One of the most important steps in teaching children mathematical activities is learning the operation of subdividing prime numbers. How can I explain to the child, if it is possible to proceed before mastering the numbers by those?
In order to learn a child’s bottom, it’s necessary that, until the moment of learning, you have already mastered such mathematical operations, like adding, knowing, and also having a clear understanding of the day itself and the plurality of that bottom. Tobto wine is guilty of reason, scho rozpodil - tse podіl chogos on equal parts. It is also necessary to learn the multiplication operation and the multiplication table.
I have already written about those that these articles can become for you.
At this stage, it is necessary to formulate in the child an understanding of what he has broken - he has broken something on equal parts. The simplest way to teach a child is to encourage him to share a number of subjects between him and his friends and members of this family.
It is permissible to take 8 identical cubes and propagate the children to divide them into two equal parts - for her that other person. Vary and simplify the task, encourage the children to divide 8 cubes not into two, but into Chotiroh osib. Analyze the result at once. Change warehouses, try with a different number of objects and people, for which it is necessary to divide these objects.
Important: Keep in mind that the child’s head was operated on with a pair of objects, in order for the result to be the same number of parts. Tse appear korisnym at the offensive stage, if the child will need to understand what he did - this is an operation, which is a reverse multiplier.
Explain to the child that, in mathematics, diya, protilege to plural, is called "podіl". Using the multiplication table, demonstrate how to learn how to apply the relationship between multiplications and under.
Butt: 4x2 \u003d 8. Guess the child, the result of the multiplication is the addition of two numbers. Let me explain that the operation is a subdivision of the reverse operation of the multiplier and illustrate it exactly.
Divide the dobutok “8” from the butt - into any of the multipliers - “2” or “4”, and the result will always be another multiplier, which is not victorious in the operation.
It is also necessary to teach a young student, as the categories are called, how to describe the operation below - "delene", "divider" and "private". Show on the butt, how the numbers are divided, dilnik and private. Close up knowledge, stench is needed for further learning!
In fact, you need to learn the child of the multiplication table “navpak”, and remember it as well as the very good multiplier table, even if you need it, if you remember the instruction in the column.
Before the cob of employment, guess at once from the child, how the numbers are called in the process of the operation below. What is a "divider", "dilimim", "private"? Navchit bezpomilkovo that shvidko vyznachi tі category. Tse will be even more corny for the hour of learning the child under the prime numbers.
Let's divide 938 by 7. For someone else, 938 is worth it, 7 is a dilnik. The result will be more private, yoga requires virahuvati.
Krok 1. We write down the numbers, dividing them in a "kutochok".
Krok 2 Show the exact number of the divided and instruct you to choose the smallest number from them, as to appear greater for the dilnik. Three three numbers 9, 3 and 8, and the number will be 9. Ask the children to analyze how many times the number 7 can be in the number 9? That's right, less than once. First, let us write down the result as 1.
Krok 3 Let's move on to the design of the underside with a stovpchik:
Multiplying the timer 7x1 and subtracting 7. Subtracting the result is written under the first number of our divisible 938 and we see it, like a fiddle, in the column. Tobto from 9 we see 7 and we take 2.
Let's write down the result.
Krok 4. The number, like mi bachimo, is less than a dilnik, that needs to be increased. For whom it is ob'ednaemo yogo with the coming uncommon number of our share - it will be 3. We attribute 3 to the possessed number 2.
Krok 5. Dali diemo for the already known algorithm. Analyzing, how many times did our dilnik 7 avenge in the first number 23? That's right, three. The number 3 is fixed for the private one. And the result of creation - 21 (7 * 3) is written below under the number 23 at the top.
Krok.6 Now it has become impossible to know the rest of our private number. Vikoristovuyuchi already knows the algorithm, we continue to work on the calculation of the stompchik. By the way of seeing at the stovpchik (23-21) we will take the difference. She's dear 2.
We have lost one number - 8. We have lost one number - 8. We will take it away from the result in the number 2, we will take it - 28.
Krok.7 Analyzing, how many times did our dilnik 7 avenge in a limited number? That's right, 4 times. Write down the digit from the result. Otzhe, mi otrimane in the result under the stovpchik chastkovo = 134.
Golovna, through which the rich schoolchildren blame the problem with mathematics - it’s not necessary to work simply arithmetic problems. And on this basis all mathematics in post school. Especially often the problem itself is in multiples and roses.
In order for a child to learn how to quickly and accurately carry out rozrahunka in the mind - the correct method of learning and fixing the habit is necessary. For whom we are glad to get popular on this day's helpers for the acquisition of newcomers to the bottom. Some are designated for children with fathers, others for independent work.
Naygolovnіshim, if you teach a child to the bottom in a stovpchik, then it is mastered by the algorithm, like, in a slander, to forgive me.
As a child, he kindly operates with a multiplication table and a “turning” rozpodil, he does not have any difficulties. It’s important for the prote to train the otrimana newcomer. Don't be fooled by what you can achieve, as you can only understand that the child has grasped the essence of the method.
In order to easily learn the child's operation, it is necessary to do the following:
So that children were satisfied with mathematics, it was necessary to arouse their interest in mathematics and mathematical activities, as a learning hour, and in other situations.
Therefore, you want to develop caution in a child, draw analogies with mathematical exercises (operations on the rahunok and podil, analysis of the “part-cile” well) for an hour of construction, Igor and watch for nature.
Vikladach, child development center specialist
Friends of Olena
site specially for the project
Video story for the fathers, how to correctly explain the child to the stovpchik:
The division of natural numbers, especially rich-valued ones, is carried out by hand using a special method, which takes away the name rozpodіl stovpchik (at the stoupchik). You can also use the name rolled up. It is especially significant that the stump can be carried out as a subdivision of natural numbers without an excess, so it is possible to subdivide natural numbers with an excess.
At this article, we’ll sort it out, how to beat it with a stump. Here we will talk about the rules for recording, and about all the promiscuous billing. The back of the hand is scribbled on the rozpodіl_ stovpchik rich-valued natural number on a single-digit number. Let's note the name of the sound on the vipades, if it is divided and dilnik є with rich natural numbers. The whole theory of statistics can be characteristically applied under the column of natural numbers with report explanations of the course of the decision and illustrations.
Navigation on the side.
It is better to remember the rules for recording dilnik, dilnik, all intermediate tabs and results when the natural numbers are divided by the columnist. Let's just say that the letter was scribbled with a hand-stitch on paper with a carded line - so there is less chance of getting out of the necessary row of that stovptsya.
On the back, in one row, the left hand is written down for the date and time, after which the symbol of the mind is displayed between the recorded numbers. For example, if we dilimate the number 6105, and the dilnik is 55, then the correct entry when you put it in the column will be like this:
Marvel at the approaching scheme, which illustrates the space for recording a detailed, dilnik, private, excess and intermediate calculation when rozpodil stovpchik.
From the suggested scheme, it is clear what is more private, what is joking (otherwise it is not more private when it is redundant) will be written below the dilnik under horizontal rice. And promizhnі calculation will be carried out lower than the dilemma, and it is necessary for a long time to fight about the place on the side. If so, follow the rule: the greater the difference in the number of characters in the records of the diary and dilnik, the more space is needed. For example, when the natural number 614 808 is divided by 51 234 (614 808 is a six-digit number, 51 234 is a five-digit number, the difference in the number of characters in the records is 6-5 = 1) and if the numbers are divided 8 058 and 4 (here the difference is in the number of signs 4-1 = 3). To confirm our words, we conclude the entries under the column of these natural numbers:
Now you can go straight to the process of subdividing the natural numbers with a step.
It was clear that it is easy to add one unambiguous natural number to another one, and there are no reasons to add a single number to a table. Prote bude korisno vіdpratsyuvati pochatkovі navichka under stovpchik tsikh simple butts.
butt.
Let us need to give us a stump 8 by 2.
Solution.
Obviously, we can vikonati filed for an additional table of multiplication and immediately wrote down evidence 8:2=4.
Ale us tsіkavit, as vikonati rozpodіl tsikh numbers stovpchik.
First of all, write down section 8 and section 2 in this way, so that the method means:
Now we are starting to z'yasovuvati, how many times a dilnik to take revenge on a dilemma. For which mi we successively multiply the dilnik by the numbers 0 , 1 , 2 , 3 , ... until the moment when the result is not subtracted by a number that is more equal to the dilemma (otherwise the number is larger, lower is added, it may be too much). If we take a number that is dearer to the dilemma, then we immediately write down the dilemma, and on the place of the private we write down the number, on which we multiply the dilnik. If we take a larger number, a lower distance, then under the dilnik we write down the number, calculated on the redundant croc, but in the place of the private private, the number is recorded, multiplying the dilnik on the redundant croc.
Let's go: 2 0 = 0; 2 1 = 2; 2 2 = 4; 2 3 = 6; 2 4 = 8 . We took away the number that is dearer to the dilemma, we write down the yogo pіd dilimim, but in the private space we write down the number 4. With this record, on the alert of an offensive sight:
Having left the final stage under single-valued natural numbers with a stump. Under the number, we write down the dilemma, it is necessary to draw a horizontal boundary, and to draw the number of numbers over the boundary line in such a way as to be afraid when looking at natural numbers with a stump. The number that is taken after the date will be too much in the future. As if it were equal to zero, the weekend numbers were divided without excess.
Our butt is acceptable
Now it is possible to complete the entry with the number 8 by 2. Mi Bachimo, that part 8:2 is good 4 (and extra good 0).
Suggestion:
8:2=4 .
Now let's look at how it looks like it was ripped off with a stump of single-digit natural numbers from too much.
butt.
Divided with a stand 7 by 3.
Solution.
At the cob stage, the record looks like this:
Let's start z'yasovuvati, how many times a dilnik avenges a dilny. Let's multiply 3 by 0, 1, 2, 3 and so on. until that moment, until we take away the number that is more expensive or more, lower division 7. Taken 3 0 = 0<7
; 3·1=3<7
; 3·2=6<7
; 3·3=9>7 (for consumption, turn up to the same ratio of natural numbers). Under dilimim, the number 6 is written down (it is taken away on the redundant cut), and on the place of the private private, the number 2 is written down (multiplication was carried out on the new cut).
Lost to spend the day, and rozpodil single-digit natural numbers 7 and 3 will be completed.
In this rank, not exactly privately more expensive 2 and too much more expensive 1.
Suggestion:
7:3 = 2 (sound 1).
Now you can go to the bottom of the stack of rich-valued natural numbers of single-valued natural numbers.
Let's take a look podіlu stovpchik algorithm. At the skin yoga stage, we induce the results that, when a rich-valued natural number 140288 is subdivided, on a single-valued natural number 4 . This butt of rebuke is unviable, shards for yoga vyshtovkhnemosya with usima possible nuances, it is possible to report them.
On the back of our mind we marveled at the pershu left-handed figure in the record of the underlined. If the number that is designated by the number is larger than the dilnik, then in the next paragraph we will have to practice with this number. If the number is smaller, lower, then we need to add to the sight the next number in the record of the divided one, and correct the number, which is indicated by the two numbers that are being looked at. For clarity, we see a number in our record, with which we will work.
The first digit in the entry of the detailed 140288 is the number 1. The number 1 is less, lower dіlnik 4, marveling at the coming angry figure in the record of the divided one. With whom, the number 14 is possible, with which we have a chance to practice far away. You can see the same number in the record of the divided.
The coming points from another to the fourth are repeated cyclically until the division of natural numbers with a step is completed.
At the same time, it is necessary for us to determine how many times the dilnik is to be avenged in number, for which it is practicable (for the sake of clarity, the number like x is significant). For which one, we multiply the dilnik by 0, 1, 2, 3, ... until the moment when the number x is taken away, or the number is greater, lower than x. If the number x comes out, then we write it down with a visible number according to the rules of writing, scoring when we look at the natural numbers with a stand. The number, which was multiplied on the yak, is written on the private space during the first pass to the algorithm (with advancing passes 2-4 points in the algorithm, the number is written to the right of the numbers that are already there). If a number comes out that is greater than the number x, then under the seen number the number is written down, taken away on the redundant croc, and on the private space (or the right number, which is already known) the number is written, on the yak the multiplication was carried out on the redundant croc. (Similar exercises were carried out in two stocks, taken apart).
Multiply dilnik 4 by the numbers 0, 1, 2, ..., the docks do not take away the number, as long as 14 or more than 14. May 4 0 = 0<14
, 4·1=4<14
, 4·2=8<14
, 4·3=12<14
, 4·4=16>14 . So, as the number 16 was subtracted on the remaining cut, if it was greater, lower than 14, then under the seen number the number 12 was written down, as it appeared on the front cut, and on the private space the number 3 was written down, to that in the front paragraph the multiplication was carried out on the new one.
At the next stage, from the seen number, we see the number with the stamp, stashed under it. Under the horizontal line, the result of the observation is recorded. However, if the result of the observation is zero, then it is not necessary to write it down (as only the observation in the same paragraph is not the rest of the day, so I will finish the process again with a stompchik). Right there, for our control, we will not take the result of the review with the dilnik and reconcile, which is lesser for the dilnik. On another occasion, a pardon was allowed here.
We need to take the number 12 as a stepper from the number 14 (for the correctness of the record, do not forget to put a minus sign for the numbers that are seen). After the completion of the tsієї dії under the horizontal boundary, the number 2 appeared. Now we are reviewing our calculation, poring over the number from the dilnik. Since the number 2 is less than the number 4, then you can calmly move to the next point.
Now, under the horizontal drawing, the right-hander in the numbers (otherwise, the right-hander in the mist, de mi did not begin to write down zero), we write down the number, I put it in the same column in the record of the dilemma. If there are no numbers in the record of the divided in the column, then it ends with the column on the column. The next number that is visible, which has disappeared under the horizontal rice, is taken as a working number, and repeated with it from 2 to 4 points to the algorithm.
Under the horizontal drawing, right-handed, in the already obvious number 2, we write down the number 0, but the number 0 itself is in the record 140 288 in the other column. In this order, under the horizontal boundary, the number 20 is established.
The whole number 20 is visible, accepted as a working number, and repeated with it for another, third and fourth points in the algorithm.
Multiply dilnik 4 by 0 , 1 , 2 , ..., we take the number 20 and the number, like more, lower 20 . May 4 0 = 0<20
, 4·1=4<20
, 4·2=8<20
, 4·3=12<20
, 4·4=16<20
, 4·5=20
. Так как мы получили число, равное числу 20
, то записываем его под отмеченным числом, а на месте частного, справа от уже имеющегося там числа 3
записываем число 5
(на него производилось умножение).
We carry out v_dn_mannya with a stovpchik. Since we can see equal natural numbers, then because of the accuracy of seeing equal natural numbers, the result will take zero. Zero is not written down (the shards are not yet the final step under the stompchik), but remember the place, on which mi yogo could be written (for clarity, the place is marked with a black rectangle).
Under the horizontal line, right-handed, in the memory of the month, we write down the number 2, the shards itself will be found in the record of the detailed 140288 in this column. In this order, under the horizontal boundary, we can have the number 2.
The number 2 is taken as a working number, it is considered yogo and we once again happen to be vikonati dії z 2-4 points in the algorithm.
Multiply the dilnik by 0, 1, 2 and so on, and equalize the numbers that come out, with the designated number 2. May 4 0 = 0<2
, 4·1=4>2. Later, under the designated number, the number 0 is written (it was taken away on the handed-over croc), but in the private right-handed space, the number 0 is written already explicit there (for 0, we multiplied on the handed croc).
Vіkonuєmo vіdnіmannya stovpchik, otrimuєmo number 2 under the horizontal boundary. We re-verify ourselves, poring over the number from the dilnik 4. so yak 2<4
, то можно спокойно двигаться дальше.
Under the horizontal boundary, right-handed, in the number 2, add the number 8 (the shards will be in this column in the entry of the divided 140 288). In this order, under the horizontal line, the number 28 appears.
We accept the same number as a worker, it is considered yoga, and we repeat 2-4 points.
Here, the everyday problems are not to blame, because you were respected up to that moment. Vykonavshi all the necessary things, come out the offensive result.
It was not enough for the rest to carry out parts of points 2, 3, 4 (we hope you are), after which the picture was completed under the natural numbers 140 288 and 4 at the point:
Respect that the number 0 is written in the bottom row. Yakbi tse buv not the last crochet under the stovpchik (tobto, yakbi in the record of the divided in the columns the right-hander was left with numbers), then they didn’t write down zeros b.
In this manner, marveling at the completed recording of the rose of the richly significant natural number 140288 on the single-digit natural number 4, we would like to keep the private number 35072 (and the excess of the rose was added to zero, the wine is in the bottom row).
Zvichayno well, with the distribution of natural numbers, you will not be able to report all your actions. Your decisions will look approximately the same as those of lower butts.
butt.
Vikoite rozpodіl stovpchik, yakshcho dіlene dіvnyuє 7136, and dіlnik є unambiguously natural number 9 .
Solution.
At the first stage of the algorithm, when subsuming natural numbers, we take a note of the form
After the second, third and fourth paragraphs of the algorithm, write down the next step, I’ll look
Repeating the cycle, matimemo
One more passer gives us a finished picture under the natural numbers 7136 and 9
In this rank, it is not privately more expensive 792 and the surplus is rozpodіlu more expensive 8 .
Suggestion:
7 136: 9 = 792 (zup. 8) .
And I'm demonstrating this butt, as if I could look at the butt.
butt.
Divide the natural number 7042035 by a unique natural number 7 .
Solution.
The most handy vikonati gave a stump. 
Suggestion:
7 042 035:7=1 006 005 .
Let's hurry up to please you: if you have well acquired the algorithm under the heading from the front paragraph of the article, then you can still win put a stack of rich-valued natural numbers. That's right, the chips from stages 2 to 4 of the algorithm are left unchanged, and the first paragraph is only slightly changed.
At the first stage, if you add richly-valued natural numbers to the table, you need to marvel not at the first left-handed figure in the record of the extended one, but at such a number, how many symbols, in the record of the dilnik. If the number, which is indicated by these numbers, is larger than the date of the visitor, then at the next point we will have to practice with this number. Even if the number is smaller, lower time, then we need to add to the sight the left hand figure at the entry of the extended one. After that, they are counted as assigned to 2, 3 and 4 points of the algorithm until the final result is taken away.
It was no longer enough to marvel at the algorithm for substantiating rich-valued natural numbers with a practical application.
butt.
Vikonaёmo podіl stovpchik rich-valued natural numbers 5562 and 206 .
Solution.
So, as in the record of dilnik 206 take part 3 signs, then we marvel at the first 3 digits of evil in the record 5562. Qi digits correspond to the number 556. Since 556 is larger, lower is 206, then the number 556 is accepted as a working, apparently yogo, and we pass to the next stage of the algorithm.
Now we multiply the dilnik 206 by the numbers 0, 1, 2, 3, ... until the moment when the number is taken away, like more 556, or more, lower 556. Maєmo (it’s possible to count the multiplication smoothly, it’s better to count the multiplication of natural numbers with a stop): 20 6 0=0<556
, 206·1=206<556
, 206·2=412<556
, 206·3=618>556 . We subtracted the number, as if it was greater than the number 556, under the seen number the number 412 was written (it was taken away on the front end), but in the private space the number 2 was written down (the number of the new one was multiplied on the front end). A note under the foot of the step looks forward:
Vikonuemo vіdnіmannya stovpchik. We will take the difference 144 if the number is less than the dilnik, so you can calmly continue to win the necessary days.
Under the horizontal line, right-handed, in the presence of a real number there, we write down the number 2, so that it is in the record to be divided 5,562 in which column:
Now mi pratsyuemo with the number 1442, we see it, and we pass the point from the other one a quarter more times.
We multiply the dilnik 206 by 0, 1, 2, 3, ... until the number 1442 is taken away, or the number, like more, below 1442. Let's go: 206 0 \u003d 0<1 442
, 206·1=206<1 442
, 206·2=412<1 332
, 206·3=618<1 442
, 206·4=824<1 442
, 206·5=1 030<1 442
, 206·6=1 236<1 442
, 206·7=1 442
. Таким образом, под отмеченным числом записываем 1 442
, а на месте частного правее уже имеющегося там числа записываем 7
:
It is carried out by the stepper, we take away zero, but it’s not possible to write it down again, but it’s better to remember the position, so we don’t know which one ends on the other, which happens to repeat the algorithm once again:
Now we can’t remember that we can’t write down the same number in the horizontal line between the right, for the forgotten position, because there are no digits in the record of the divided one in the column. Otzhe, on which rozpodіl stovpchik completed, and we complete the record:
Training aids and simulators in the online store "Integral" for grade 4
Helper to assistant M.I. Moro Posіbnik to assistant L.G. Peterson
1) During the three-month season, 15 football games were held. How many games are played equally, how many football matches are played in a month?
2) Mike was on the beach for five days and knew 20 turtles. I plan to give all my mushls in the equal world to my friends. How many turtles take off their skins?
3) Sem pratsyuvav 25 years stretching the rest of five days. Pripuskayuchi, scho vіn pratsyuvav equal for a few years a leather day, like a long vіn pratsyuvav today?
4) The restaurant sold 35 salads last year. How many salads were sold to the average person today?
5) Mike, Nancy and Sari have a total of 15 hums. Like the gums are divided equally, how many skins are cut off the skin of a person?
6) Maria May 30 black sacks. Do you want to give a gift of six friends?
7) Sarah keeps 50 cents from her bank. How many cents does Sari have?
8) Let's go to the meeting with Dan and Mike. Zagalny rahunok becoming 24 dollars. The stench virіshili equally split the rahunok, how many people pay the skin of the people?
9) Fred fish with Den. Pong catch ten trout. If it stinks to cut trout, then how can you cut the skin?
10) Keith has 25 dollars in five dollar bills. How many dollars cost 5 dollars from a new one?
11) William wants to divide the peanut collection into groups of 61 persons. William has 305 mountains. How many groups will be created?
12) The class has 14 students and 14 credits. How can credits be shared equally among scientists, how many skin caregivers?
13) The class has 28 students and 1316 blocks. How can the blocks be distributed equally among the scientists, how many skin cues?
14) The class has 53 students and 371 blocks. How many blocks are divided between students, how many blocks are taken from each student?
15) Jose's set of olives has 1426 olives. If the olives are divided into 23 groups, then how big is the skin group?
16) Can you buy skils of zashitiv for 14 rubles for 84 rubles?
17) Harvest of apples becoming 81 kg. How many boxes are needed to lay out an apple, so that one box can cover 9 kg?
18) A car to transport 7 tons of air per 1 flight. How many flights do you need to work to transport 140 tons of dog?
19) From the warehouse to the store, you need to transport 176 kg of zukra. How many bags are needed for transporting zucru, so how can 8 kg of zucru be placed in a teddy bear?
20) 14 kg of cement is required per square meter. For how many square meters to stick 126 kg of cement?
21) A farmer harvests cabbage and cibules. Cabbage vin zibrav 10 455 kg, and cibuli 123 times less. How many kg of cibules for choosing a farmer?
22) Three lads divided the number 26668 by 59. The first one had 457, the other - 452, and the third - 251. Is this correct?
23) For the winter, the farmer prepared 2720 kg of compound feed for sheep. 85 kg were harvested for the skin. How many sheep does the farmer have?
24) 13 beds of carrots were planted near the school garden. 5863 kg of carrots were selected for Usyi Bulo. How many kg of carrots were taken from the skin beds?
1. Write down the tasks of the speech at the sight of numerical verses and rozv'yazhi їх.
1.1. Divide the number 72 by the number 8.
1.2. Divide the number 81 by 9.
1.3. Divide the number 62 by the number 21.
2. Find out the length of the numbers.
1. Wikonay rozpodіl.
4. Complete the table.
| c | 221 | 167 | 820 | 114 | 438 | 880 | 196 |
| c+40 | ... | ... | ... | ... | ... | ... | ... |
| d | 553 | 557 | 541 | 545 | 565 | 533 | 561 |
| d+68 | ... | ... | ... | ... | ... | ... | ... |
| Vikonai filed that reverb. | ||||||||||||||||
| 24: 3 = | 447: 3 = | 450: 5 = | 146: 2 = | |||||||||||||
| 189: 3 = | 297: 3 = | 400: 5 = | 75: 1 = | |||||||||||||
| 804: 3 = | 165: 1 = | 108: 1 = | 410: 5 = | |||||||||||||
| 242: 1 = | 505: 5 = | 72: 1 = | 728: 7 = | |||||||||||||
| 231: 3 = | 565: 5 = | 720: 9 = | 390: 5 = | |||||||||||||
| 29: 1 = | 238: 2 = | 220: 2 = | 246: 3 = | |||||||||||||
| 536: 2 = | 258: 3 = | 736: 8 = | 360: 5 = | |||||||||||||
| 390: 2 = | 880: 5 = | 550: 5 = | 510: 5 = | |||||||||||||
| 111: 1 = | 96: 4 = | 686: 7 = | 204: 2 = | |||||||||||||
| 180: 1 = | 310: 5 = | 368: 4 = | 198: 2 = | |||||||||||||
| 567: 3 = | 54: 2 = | 425: 5 = | 160: 2 = | |||||||||||||
| 87: 3 = | 510: 5 = | 684: 9 = | 420: 5 = | |||||||||||||
Date: ________________ PIB: _________________________________ Rating: _________ |
||||||||||||||||
| Vikonai filed that reverb. | ||||||||||||||||
| 93: 3 = | 276: 2 = | 372: 4 = | 380: 5 = | |||||||||||||
| 26: 1 = | 276: 3 = | 570: 6 = | 395: 5 = | |||||||||||||
| 211: 1 = | 572: 4 = | 424: 4 = | 546: 6 = | |||||||||||||
| 352: 2 = | 552: 4 = | 595: 7 = | 594: 6 = | |||||||||||||
| 423: 3 = | 552: 3 = | 408: 4 = | 679: 7 = | |||||||||||||
| 290: 2 = | 660: 5 = | 846: 9 = | 330: 3 = | |||||||||||||
| 614: 2 = | 20: 2 = | 545: 5 = | 832: 8 = | |||||||||||||
| 984: 3 = | 298: 2 = | 246: 3 = | 602: 7 = | |||||||||||||
| 156: 1 = | 336: 4 = | 783: 9 = | 220: 2 = | |||||||||||||
| 46: 2 = | 570: 3 = | 616: 8 = | 364: 4 = | |||||||||||||
| 230: 1 = | 424: 4 = | 445: 5 = | 435: 5 = | |||||||||||||
| 747: 3 = | 352: 2 = | 279: 3 = | 623: 7 = | |||||||||||||
Rozpodil is one of the most basic mathematical operations (adding, adding, multiplying). Podіl, like those other operations are important in mathematics, and in everyday life. For example, if you are a class (person 25) give a penny and buy a present from the reader, but you don’t spend everything, you will lose your reshta. So the axis of the task you will need to share on all. The robot is starting an operation on the way, as it will help you to complete the task.
Podil - cіkava operation, why do we change with you in this article!
Otzhe, not a lot of theory, and then practice! What did you do? Rozpodіl - tse breaking on equal parts of chogos. Tobto, you can put a package of tsukerok, which you need to break into even parts. For example, a bag has 9 zuceroks, and a person, if you want to take them, has three. Then you need to add 9 zuceroks for three osib.
It is written down like this: 9:3, it will be the number 3. So I subdivided the number 9 to the number 3, showing the number of numbers three, which can be found in the number 9. 3 * 3 = 9. Right? Absolutely.
Otzhe, let's look at the butt of 12:6. The back is meaningfully named for the skin component of the butt. 12 - dilene, tobto. a number that is divided into parts. 6 - dilnik, tse number of parts, where to divide more sub-lene. And the result will be a number that I can call "private".
Divide 12 by 6, depending on the number 2. You can change the solution by multiplying: 2 * 6 = 12. Come out, that the number 6 is missed 2 times by the number 12.
What did it take too much? He himself rose, only as a result, the number does not come out equal, as shown above.
For example, let's add 17 to 5. If the largest number that can be divided by 5 to 17 is 15, then it will be 3 plus 2, and it will be written like this: 17:5=3(2).
For example, 22:7. So the maximum number is indicated by itself, which is divided by 7 to 22. The whole number is 21. It will be the same: 3 + 1 extra.
A private way to split the number would be split by the number 3 and the number 9. If you want to know whether the number extends by 3 or 9 without excess, you need:
Find the sum of the digits of the subdivision.
Divide by 3 or 9 (depending on what you need).
If you want to go out without too much, then the number will be shared without too much.
For example, the number is 18. The sum of the digits is 1+8 = 9. The sum of the digits is the same as 3, i is 9. The number 18:9=2, 18:3=6. Podіleno without excess.
For example, the number is 63. The sum of the digits 6 + 3 = 9. Divide like by 9, so by 3. 63:9=7, and 63:3=21. on 3 chi 9, chi nі.
Plurality and rozpodіl - tse protilezhnі one to one operation. The plural can be twisted like a reversal of the split, and the split is like a reversal of the plural. You can learn more about multiplication and learn the operation from our article about multiplication. The yakіy report describes the plurality of yak correctly vikonuvati. In the same place you will know the multiplication table and apply it for training.
Let's put the butt of the re-verification under that plural. Acceptable, given the butt 6 * 4. Matching: 24. Then, reversing the bottom line: 24: 4 = 6, 24: 6 = 4. Correctly spelled. In this case, the re-verification is carried out by means of a rozpodіlu vіdpovіdі on one of the multiples.
But a butt was given for 56:8. Verification: 7. Then reverification will be 8 * 7 = 56. Correct? So. At times, the re-verification is carried out by the way of multiple revisions.
In the third class, it’s less likely to start over and get down. To this, the third-graders are violating the simplest tasks:
Head 1. The practitioner at the factory was given the task of distributing 56 pieces of 8 packs. Do you need to put how many bags in the leather package, so that the same quantity in the skin will come out?
Manager 2. On the eve of the new fate at school, children in the class, who learns 15 specialties, saw 75 tsukerok. How many tsukerok can take away a skin child?
Manager 3. Roma, Sasha and Mishko took 27 apples from the apple tree. How many skins do we cut apples, so it is necessary to add them at the same time?
Head office 4. Chotiri friends bought 58 ovens. And then we realized that we could not share them equally. How many lads do you need to buy an oven, shobi leather otrimav 15 pieces?
Podіl in the fourth class - serious, lower in the third. Mustaches are carried out by way of a rozpodіlu in stovpchik, and the numbers, like taking a fate from the rozpodіlі, are not small. What did the stovpchik do? You can find out the evidence below:
What did the stovpchik do? This way allows you to shukati at the vіdpovіd rozpodіl great numbers. Like simple numbers like 16 and 4, you can add it, and you can understand - 4. That 512:8 in the mind is not easy for a child. And raspovisti about the technique of executing similar applications is our task.
Let's look at the butt 512:8.
1 crochet. Let's write down the date and time as follows:
Private will be written down under the divider, and rozrahunki under dilimim.
2 crochet. Pochinaemo zliva to the right. We take the number 5 on the back: 
3 croc. The number 5 is less than the number 8, and it means not to give up. So we take one more digit of the subdivision:
Now 51 more for 8. More private.
4 croc. We put a speck under the dilnik.
5 croc. After 51, the number 2 is worth more, so the second one will have one more number, that is. private is a two-digit number. We put a point to a friend:
6 croc. Let's start the operation. The largest number, the distance without excess by 8 to 51 - 48. Adding 48 by 8, we take 6. Record the number 6 instead of the first point of the dilnik:
7 croc. Then we write down the number exactly under the number 51 and put the sign "-":
8 croc. Potim za 51 vіdnimaєmo 48 i otrimuєmo vіdpovіd 3.
* 9 krok*. Enter the number 2 and write down the order from the number 3:
10 krok The number 32, which happened, is divisible by 8 and takes the other figure of the same - 4.
Otzhe, vіdpovіd 64, without excess. The yakbes divided the number 513, then the surplus would be alone.
Rozpodіl three-digit numbers vykonuєtsya method rozpodіlu on stovpchik, which Bulo explained from the butt above. An example of a three-digit number.
Podіl drobіv negarazd smoothly, as if it were given. For example, (2/3): (1/4). The method of such a subdivision is simple. 2/3 - dilene, 1/4 - dilnik. You can replace the rozpodіlu sign (:) with a plural ( ), it is necessary to commemorate the numeral and banner of the divider with the help of the missions. Tobto otrimuєmo: (2/3)(4/1), (2/3) * 4, the whole one - 8/3 or 2 numbers and 2/3. Let's aim a butt, with an illustration for the best understanding. Let's look at the fractions (4/7): (2/5):
Like in the front butt, turn over dilnik 2/5 and take 5/2, replacing it with a plural. Take only (4/7) * (5/2). Probably short and fast: 10/7, then we blame the whole part: 1 number and 3/7.
Let's imagine the number 148 951 784 296, and let's add three digits each: 148 951 784 296. Also, right-handed: 296 - class of one, 784 - class of thousands, 951 - class of millions, 148 - class of millions. In his line, in the skin class, three digits may have their own rank. The right-hander is poured: the first digit is one, the other digit is tens, the third is hundreds. For example, the class of ones is 296, 6 is ones, 9 is tens, 2 is hundreds.
The division of natural numbers is the simplest division, described in this article. It can be like a surplus, so without a surplus. A dilnik and a dilemma can be a shot, a whole number. 
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Presentation is another way to show the topic below. Below you will know the strength for an excellent presentation, in a kind of goodness it is explained how to share, what it was like, what it was like a dilnik, dilnik and privately. Do not spend an hour for nothing, but consolidate your knowledge!
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Rozpodіl rich-valued numbers easier to win with a stompchik. Podіl stovpchik і also called rolled up.
Before that, as if rozpochati vykonanny under the stovpchik, we will reportly look at the very form of the record under the stovpchik. On the back of the hand, we write down the distance and right-handed, we put the vertical boundary between:
Behind the vertical boundary, on the contrary, a sub-division, we write a dilnik and under it, a horizontal boundary is drawn:
Under horizontal rice, step by step, you will write down more privately, what will appear in the result and calculate:
Under the dilemma, the following charges will be recorded:
I will repeat the form of the entry under the column looking like this:
Let's say we need to divide 780 by 12, write down the division in the column and proceed to the bottom:
Rozpodіl stovpchik vykonuєtsya step by step. First, what is necessary for us to work, to designate an inconsequential subdivision. We marvel at the first number of the subdivision:
the whole number is 7, so it’s less than the dilnik, then we can’t almost hit the new one, it’s also necessary to take one digit from the dilny, the number 78 is bigger than the dilnik, so we start to hit the new one:
Our vipad will have the number 78 inaccurate dilimim It is called incomprehensible to that which is only a part of dilemma.
If we signify an incomprehensible division, we can recognize how many digits will be in private, for which we need to worry, how many digits have been lost in a dilemma after an incomprehensible dilemma, in our dilemma there is only one digit - 0, which means that privately add up to 2 digits.
Having recognized the number of numbers that can be found in private, you can put specks on this space. Even when the number of digits was completed, the number of numbers turned out to be greater or less, a dot was indicated below, it means that a pardon was allowed here:
Let's get down to the bottom. We need to assign the number of times 12 to be in the number 78. For whom we successively multiply the dilnik on the natural numbers 1, 2, 3, ..., until we see the number as close as possible to the uneven subdivided abo equal to you, but do not exceed it. In this rank, we take the number 6, write it down, and from 78 (according to the rules of the stovpchik) we can see 72 (12 6 \u003d 72). After that, as we saw 72 out of 78, we have a surplus of 6:
To give respect, that the excess of the rozpodіlu will show us that we have chosen the number correctly. If it’s too much money for a dilnik, or more for a new one, then we didn’t choose the number correctly and we need to take a bigger number.
To the excess, which is 6, the number of the divisible will come - 0. As a result, the number of the divisible will come - 60. It seems that the number of times 12 is offset in the number 60. We take the number 5, write it down in private after the numbers 6, but 6 0 is visible 60 12 5 = 60). The leftover wiish has zero:
So, as in dilimo, there were no more numbers left, so 780 was divided into 12 nationalities. As a result, we knew privately under the stompchik - it was written down under the dilnik:
Let's look at the butt, like a private one has zeros. Let's say we need to divide 9027 by 9.
It is visible inconsistently - the whole number 9. It is written in private 1 and 9 it is visible 9. The excess is zero. Ring out, as if the intermediate billings have a surplus of zero, you can’t write it down:
I’m going to come forward with the number of the sublime - 0. Guess what, when you spread zero, the number will be zero. Zero is recorded in private (0: 9 = 0) and 0 is visible in intermediate counts from 0. Sound, so as not to pile up intermediate counts, do not write counts with zero:
I’m going to come forward with the number of dilemma - 2. In the middle calculations, it turned out that the same division (2) is smaller, lower (9). At this point, it’s private to write down zero and enter the next figure of the dilemma:
Apparently, the number of times 9 is omitted in the number 27. We take the number 3, write it down in private, and from 27 we see 27. The excess is zero:
Since the dilemma had no more digits, the number 9027 was divided into 9 nationalities:
Let's look at the butt, if the length ends with zeros. Let us need to add 3000 to 6.
It is visible inconsistently - the whole number is 30. It is written in private 5 and 30, it is visible 30. The excess is zero. As it was assigned, zero in the excess in the intermediate calculations is recorded neob'yazkovo:
I’ll come forward with the number of the divisible - 0. So, if the number is zero, the number will be zero, it will be written in private zero and in the intermediate calculations from 0 we can see 0:
I’ll take the number of the divisible - 0. We’ll write down one more zero in private and in the intermediate billings from 0 we’ll see 0. in the very end, count the number and write it down in order to show that you have nailed it natally:
So, as in dilimo there were no more numbers left, it means that 3000 was divided into 6 nationalities:
Give us the need to divide 1340 by 23.
It is shown that the difference is not the same - the number 134. It is recorded in private 5 and 134, it is visible 115. The excess was 19:
We’ll come up with the number of the divisible - 0. It’s obvious that the number of times 23 is taken in the number 190. We take the number 8, write it down in private, and from 190 we see 184. Take away the excess 6:
So, as the dilemma didn’t have any more numbers, he ended up. As a result, it turned out to be more private 58 and more 6:
1340: 23 = 58 (surplus 6)
It was left to look at the butt of the podіlu іz surplus, if the distance is less than the dilnik. Let us need to divide 3 by 10. If only 10 is never missed in the number 3, then it is written in 0 and 3 we see 0 (10 0 = 0). Conducted horizontally between and recorded excess - 3:
3: 10 = 0 (surplus 3)
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