Unfortunately, the modern educational program does not always involve explaining each topic to students, especially such a complex one as division by a column. In such cases, parents themselves have to deal with students at home.

Step-by-step instruction for learning to divide by a column

First you need to determine the basis of the child: repeat with him the names of the division elements (divisible, divisor, quotient, remainder), digits of the number and the multiplication table. Without this knowledge, the child will not be able to master the division. First you need to show the operation on simple examples from the multiplication table, that is, 56: 7 = 8. Next, show an example of dividing a three-digit number without a remainder, when the first digit of the dividend is greater than the divisor, for example, 422: 2. It is necessary to divide each digit in order by the divisor as follows: 4 divided by 2 will be 2, we write down, 2 by 2 is 1, we write, 2 by 2 is again one, we write down. The result is 211. The result must be rechecked by inverse multiplication.

In the business of learning to divide by a column, practice and repetition of each stage is necessary. Pick up a few more of the same simple operations, for example, 936 divided by 3, 488 divided by 4, etc. Comment on your actions each time in the same way, so that they are imprinted in the child’s head, and he repeats them to himself when dividing:

• We take the first digit of the number, divide it by the divisor. How many times can a divisor be in a dividend?
• If the first digit is less than the divisor, we take the number from the first two digits, divide, and write the result.
• We multiply the divisor by the quotient and subtract from the dividend, sign the result of the subtraction.
• We demolish the next digit of the dividend: can it be divided by a divisor? If not, then we demolish one more digit and divide, write down the result.
• We multiply the last digit of the quotient by the divisor and subtract from the remaining dividend. We get the rest.

On an example, it looks like this: we divide 563 by 11. 5 cannot be divided by 11, we take 56. 11 can fit 5 times in 56, we write it in a quotient. 5 multiplied by 11 is 55. 56 minus 55 will be 1. 1 cannot be divided by 11, we demolish 3. In 13 11 will fit only 1 time, we write it down. 1 multiplied by 11 will be 11, subtract from 13, it turns out 2. Answer: quotient 51, remainder 2.

It is very important that the child correctly signs the result of subtraction and demolishes the numbers, and each digit of the quotient is always determined only by the selection of numbers. Work with your child regularly, but not for very long: gradually he will fill his hand and will click on such tasks as nuts.

You will need:

Basics of mathematics

First, make sure your child has mastered the simpler operations: addition, subtraction, multiplication. Without these basics, it will be difficult for him to understand the division.

If you see any gaps in knowledge, then repeat the previous material.

Division principle

Before proceeding with the explanation of the division algorithm, the child should form an understanding of the process itself.

Explain to the little student that "division" is the division of a single whole into equal parts.

Take a box of pencils that will act as a single whole (you can take any items - cubes, matches, apples, etc.), and invite the child to divide them equally between you and yourself. Then, ask him to count how many pencils were originally in the box and how many he distributed to each.

As the child understands, increase the number of items and the number of participants. Further, it should be noted that it is not always possible to divide equally and some items remain "no man's". For example, offer to divide 9 pears between grandma, grandpa, dad and mom. The child must learn that everyone will receive 2 pears, and one will be in the balance.

Relationship with the multiplication table

Show your child that "dividing" is the opposite of "multiplying".

• Take the multiplication table and show the student the relationship between the two operations.
• For example, 4x5=20. Remind your child that the number 20 is the product of two numbers 4 and 5.
• Then, visually show that division is the opposite process: 20/5=4, 20/4=5.

Pay attention to the child that the correct answer will always be a factor that is not involved in the division.

• Explore other examples.

If your child knows the multiplication table perfectly, and understands the relationship between two mathematical operations, he will easily master division. Whether to memorize it in reverse order is your choice.

Definition of concepts

Before starting classes, identify and learn the names of the elements that are involved in the division process.

"Dividend" is the number to be divided.

"Divider" - This is the number by which the "dividend" is divided.

"Private" is the result that we get in the process of calculation.

For clarity, you can give an example:

For your son/daughter's birthday, you bought 96 candies for the child to treat to his friends. Total invitees - 8.

Explain that the bag of 96 candies is "dividable". Eight children - "divider". And the number of sweets that each child will receive is “private”.

Algorithm for division into a column without a remainder

Now show the child the calculation algorithm using an example about sweets.

• Take a blank sheet of paper/notebook and write the numbers 96 and 8.
• Separate them with perpendicular lines.

• Show the elements clearly.
• Point out that the result of the calculation is written under the "divisor", and the calculations - under the "dividend".
• Invite a young student to look at the number 96 and determine the number that is greater than 8.
• Of the two numbers 9 and 6, this number will be 9.
• Ask the child how many digits 8 can "fit" in 9. The kid, remembering the multiplication table, will easily determine that only once. Therefore, write the number 1 under the underscore.
• Next, multiply the divisor 8 by the result 1. Write the resulting figure 8 under the first digit of the divisible number.
• Between them, put a "subtraction" sign, and sum up. That is, if you subtract 8 from 9, you get 1. Write down the result.

At this point, explain to your child that the result of a subtraction should always be less than the divisor. If it turned out the other way around, then the baby incorrectly determined how many 8 are contained in 9.

• Ask the child again to determine the number that is greater than the divisor 8. As you can see, the number 1 is less than 8. Therefore, we should combine it with the next digit of the divisible number - 6.
• Add 6 to one and get 16.
• Next, ask the kid how many 8 are in 16. Add the correct answer 2 to the first.

• Multiply 8 by 2 again. Write the result under the number 16.
• By "subtracting" (16-16) we get 0, which means that our calculation result is 12.

Let's first consider the simple cases of division, when the quotient is a single-digit number.

Let's find the value of the private numbers 265 and 53.

To make it easier to pick up the private number, we divide 265 not by 53, but by 50. To do this, we divide 265 by 10, it will be 26 (remainder 5). And we divide 26 by 5, it will be 5. The number 5 cannot be immediately written in private, since this is a trial number. First you need to check if it fits. Let's multiply . We see that the number 5 came up. And now we can record it in private.

The value of the private numbers 265 and 53 is 5. Sometimes, when dividing, the trial digit of the private does not fit, and then it needs to be changed.

Let's find the value of the private numbers 184 and 23.

The quotient will be a single digit.

To make it easier to pick up the private number, we divide 184 not by 23, but by 20. To do this, we divide 184 by 10, it will be 18 (remainder 4). And we divide 18 by 2, it will be 9. 9 is a trial number, we won’t write it in private right away, but we’ll check if it fits. Let's multiply . And 207 is greater than 184. We see that the number 9 does not fit. The quotient will be less than 9. Let's see if the number 8 is suitable. Multiply . We see that the number 8 is suitable. We can record it privately.

The value of the private numbers 184 and 23 is 8.

Let's consider more difficult cases of division. Find the value of the private numbers 768 and 24.

The first incomplete dividend is 76 tens. So, there will be 2 digits in the quotient.

Let's determine the first digit of the quotient. Divide 76 by 24. To make it easier to find the quotient, we divide 76 not by 24, but by 20. That is, you need to divide 76 by 10, there will be 7 (remainder 6). Divide 7 by 2 to get 3 (remainder 1). 3 is the trial digit of the quotient. Let's check if it fits first. Let's multiply . . The remainder is less than the divisor. This means that the number 3 has come up and now we can write it down in place of tens of quotients.

Let's continue the division. The next incomplete dividend is 48 units. Let's divide 48 by 24. To make it easier to find the private number, we divide 48 not by 24, but by 20. That is, we divide 48 by 10, there will be 4 (remainder 8). And 4 divided by 2 will be 2. This is a trial digit of the private. We must first check if it will fit. Let's multiply . We see that the number 2 has come up and, therefore, we can write it down in place of the units of the quotient.

The value of the private numbers 768 and 24 is 32.

Let's find the value of the private numbers 15 344 and 56.

The first incomplete dividend is 153 hundreds, which means that there will be three digits in the private.

Let's determine the first digit of the quotient. Let's divide 153 by 56. To make it easier to pick up the private number, we divide 153 not by 56, but by 50. To do this, we divide 153 by 10, there will be 15 (remainder 3). And 15 divided by 5 will be 3. 3 is the trial digit of the quotient. Remember: you cannot immediately write it in private, but you must first check whether it fits. Let's multiply . And 168 is greater than 153. So, in the quotient it will be less than 3. Let's check if the number 2 is suitable. Multiply. BUT . The remainder is less than the divisor, which means that the number 2 is suitable, it can be written in place of hundreds in the quotient.

We form the following incomplete dividend. That's 414 tens. Let's divide 414 by 56. To make it more convenient to choose the quotient figure, we will divide 414 not by 56, but by 50. . . Remember: 8 is a trial number. Let's check it out. . And 448 is greater than 414, which means that in the quotient it will be less than 8. Let's check if the number 7 is suitable. Multiply 56 by 7, we get 392. . The remainder is less than the divisor. So, the number came up and in the quotient in place of tens we can write 7.

Let's continue the division. The next incomplete dividend is 224 units. Divide 224 by 56. To make it easier to pick up the quotient, divide 224 by 50. That is, first by 10, it will be 22 (remainder 4). And 22 divided by 5 will be 4 (remainder 2). 4 is a trial number, let's check if it works. . And we see that the figure has come up. We write 4 in place of units in the quotient.

The value of the private numbers 15 344 and 56 - 274.

Today we learned to divide in writing by a two-digit number.

Bibliography

1. Mathematics. Textbook for 4 cells. early school At 2 o'clock / M.I. Moro, M.A. Bantova - M.: Enlightenment, 2010.
2. Uzorova O.V., Nefedova E.A. Great math book. 4th grade. - M.: 2013. - 256 p.
3. Mathematics: textbook. for the 4th class. general education institutions with Russian. lang. learning. At 2 p.m. Part 1 / T.M. Chebotarevskaya, V.L. Drozd, A.A. joiner; per. with white lang. L.A. Bondareva. - 3rd ed., revised. - Minsk: Nar. asveta, 2008. - 134 p.: ill.
4. Mathematics. 4th grade. Textbook. At 2 p.m./Heidman B.P. and others - 2010. - 120 p., 128 p.

1. ppt4web.ru ().
2. Myshared.ru ().
3. Viki.rdf.ru ​​().

Homework

Perform division

The division into a column is an integral part of the educational material of a younger student. Further progress in mathematics will depend on how correctly he learns to perform this action.

How to properly prepare a child for the perception of new material?

Column division is a complex process that requires certain knowledge from the child. To perform division, you need to know and be able to quickly subtract, add, multiply. Knowledge of the digits of numbers is also important.

Each of these actions should be brought to automatism. The child should not think for a long time, and also be able to subtract, add not only the numbers of the first ten, but within a hundred in a few seconds.

It is important to form the correct concept of division as a mathematical operation. Even when studying the multiplication and division tables, the child must clearly understand that the dividend is the number that will be divided into equal parts, the divisor indicates how many parts the number needs to be divided into, the quotient is the answer itself.

How to explain the algorithm of mathematical action step by step?

Each mathematical action implies strict adherence to a certain algorithm. The long division examples should be done in this order:

1. Writing an example in a corner, while the places of the dividend and divisor must be strictly observed. To help the child not get confused in the first stages, we can say that we write a larger number on the left, and a smaller number on the right.
2. Allocate a part for the first division. It must be divided by the dividend with a remainder.
3. Using the multiplication table, we determine how many times the divisor can fit in the selected part. It is important to indicate to the child that the answer should not exceed 9.
4. Multiply the resulting number by the divisor and write it on the left side of the corner.
5. Next, you need to find the difference between the part of the dividend and the resulting product.
6. The resulting number is written under the line and the next bit number is taken down. Such actions are performed until the period until the remainder remains 0.

A good example for students and parents

The division into a column can be clearly explained with this example.

1. 2 numbers are written in a column: the dividend is 536 and the divisor is 4.
2. The first part for division must be divisible by 4 and the quotient must be less than 9. The number 5 is suitable for this.
3. 4 fit in 5 only 1 time, so we write 1 in the answer, and 4 under 5.
4. Next, subtraction is performed: 4 is subtracted from 5 and 1 is written under the line.
5. The next bit number - 3 - is demolished to one. In thirteen (13) - 4 will fit 3 times. 4x3 \u003d 12. Twelve is written under the 13th, and 3 - in private, as the next bit number.
6. 12 is subtracted from 13, 1 is obtained in the answer. The next bit number is again demolished - 6.
7. 16 is again divided by 4. In response, write 4, and in the division column - 16, draw a line and 0 in the difference.

By solving the stacking problems with your child several times, you can achieve success in completing tasks quickly in high school.

The division of natural numbers, especially multi-valued ones, is conveniently carried out by a special method, which is called division by a column (in a column). You can also see the name corner division. Immediately, we note that the column can be carried out both division of natural numbers without a remainder, and division of natural numbers with a remainder.

In this article, we will understand how division by a column is performed. Here we will talk about the writing rules, and about all intermediate calculations. First, let us dwell on the division of a multi-valued natural number by a single-digit number by a column. After that, we will focus on cases where both the dividend and the divisor are multi-valued natural numbers. The whole theory of this article is provided with characteristic examples of division by a column of natural numbers with detailed explanations of the solution and illustrations.

Page navigation.

Rules for recording when dividing by a column

Let's start by studying the rules for writing the dividend, divisor, all intermediate calculations and results when dividing natural numbers by a column. Let's say right away that it is most convenient to divide in a column in writing on paper with a checkered line - so there is less chance of going astray from the desired row and column.

First, the dividend and the divisor are written in one line from left to right, after which a symbol of the form is displayed between the written numbers. For example, if the dividend is the number 6 105, and the divisor is 5 5, then their correct notation when divided into a column will be:

Look at the following diagram, which illustrates the places for writing the dividend, divisor, quotient, remainder, and intermediate calculations when dividing by a column.

It can be seen from the above diagram that the desired quotient (or incomplete quotient when dividing with a remainder) will be written below the divisor under the horizontal line. And intermediate calculations will be carried out below the dividend, and you need to take care of the availability of space on the page in advance. In this case, one should be guided by the rule: the greater the difference in the number of characters in the entries of the dividend and divisor, the more space is required. For example, when dividing a natural number 614,808 by 51,234 by a column (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), intermediate calculations will require less space than when dividing numbers 8 058 and 4 (here the difference in the number of characters is 4−1=3 ). To confirm our words, we present the completed records of division by a column of these natural numbers:

Now you can go directly to the process of dividing natural numbers by a column.

Division by a column of a natural number by a single-digit natural number, division algorithm by a column

It is clear that dividing one single-digit natural number by another is quite simple, and there is no reason to divide these numbers into a column. However, it will be useful to practice the initial skills of division by a column on these simple examples.

Example.

Let us need to divide by a column 8 by 2.

Decision.

Of course, we can perform division using the multiplication table, and immediately write down the answer 8:2=4.

But we are interested in how to divide these numbers by a column.

First, we write the dividend 8 and the divisor 2 as required by the method:

Now we start to figure out how many times the divisor is in the dividend. To do this, we successively multiply the divisor by the numbers 0, 1, 2, 3, ... until the result is a number equal to the dividend (or a number greater than the dividend, if there is a division with a remainder). If we get a number equal to the dividend, then we immediately write it under the dividend, and in place of the private we write the number by which we multiplied the divisor. If we get a number greater than the divisible, then under the divisor we write the number calculated at the penultimate step, and in place of the incomplete quotient we write the number by which the divisor was multiplied at the penultimate step.

Let's go: 2 0=0 ; 2 1=2; 2 2=4 ; 2 3=6 ; 2 4=8 . We got a number equal to the dividend, so we write it under the dividend, and in place of the private we write the number 4. The record will then look like this:

The final stage of dividing single-digit natural numbers by a column remains. Under the number written under the dividend, you need to draw a horizontal line, and subtract numbers above this line in the same way as it is done when subtracting natural numbers with a column. The number obtained after subtraction will be the remainder of the division. If it is equal to zero, then the original numbers are divided without a remainder.

In our example, we get

Now we have a finished record of division by a column of the number 8 by 2. We see that the quotient 8:2 is 4 (and the remainder is 0 ).

Answer:

8:2=4 .

Now consider how the division by a column of single-digit natural numbers with a remainder is carried out.

Example.

Divide by a column 7 by 3.

Decision.

At the initial stage, the entry looks like this:

We begin to find out how many times the dividend contains a divisor. We will multiply 3 by 0, 1, 2, 3, etc. until we get a number equal to or greater than the dividend 7. We get 3 0=0<7 ; 3·1=3<7 ; 3·2=6<7 ; 3·3=9>7 (if necessary, refer to the article comparison of natural numbers). Under the dividend we write the number 6 (it was obtained at the penultimate step), and in place of the incomplete quotient we write the number 2 (multiplication was carried out on it at the penultimate step).

It remains to carry out the subtraction, and the division by a column of single-digit natural numbers 7 and 3 will be completed.

So the partial quotient is 2 , and the remainder is 1 .

Answer:

7:3=2 (rest. 1) .

Now we can move on to dividing multi-valued natural numbers by single-digit natural numbers by a column.

Now we will analyze column division algorithm. At each stage, we will present the results obtained by dividing the many-valued natural number 140 288 by the single-valued natural number 4 . This example was not chosen by chance, since when solving it, we will encounter all possible nuances, we will be able to analyze them in detail.

First, we look at the first digit from the left in the dividend entry. If the number defined by this figure is greater than the divisor, then in the next paragraph we have to work with this number. If this number is less than the divisor, then we need to add the next digit to the left in the dividend record, and work further with the number determined by the two digits in question. For convenience, we select in our record the number with which we will work.

The first digit from the left in the dividend 140,288 is the number 1. The number 1 is less than the divisor 4, so we also look at the next digit on the left in the dividend record. At the same time, we see the number 14, with which we have to work further. We select this number in the notation of the dividend.

The following points from the second to the fourth are repeated cyclically until the division of natural numbers by a column is completed.

Now we need to determine how many times the divisor is contained in the number we are working with (for convenience, let's denote this number as x ). To do this, we successively multiply the divisor by 0, 1, 2, 3, ... until we get the number x or a number greater than x. When a number x is obtained, then we write it under the selected number according to the notation rules used when subtracting by a column of natural numbers. The number by which the multiplication was carried out is written in place of the quotient during the first pass of the algorithm (during subsequent passes of 2-4 points of the algorithm, this number is written to the right of the numbers already there). When a number is obtained that is greater than the number x, then under the selected number we write the number obtained at the penultimate step, and in place of the quotient (or to the right of the numbers already there) we write the number by which the multiplication was carried out at the penultimate step. (We carried out similar actions in the two examples discussed above).

We multiply the divisor of 4 by the numbers 0 , 1 , 2 , ... until we get a number that is equal to 14 or greater than 14 . We have 4 0=0<14 , 4·1=4<14 , 4·2=8<14 , 4·3=12<14 , 4·4=16>fourteen . Since at the last step we got the number 16, which is greater than 14, then under the selected number we write the number 12, which turned out at the penultimate step, and in place of the quotient we write the number 3, since in the penultimate paragraph the multiplication was carried out precisely on it.


At this stage, from the selected number, subtract the number below it in a column. Below the horizontal line is the result of the subtraction. However, if the result of the subtraction is zero, then it does not need to be written down (unless the subtraction at this point is the very last action that completely completes the division by a column). Here, for your control, it will not be superfluous to compare the result of subtraction with the divisor and make sure that it is less than the divisor. Otherwise, a mistake has been made somewhere.

We need to subtract the number 12 from the number 14 in a column (for the correct notation, you must not forget to put a minus sign to the left of the subtracted numbers). After the completion of this action, the number 2 appeared under the horizontal line. Now we check our calculations by comparing the resulting number with a divisor. Since the number 2 is less than the divisor 4, you can safely move on to the next item.


Now, under the horizontal line to the right of the numbers located there (or to the right of the place where we did not write zero), we write down the number located in the same column in the record of the dividend. If there are no numbers in the record of the dividend in this column, then the division by a column ends here. After that, we select the number formed under the horizontal line, take it as a working number, and repeat with it from 2 to 4 points of the algorithm.

Under the horizontal line to the right of the number 2 already there, we write the number 0, since it is the number 0 that is in the record of the dividend 140 288 in this column. Thus, the number 20 is formed under the horizontal line.


We select this number 20, take it as a working number, and repeat the actions of the second, third and fourth points of the algorithm with it.

We multiply the divisor of 4 by 0 , 1 , 2 , ... until we get the number 20 or a number that is greater than 20 . We have 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 subtraction by a column. Since we subtract equal natural numbers, then, due to the property of subtracting equal natural numbers, we get zero as a result. We do not write zero (since this is not the final stage of dividing by a column), but we remember the place where we could write it down (for convenience, we will mark this place with a black rectangle).


Under the horizontal line to the right of the memorized place, we write down the number 2, since it is she who is in the record of the dividend 140 288 in this column. Thus, under the horizontal line we have the number 2 .


We take the number 2 as a working number, mark it, and once again we will have to perform the steps from 2-4 points of the algorithm.

We multiply the divisor by 0 , 1 , 2 and so on, and compare the resulting numbers with the marked number 2 . We have 4 0=0<2 , 4·1=4>2. Therefore, under the marked number, we write the number 0 (it was obtained at the penultimate step), and in place of the quotient to the right of the number already there, we write the number 0 (we multiplied by 0 at the penultimate step).


We perform subtraction by a column, we get the number 2 under the horizontal line. We check ourselves by comparing the resulting number with the divisor 4 . Since 2<4 , то можно спокойно двигаться дальше.


Under the horizontal line to the right of the number 2, we add the number 8 (since it is in this column in the record of the dividend 140 288). Thus, under the horizontal line is the number 28.


We accept this number as a worker, mark it, and repeat steps 2-4 of paragraphs.

There shouldn't be any problems here if you've been careful up to now. Having done all the necessary actions, the following result is obtained.

It remains for the last time to carry out the actions from points 2, 3, 4 (we provide it to you), after which you will get a complete picture of dividing natural numbers 140 288 and 4 in a column:

Please note that the number 0 is written at the very bottom of the line. If this were not the last step of dividing by a column (that is, if there were numbers in the columns on the right in the record of the dividend), then we would not write this zero.

Thus, looking at the completed record of dividing the multi-digit natural number 140 288 by the single-valued natural number 4, we see that the number 35 072 is private (and the remainder of the division is zero, it is in the very bottom line).

Of course, when dividing natural numbers by a column, you will not describe all your actions in such detail. Your solutions will look something like the following examples.

Example.

Perform long division if the dividend is 7136 and the divisor is a single natural number 9.

Decision.

At the first step of the algorithm for dividing natural numbers by a column, we get a record of the form

After performing the actions from the second, third and fourth points of the algorithm, the record of division by a column will take the form

Repeating the cycle, we will have

One more pass will give us a complete picture of division by a column of natural numbers 7 136 and 9

Thus, the partial quotient is 792 , and the remainder of the division is 8 .

Answer:

7 136:9=792 (rest 8) .

And this example demonstrates how long division should look like.

Example.

Divide the natural number 7 042 035 by the single digit natural number 7 .

Decision.

It is most convenient to perform division by a column.

Answer:

7 042 035:7=1 006 005 .

Division by a column of multivalued natural numbers

We hasten to please you: if you have well mastered the algorithm for dividing by a column from the previous paragraph of this article, then you already almost know how to perform division by a column of multivalued natural numbers. This is true, since steps 2 to 4 of the algorithm remain unchanged, and only minor changes appear in the first step.

At the first stage of dividing into a column of multi-valued natural numbers, you need to look not at the first digit on the left in the dividend entry, but at as many of them as there are digits in the divisor entry. If the number defined by these numbers is greater than the divisor, then in the next paragraph we have to work with this number. If this number is less than the divisor, then we need to add to the consideration the next digit on the left in the record of the dividend. After that, the actions indicated in paragraphs 2, 3 and 4 of the algorithm are performed until the final result is obtained.

It remains only to see the application of the algorithm for dividing by a column of multi-valued natural numbers in practice when solving examples.

Example.

Let's perform division by a column of multivalued natural numbers 5562 and 206.

Decision.

Since 3 characters are involved in the record of the divisor 206, we look at the first 3 digits on the left in the record of the dividend 5 562. These numbers correspond to the number 556. Since 556 is greater than the divisor 206, we take the number 556 as a working one, select it, and proceed to the next stage of the algorithm.

Now we multiply the divisor 206 by the numbers 0 , 1 , 2 , 3 , ... until we get a number that is either equal to 556 or greater than 556 . We have (if the multiplication is difficult, then it is better to perform the multiplication of natural numbers in a column): 206 0=0<556 , 206·1=206<556 , 206·2=412<556 , 206·3=618>556 . Since we got a number that is greater than 556, then under the selected number we write the number 412 (it was obtained at the penultimate step), and in place of the quotient we write the number 2 (since it was multiplied at the penultimate step). The column division entry takes the following form:

Perform column subtraction. We get the difference 144, this number is less than the divisor, so you can safely continue to perform the required actions.

Under the horizontal line to the right of the number available there, we write the number 2, since it is in the record of the dividend 5 562 in this column:

Now we work with the number 1442, select it, and go through steps two through four again.

We multiply the divisor 206 by 0 , 1 , 2 , 3 , ... until we get the number 1442 or a number that is greater than 1442 . Let's go: 206 0=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 :

We subtract by a column, we get zero, but we don’t write it down right away, but only remember its position, because we don’t know if the division ends here, or we will have to repeat the steps of the algorithm again:

Now we see that under the horizontal line to the right of the memorized position, we cannot write down any number, since there are no numbers in the record of the dividend in this column. Therefore, this division by a column is over, and we complete the entry:

• Mathematics. Any textbooks for grades 1, 2, 3, 4 of educational institutions.
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