here if you then do your conscious multiplied by your divisor, conscious multiplied by the divisor and, added with the remainder, conscious times divisor added with the remainder, you will have to give the value of the dividend, that's right, then, this one here it is a validation that you have that your division is correct or not, ok. Now let's move on to the examples, let's go!
Well people, so here I brought you the examples, but before doing these examples I need you to know the meaning of the idea of division. What does it mean to perform a division? Carrying out a division means distributing, distributing a quantity, splitting a quantity, but all these things I do: distributing, distributing, dividing, is always dividing into equal parts, so remember this well when carrying out your divisions, I always share equally.
So what I brought here for you today 72 / 6, it means that I need to take 72 candies and divide them among 6 people, so remember that the amount of candies that each person will receive must be the same as the other one will receive ok . So let's go to the division algorithm. I should think what then?
How many times does the divisor 6 fit in 72? So when I start to carry out a division I start with the ten, because I have tens and ones, I'll start here. So how many times does that 6 fit inside the 7?
Is it possible to do that? How many times does the divisor 6 fit inside the 7? Once isn't it?
Because 1 times 6 is 6, so here I do that subtraction. So from 7 I take 6 left 1 for me. Alright, I still haven't finished the division, what do I need to do?
I need to lower this digit 2. So I'm going to lower the 2, then he added it here with the 1 and formed 12. And now I should think 12, can I divide it by 6?
Think about how many times the 6 fits in the 12? Think of the 6 times table, do you have the answer 12 or a number close to 12? You've thought and found out you have it, haven't you?
In the 6 times table if I do 2 times 6 it's 12. So here I have 00. What happened here?
We did a division of 72 by 6 and I got 12 and remainder 0. If the remainder was 0, then what do I have here? It means I have an exact division, because our remainder was 0.
Let's move on to division two. Look here, I have 1332 / 9. What do I need to think about now?
If I take it then I have it there in the unit, tens, hundreds and units of thousands. I'm always going to start here on the left, if I take 1 can I take 1 / 9 or can I think the 9 fits inside the 1? It doesn't fit, so what do I have to do?
I'm going to make a little arch here and I'm going to form 13, I put the two digits together, so I have 13. Now let 's think about whether it is possible to put 9 inside 13 or is it possible to take 13 and distribute it to 9 people? Now it's possible so how many times does this 9 fit inside the 13?
Do you know? Fits 1 time, 1 x 9 is 9, because what would happen if I put 9 twice, how many are 2 x 9 are 18 and then it would go beyond this initial quantity that I have here. So that's why I put it only once and now here I do the subtraction.
I'm going to have to change 9 to 13, that's 4 and 0. Well, now, what do I do? I have a 3 digit to download here.
So I lowered the 3, it made 43, now we have to think about the 9 times table, how many times does the 9 give 43 or is it close to 43? So you go there and think about the multiplication table. Oh!
I know that 2 x 9 is 18 and then it would pass from this initial value that I have here, 3 x 9 is 27, 4 x 9 is 36, 5 x 9 is 45, it will pass then, I went back to putting 4 x here 9 which is 36, so 4 x 9 is 36 then I do the subtraction, so here I will have to change it will be six for 13 is seven and here it is 0. Then look here, I have one more digit 2 to lower here, so now I have 72 so I'm going to think how many times the name fits inside 72, continuing the nine times table, 5 x 9 is 45 will it be more? If I do 6 x 9?
6 x 9 is 54, that's enough, let's try one more. 7 x 9 is 63, so the 7 x 9 is already close! Let's try one more.
8 x 9 is 72, so if I do 8 x 9 I have 72 here is 0 here is 0. So once again I found division with remainder 0, that means I have an exact division as well. Ok and in this division just to remember the name,, 1332 is called a dividend, 9 is the divisor, 148 is the quotient which is the result of the division and here zero is our remainder.
Okay, now if you want to validate your answer to see if it's ok, what should you do anyway? Well then take the 148 and multiply it by 9 right? quotient times divisor 9 x 8 72, 9 x 4 is 36, 36 with seven is 43, 9 x 1, 9 with 4, 13 then I add the remainder 0, I have 1332.
And who is this 1332? Is it not the dividend? So that means I did the division correctly ok!
Now let's move on to the next examples. Come on! So here we go to the next examples.
So look what I brought: 735 / 21, now what am I going to think / So remember that it always starts here on the left. So I should think is it possible to take 7 candies and divide them into 21 people in full? It's not right, only if you go there and cut the bullet, but I want to divide it in an integer way, that's why I'm working with natural numbers.
Then I saw that 7 is not possible to divide for 21 people. So now I make that little arch here, it turned into 73 and now it's possible to take 73 candies and divide them among 21 people. Does it work now?
Now it's going to work, because if I think 21 fits inside 73, but now how am I going to find out how many times 21 fits in 73 you're going to do the multiplication. So we do the math on the side. 21x.
You go by trial and error. Do you have a more or less idea? Ah, I'll put 2 Gis!
Will it work for 2 ? Let's try 2 x 1 is 2, 2 x 2 is 4, look, it's 42. So if I do it twice the 21 goes to 42, could it be that if I put 1 more time I put 3?
21 multiplied by three. 3 x 1 is 3. 3 x 2 is 6.
Look , it's 63, it's close. What if I put 1a plus? If I did 21 x 4 it would be 4 and 2 x 4 would be 8, it was 84, it went from 73 so I can't use this one and I won't even use this one.
So I'm going to use 3, because 3 x 21 is 63. So I saw the 3 x 21 is 63. Now let's do the subtraction, 3 take 3 gives 0, 7 take 6 gives 1.
Okay, what do I do now? ? Don't have the number 5 to download here?
Below the number 5 then formed the number 105, right now procedure, I need to find out how many times the 21 fits inside the 105. What do I do? Well, I already know here that 21 x 4 is 84, could it be that if I did the 21 x 5 now, which would be our next one?
5 x 1 equals 5, 5 x 2 equals 10. Look here, it worked just fine! It means that if I take 5 x 21 it will be 105 and here it will be 000.
So our quotient is 35 and the remainder is 0. So I have an exact division again. So I have an exact division here, because our remainder was 0 ok.
Very well and, remembering that if you want to validate your division answer, what exactly should you do? Take the quotient and multiply it by the divisor and add it to your remainder. This has to result in an ok dividend value!
Folks, so now, we're going to move on to the next example, our next division. So look here what I have 3780 divided into 35. If I take this 3 it is possible to divide 3 bullets to 35 people, of equal parts?
It is not! No way! So I'm going to have to make a little arch here, and form the number 37, I joined the two digits and formed 37!
Now does 35 fit inside this 37? It fits, right? How many times does it fit?
1 time only! So I'm going to do 1x 35 = 35, now I do the subtraction calculation 7 taking 5 gives 2, 3 takes 3 = 03. And now what should I do anyway?
Look, there are numbers to download, so now I'm going to lower the 8, now I've formed 28, the number 28 and, then I ask you: is it possible to divide 28 balls for 35 people? Isn't it right? Because if I do that what will happen?
Each person will have 0 bullets, because 0 x 35 is zero, so it's still 28 bullets for me. I didn't do the division because each one would end up with zero, now I have the next number to download which is 8, the 0 sorry, then it made 280. Then what happens!
I have to find out how many times 280 goes into 35. So let's do our multiplication. I'll try then times 5?
5 x 5 equals 25 goes up 2, 5 x 3 equals 15, 17 look is much more than five, let's try the 35 x 6 then, 5 x 6 gives 30, 6 x 3 gives 18, 21. Look, it's still 210. What else can I try: 35 x 7, 5 x 5 is 35, goes up 3, 5 x 3 is 21, 24 is not yet!
Let's try the next 35 x 8. 8x 5 is 40. 8x 3 is 24 with 4 which goes up 28, so it's just right.
So I have 8 times 8 x 35 is 280. Here subtract with the remainder 0. So once again I found exact division!
Guys , pay attention to something, pay attention to this 0 here that was placed, because even if it was placed, remember right when I lowered this 8 here what happened / Formed 28 then 28 cannot divide 35 people so what the person would receive 0 bullets, because it was not possible to do in 0 x 35 it gave 0. I explained it this way because it is very common for students to carry out this division here oh, so he does the whole process 3780 I divided it by 35, so put there 1 time there was 2 left, then he dropped eight, then what did he do? 28 / 35.
He saw that it didn't work, what is he doing here? The student goes and simply lowers 10, which is here, he forms 280, he goes there and puts 8, then he does the subtraction, he finds the remainder 0. Then I ask you, look here, it gives 18, if I validate my answer 18 x 35 it won't give 3780 ok so be very smart with that, so here I had to add that 0, because when I lowered the 8, that 8 together with that 2 formed 28 and it wasn't enough to divide by 35.
So that's why that I put 0, that each child would know 0 bullets. Very well! It makes a good point that it is very common for the student to make a mistake in this type of account when the value formed here after I lower the rest is still smaller than its divisor ok!
So we move on to the next example. Come on! So we move on to our last example of the day!
Look, I brought you 238/18. How am I supposed to start a division? I must take the digit here on the left.
In this case, there are hundreds. If I take this 2 can I divide it for 18 people in equal parts? No, so I have to do the join.
I make that little arch and form 23. So now I'm going to take 23 candies and divide them among 18 people, is it possible now to carry out this division? Is it possible for 18 to fit inside 23?
It's possible! So how many times does it fit? Look , it 's easy here, just 1 time.
Because if I do it 2 times, it will go over this value 23. Look here, if I do 18 x 2, 2 x 8 gives 16, 2 x 1 gives 2, one two three, look, it gives 36 if I do it twice, so that's why that I start with a 1 which is enough. Well, now here we're going to do the subtraction, just remembering here that I'm going to take 8 out of 3, it won't be possible for me to do that , right, because 3 is smaller, so I'll have to make a change.
So here was 1 and here I passed 1 and there was 13 and now out of 13 I take 8 left over 5, 1 taking 1 is 0. Okay, what do I do now? Now I have the number 8 to lower here, it made 58, let's find out how many times 18 goes into 58?
So let's do 18 x 2 I already know it's 36, let's do it times 3, 3 x 8 is 24, 3 x 1 is 3 with 2 which goes up 5. 54, because if I do it now, look here, 18 x 4, 4 x 8 is 32, 4 x 1 is 4, 7 passes what I need so I'm going to use 18x 3. So it means that 18 fits 3 times in 58, which is 54, now 8 out of 8 I take 4 is 14 left over 0.
What happened here now we, different from those others? Do you have any more numbers to download? No, so what happened here?
I had a division now that had a remainder of 4, so I had a non-exact division here, then a non-exact division happened, because my remainder did not give 0, so I keep these bullets, you know, I can't divide 238 by 18, there will always be a little bit left over here, there were 13 candies for each child, but this one I keep back in the jar, there are 4 left over, I don't give it to anyone anymore ok. So here is an example of non-exact division. Alright people!
Remembering that you can validate your answer. You take your 13, let's remember, which is your quotient and multiply it by the divisor, it's going to be 8 x 3 24, 8 x 1 is 8, 10 then it's going to be 1 x 3 is 3, 1 x1 is 1, it's going to be 4 , 3 and 2 is 234, what do I need to do right now? Add my remainder, my remainder was 4, 234 here from 8, 3 and 2, look what happened.
I multiplied my quotient by the divisor, added my remainder, what did I get here? Who is this guy right here? It's the dividend, right people!
So that was our class today, I hope you understood this division content, which is very important, you learn it now and you use it until you manage to pass the entrance exam, or pass the Enem, or if you don't pass the Enem , college entrance exam, you'll use it for the rest of your life, right, because we're not going to use a calculator, we're always going to use our minds, right? So I hope you enjoyed it, understood it and I want you to rock your tests! Happy studying and until the next class!
