Column division(you can also see the name division corner) is a standard procedure inarithmetic, designed to divide simple or complex multi-digit numbers by breakingdivision into a number of simpler steps. As in all division problems, a single number, calleddivisible, is divided into another, calleddivider, producing a result calledprivate.

A column can be used to divide both natural numbers without a remainder, and division of natural numbers with the rest.

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 whendivision of natural numbers by a column. Let's say right away that in writing to perform division by a columnit is most convenient on paper with a checkered line - so there is less chance of straying from the desired row and column.

First, the dividend and the divisor are written in one line from left to right, after which between the writtennumbers represent the symbol of the form.

For example, if the dividend is the number 6105, and the divisor is 55, then their correct notation when dividing inthe column will look like this:

Look at the following diagram illustrating the places to write 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 bewritten below the divisor under the horizontal bar. And intermediate calculations will be carried out belowdivisible, and you need to take care of the availability of space on the page in advance. In doing so, one should be guidedrule: the greater the difference in the number of characters in the records of the dividend and divisor, the morespace will be required.

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

How to divide into a column is best explained with an example.Calculate:

512:8=?

First, write down the dividend and the divisor in a column. It will look like this:

Their quotient (result) will be written under the divisor. Our number is 8.

1. We define an incomplete quotient. 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 workwith this number. If this number is less than the divisor, then we need to add to the consideration the followingon the left, the digit in the record of the dividend, and work further with the number determined by the two considerednumbers. For convenience, we select in our record the number with which we will work.

2. Take 5. The number 5 is less than 8, so you need to take one more digit from the dividend. 51 is greater than 8. So.this is an incomplete quotient. We put a point in the quotient (under the corner of the divider).

After 51 there is only one number 2. So we add one more point to the result.

3. Now, remembering multiplication table by 8, we find the product nearest to 51 → 6 x 8 = 48→ write the number 6 in the quotient:

We write 48 under 51 (if we multiply 6 from the quotient by 8 from the divisor, we get 48).

Attention! When written under an incomplete quotient, the rightmost digit of the incomplete quotient must be aboverightmost digit works.

4. Between 51 and 48 on the left we put "-" (minus). Subtract according to the rules of subtraction in column 48 and below the linewrite down the result.

However, if the result of the subtraction is zero, then it need not be written down (unless the subtraction inthis paragraph is not the very last action that completely completes the division process column).

The remainder turned out to be 3. Let's compare the remainder with the divisor. 3 is less than 8.

Attention!If the remainder is greater than the divisor, then we made a mistake in the calculation and there is a productcloser than the one we took.

5. Now under the horizontal line to the right of the numbers located there (or to the right of the place where we do notbegan to write down zero) we write down the figure located in the same column in the record of the dividend. If inthere are no digits in this column, then the division by a column ends here.

The number 32 is greater than 8. And again, using the multiplication table for 8, we find the nearest product → 8 x 4 = 32:

The remainder is zero. This means that the numbers are divided completely (without a remainder). If after the lastsubtracting zero, and there are no more digits left, then this is the remainder. We add it to the private inbrackets (e.g. 64(2)).

Division by a column of multivalued natural numbers.

Division by a natural multi-digit number is done in a similar way. At the same time, in the firstThe “intermediate” dividend includes so many high-order digits that it turns out to be more than the divisor.

For example, 1976 divided by 26.

• The number 1 in the most significant digit is less than 26, so consider a number made up of two digits senior ranks - 19.
• The number 19 is also less than 26, so consider the number made up of the digits of the three most significant digits - 197.
• The number 197 is greater than 26, divide 197 tens by 26: 197: 26 = 7 (15 tens left).
• We translate 15 tens into units, add 6 units from the category of units, we get 156.
• Divide 156 by 26 to get 6.

So 1976: 26 = 76.

If at some division step the “intermediate” dividend turned out to be less than the divisor, then in the quotient0 is written, and the number from this digit is transferred to the next, lower digit.

Division with a decimal fraction in a quotient.

Decimal fractions online. Convert decimals to common fractions and common fractions to decimals.

If a natural number is not evenly divisible by a single-digit natural number, you can continuebitwise division and get a quotient decimal.

For example, 64 divided by 5.

• Divide 6 tens by 5 to get 1 tens and 1 tens remainder.
• We translate the remaining ten into units, add 4 from the category of units, we get 14.
• 14 units divided by 5, we get 2 units and 4 units in the remainder.
• We translate 4 units into tenths, we get 40 tenths.
• Divide 40 tenths by 5 to get 8 tenths.

So 64:5 = 12.8

Thus, if when dividing a natural number by a natural one-digit or multi-digit numberthe remainder is obtained, then you can put in a private comma, convert the remainder to the units of the next,smaller digit and continue dividing.

A column? How to work out the skill of division in a column at home if the child did not learn something at school? Dividing by a column is taught in grades 2-3, for parents, of course, this is a passed stage, but if you wish, you can remember the correct entry and explain to your student what he will need in life.

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What should a child in grades 2-3 know in order to learn how to divide in a column?

How to properly explain to a child in grades 2-3 the division by a column so that he does not have problems in the future? First, let's check if there are any gaps in knowledge. Make sure that:

• the child freely performs addition and subtraction operations;
• knows the digits of numbers;
• knows by heart.

How to explain to the child the meaning of the action "division"?

• The child needs to explain everything with a good example.

Ask to share something between family members or friends. For example, sweets, cake pieces, etc. It is important that the child understands the essence - you need to share equally, i.e. without a trace. Practice with different examples.

Let's say 2 groups of athletes have to take seats on the bus. It is known how many athletes are in each group and how many seats are in the bus. You need to find out how many tickets you need to buy one and the second group. Or 24 notebooks need to be distributed to 12 students, how many will get each.

• When the child learns the essence of the principle of division, show the mathematical notation of this operation, name the components.
• Explain what division is the opposite of multiplication, multiplication inside out.

It is convenient to show the relationship between division and multiplication using the example of a table.

For example, 3 times 4 equals 12.
3 is the first multiplier;
4 - second multiplier;
12 - product (the result of multiplication).

If 12 (the product) is divided by 3 (the first factor), we get 4 (the second factor).

Components when dividing called differently:

12 - divisible;
3 - divider;
4 - quotient (the result of division).

How to explain to a child the division of a two-digit number by a single number is not in a column?

It is easier for us, adults, to write down “in the old fashioned way” with a “corner” - and that's it. BUT! Children have not yet passed the division in a column, what should I do? How to teach a child to divide a two-digit number by a single number without using a column notation?

Let's take 72:3 as an example.

Everything is simple! We decompose 72 into such numbers that are easy to verbally divide by 3:
72=30+30+12.

Everything immediately became clear: we can divide 30 by 3, and the child can easily divide 12 by 3.
All that remains is to add up the results, i.e. 72:3=10 (obtained when 30 divided by 3) + 10 (30 divided by 3) + 4 (12 divided by 3).

72:3=24
We did not use long division, but the child understood the reasoning and performed the calculations without difficulty.

After simple examples, you can proceed to the study of division in a column, teach your child to write examples correctly in a “corner”. To begin with, use only examples for division without a remainder.

How to explain to a child the division into a column: a solution algorithm

Large numbers are difficult to divide in the mind, it is easier to use the notation of division by a column. To teach a child to perform calculations correctly, follow the algorithm:

• Determine where the dividend and divisor are in the example. Ask the child to name the numbers (what will we divide by).

213:3
213 - divisible
3 - divider

• Write down the dividend - "corner" - divisor.

• Determine which part of the dividend we can use to divide by a given number.

We argue like this: 2 is not divisible by 3, which means we take 21.

• Determine how many times the divisor "fits" in the selected part.

21 divided by 3 - take 7.

• Multiply the divisor by the selected number, write the result under the "corner".

Multiply 7 by 3 - we get 21. We write it down.

• Find the difference (remainder).

At this stage of reasoning, teach the child to check himself. It is important that he understands that the result of the subtraction must ALWAYS be less than the divisor. If it turned out wrong, you need to increase the selected number and perform the action again.

• Repeat the steps until the remainder is 0.

How to reason correctly to teach a child in grades 2-3 to divide in a column

How to explain division to a child 204:12=?
1. We write in a column.
204 is the dividend, 12 is the divisor.

2. 2 is not divisible by 12, so we take 20.
3. To divide 20 by 12, we take 1. We write 1 under the “corner”.
4. Multiply 1 by 12, we get 12. We write under 20.
5. 20 minus 12 is 8.
We check ourselves. Is 8 less than 12 (divisor)? Ok, that's right, let's move on.

6. Next to 8 we write 4. 84 divided by 12. By how much do you need to multiply 12 to get 84?
It’s hard to say right away, let’s try to act by the selection method.
Take, for example, 8, but do not write down yet. We count verbally: 8 times 12 will be 96. And we have 84! Not suitable.
Let's try less... For example, let's take 6. We check ourselves verbally: 6 times 12 equals 72. 84-72=12. We got the same number as our divisor, but it must be either zero or less than 12. So, the optimal number is 7!

7. We write 7 under the "corner" and perform the calculations. Multiply 7 by 12 to get 84.
8. We write the result in a column: 84 minus 84 equals zero. Hooray! We made the right decision!

So, you have taught the child to divide in a column, now it remains to work out this skill, bring it to automatism.

Why is it difficult for children to learn to divide in a column?

Remember that problems with mathematics arise from the inability to quickly do simple arithmetic operations. In elementary school, you need to work out and bring addition and subtraction to automaticity, learn the multiplication table “from cover to cover”. All! The rest is a matter of technique, and it is developed with practice.

Be patient, do not be lazy to once again explain to the child what he did not learn in the lesson, it is tedious but meticulous to understand the reasoning algorithm and say each intermediate operation before voicing the finished answer. Give additional examples to practice skills, play math games - this will bear fruit and you will see the results and rejoice at the success of the child very soon. Be sure to show where and how you can apply the acquired knowledge in everyday life.

Dear readers! Tell us how you teach your children to divide in a column, what difficulties you had to face and how you overcame them.

At school, these actions are studied from simple to complex. Therefore, it is certainly necessary to master the algorithm for performing the above operations using simple examples. So that later there will be no difficulties with dividing decimal fractions into a column. After all, this is the most difficult version of such tasks.

This subject requires consistent study. Gaps in knowledge are unacceptable here. This principle should be learned by every student already in the first grade. Therefore, if you skip several lessons in a row, you will have to master the material yourself. Otherwise, later there will be problems not only with mathematics, but also with other subjects related to it.

The second prerequisite for a successful study of mathematics is to move on to examples of division in a column only after addition, subtraction and multiplication have been mastered.

It will be difficult for a child to divide if he has not learned the multiplication table. By the way, it is better to learn it from the Pythagorean table. There is nothing superfluous, and multiplication is easier to digest in this case.

How are natural numbers multiplied in a column?

If there is a difficulty in solving examples in a column for division and multiplication, then it is necessary to start solving the problem with multiplication. Because division is the inverse of multiplication:

1. Before multiplying two numbers, you need to look at them carefully. Choose the one with more digits (longer), write it down first. Place the second one under it. Moreover, the numbers of the corresponding category should be under the same category. That is, the rightmost digit of the first number must be above the rightmost digit of the second.
2. Multiply the rightmost digit of the bottom number by each digit of the top number, starting from the right. Write the answer under the line so that its last digit is under the one by which it was multiplied.
3. Repeat the same with the other digit of the bottom number. But the result of the multiplication must be shifted one digit to the left. In this case, its last digit will be under the one by which it was multiplied.

Continue this multiplication in a column until the numbers in the second multiplier run out. Now they need to be folded. This will be the desired answer.

Algorithm for multiplying into a column of decimal fractions

First, it is supposed to imagine that not decimal fractions are given, but natural ones. That is, remove commas from them and then proceed as described in the previous case.

The difference begins when the answer is written. At this point, it is necessary to count all the numbers that are after the decimal points in both fractions. That is how many of them you need to count from the end of the answer and put a comma there.

It is convenient to illustrate this algorithm with an example: 0.25 x 0.33:

How to start learning to divide?

Before solving examples for division into a column, it is supposed to remember the names of the numbers that are in the example for division. The first of them (the one that divides) is the divisible. The second (divided by it) is a divisor. The answer is private.

After that, using a simple everyday example, we will explain the essence of this mathematical operation. For example, if you take 10 sweets, then it is easy to divide them equally between mom and dad. But what if you need to distribute them to your parents and brother?

After that, you can get acquainted with the rules of division and master them with specific examples. Simple ones at first, and then moving on to more and more complex ones.

Algorithm for dividing numbers into a column

First, we present the procedure for natural numbers that are divisible by a single-digit number. They will also be the basis for multi-digit divisors or decimal fractions. Only then it is supposed to make small changes, but more on that later:

• Before doing division in a column, you need to find out where the dividend and divisor are.
• Write down the dividend. To the right of it is a divider.
• Draw a corner on the left and bottom near the last corner.
• Determine the incomplete dividend, that is, the number that will be the minimum for division. Usually it consists of one digit, maximum of two.
• Choose the number that will be written first in the answer. It must be the number of times the divisor fits in the dividend.
• Write down the result of multiplying this number by a divisor.
• Write it under an incomplete divisor. Perform subtraction.
• Carry to the remainder the first digit after the part that has already been divided.
• Pick up the answer again.
• Repeat multiplication and subtraction. If the remainder is zero and the dividend is over, then the example is done. Otherwise, repeat the steps: demolish the number, pick up the number, multiply, subtract.

How to solve long division if there is more than one digit in the divisor?

The algorithm itself completely coincides with what was described above. The difference will be the number of digits in the incomplete dividend. Now there should be at least two of them, but if they turn out to be less than the divisor, then it is supposed to work with the first three digits.

There is another nuance in this division. The fact is that the remainder and the figure carried to it are sometimes not divisible by a divisor. Then it is supposed to attribute one more figure in order. But at the same time, the answer must be zero. If three-digit numbers are divided into a column, then more than two digits may need to be demolished. Then the rule is introduced: zeros in the answer should be one less than the number of digits taken down.

You can consider such a division using the example - 12082: 863.

• The incomplete divisible in it is the number 1208. The number 863 is placed in it only once. Therefore, in response, it is supposed to put 1, and write 863 under 1208.
• After subtraction, the remainder is 345.
• To him you need to demolish the number 2.
• In the number 3452, 863 fits four times.
• Four must be written in response. Moreover, when multiplied by 4, this number is obtained.
• The remainder after subtraction is zero. That is, the division is completed.

The answer in the example is 14.

What if the dividend ends in zero?

Or a few zeros? In this case, a zero remainder is obtained, and there are still zeros in the dividend. Do not despair, everything is easier than it might seem. It is enough just to attribute to the answer all the zeros that remained undivided.

For example, you need to divide 400 by 5. The incomplete dividend is 40. Five is placed in it 8 times. This means that the answer is supposed to be written 8. When subtracting, there is no remainder. That is, the division is over, but zero remains in the dividend. It will have to be added to the answer. Thus, dividing 400 by 5 gives 80.

What if you need to divide a decimal?

Again, this number looks like a natural number, if not for the comma separating the integer part from the fractional part. This suggests that the division of decimal fractions into a column is similar to the one described above.

The only difference will be the semicolon. It is supposed to be answered immediately, as soon as the first digit from the fractional part is taken down. In another way, it can be said like this: the division of the integer part has ended - put a comma and continue the solution further.

When solving examples for dividing into a column with decimal fractions, you need to remember that any number of zeros can be assigned to the part after the decimal point. Sometimes this is necessary in order to complete the numbers to the end.

Division of two decimals

It may seem complicated. But only at the beginning. After all, how to perform division in a column of fractions by a natural number is already clear. So, we need to reduce this example to the already familiar form.

Make it easy. You need to multiply both fractions by 10, 100, 1,000, or 10,000, or maybe a million if the task requires it. The multiplier is supposed to be chosen based on how many zeros are in the decimal part of the divisor. That is, as a result, it turns out that you will have to divide a fraction by a natural number.

And it will be in the worst case. After all, it may turn out that the dividend from this operation becomes an integer. Then the solution of the example with division into a column of fractions will be reduced to the simplest option: operations with natural numbers.

As an example: 28.4 divided by 3.2:

• First, they must be multiplied by 10, since in the second number there is only one digit after the decimal point. Multiplying will give 284 and 32.
• They are supposed to be divided. And at once the whole number is 284 by 32.
• The first matched number for the answer is 8. Multiplying it gives 256. The remainder is 28.
• The division of the integer part is over, and a comma is supposed to be put in the answer.
• Demolish to remainder 0.
• Take 8 again.
• Remainder: 24. Add another 0 to it.
• Now you need to take 7.
• The result of the multiplication is 224, the remainder is 16.
• Demolish another 0. Take 5 and get exactly 160. The remainder is 0.

Division completed. The result of the 28.4:3.2 example is 8.875.

What if the divisor is 10, 100, 0.1, or 0.01?

As with multiplication, long division is not needed here. It is enough just to move the comma in the right direction for a certain number of digits. Moreover, according to this principle, you can solve examples with both integers and decimal fractions.

So, if you need to divide by 10, 100 or 1000, then the comma is moved to the left by as many digits as there are zeros in the divisor. That is, when a number is divisible by 100, the comma should move to the left by two digits. If the dividend is a natural number, then it is assumed that the comma is at the end of it.

This action produces the same result as if the number were to be multiplied by 0.1, 0.01, or 0.001. In these examples, the comma is also moved to the left by a number of digits equal to the length of the fractional part.

When dividing by 0.1 (etc.) or multiplying by 10 (etc.), the comma should move to the right by one digit (or two, three, depending on the number of zeros or the length of the fractional part).

It is worth noting that the number of digits given in the dividend may not be sufficient. Then the missing zeros can be assigned to the left (in the integer part) or to the right (after the decimal point).

Division of periodic fractions

In this case, you will not be able to get the exact answer when dividing into a column. How to solve an example if a fraction with a period is encountered? Here it is necessary to move on to ordinary fractions. And then perform their division according to the previously studied rules.

For example, you need to divide 0, (3) by 0.6. The first fraction is periodic. It is converted to the fraction 3/9, which after reduction will give 1/3. The second fraction is the final decimal. It is even easier to write down an ordinary one: 6/10, which is equal to 3/5. The rule for dividing ordinary fractions prescribes to replace division with multiplication and the divisor with the reciprocal of a number. That is, the example boils down to multiplying 1/3 by 5/3. The answer is 5/9.

If the example has different fractions...

Then there are several possible solutions. First, you can try to convert an ordinary fraction to a decimal. Then divide already two decimals according to the above algorithm.

Secondly, every final decimal fraction can be written as a common fraction. It's just not always convenient. Most often, such fractions turn out to be huge. Yes, and the answers are cumbersome. Therefore, the first approach is considered more preferable.

Division multi-digit or multi-digit numbers it is convenient to produce in writing in a column. Let's see how to do it. Let's start by dividing a multi-digit number by a single-digit one, and gradually increase the capacity of the dividend.

So let's share 354 on 2 . First, let's place these numbers as shown in the figure:

We place the dividend on the left, the divisor on the right, and we will write the quotient under the divisor.

Now we begin to divide the dividend by the divisor bit by bit from left to right. We find first incomplete dividend, for this we take the first digit on the left, in our case 3 and compare with the divisor.

3 more 2 , Means 3 and there is an incomplete dividend. We put a point in the quotient and determine how many more digits there will be in the quotient - the same number as left in the dividend after highlighting the incomplete dividend. In our case, there are as many digits in the quotient as in the dividend, that is, hundreds will be the highest digit:

In order to 3 divide by 2 we recall the multiplication table by 2 and find the number when multiplied by 2 we get the largest product that is less than 3.

2 × 1 = 2 (2< 3)

2 × 2 = 4 (4 > 3)

2 less 3 , A 4 more, then we take the first example and the multiplier 1 .

We write down 1 to the quotient in place of the first point (to the digit of hundreds), and the found product is written under the dividend:

Now we find the difference between the first incomplete dividend and the product of the quotient found and the divisor:

The resulting value is compared with the divisor. 15 more 2 , so we have found the second incomplete dividend. To find the result of a division 15 on 2 revisit the multiplication table 2 and find the largest product that is less than 15 :

2 × 7 = 14 (14< 15)

2 x 8 = 16 (16 > 15)

Desired multiplier 7 , we write it in a quotient in place of the second point (in tens). We find the difference between the second incomplete dividend and the product of the found digit of the quotient and divisor:

We continue the division, for which we find third incomplete dividend. We lower the next bit of the dividend:

We divide the incomplete divisible by 2, put the resulting value in the category of private units. Let's check the correctness of the division:

2 x 7 = 14

We write the result of dividing the third incomplete divisible by the divisor into a quotient, we find the difference:

We got the difference equal to zero, which means the division is made Right.

Let's complicate the task and give another example:

1020 ÷ 5

Let's write our example in a column and define the first incomplete quotient:

The thousands place of the dividend is 1 , compare with the divisor:

1 < 5

We add the hundreds place to the incomplete dividend and compare:

10 > 5 We have found an incomplete dividend.

Divide 10 on 5 , we get 2 , write the result into a quotient. The difference between the incomplete dividend and the result of multiplying the divisor and the found digit of the quotient.

10 – 10 = 0

0 we do not write, we omit the next digit of the dividend - the digit of tens:

Compare the second incomplete dividend with the divisor.

2 < 5

We should add one more digit to the incomplete divisible, for this we put it in the quotient, on the digit of tens 0 :

20 ÷ 5 = 4

We write the answer in the category of units of the private and check: we write the product under the second incomplete dividend and calculate the difference. We get 0 , Means example solved correctly.

And 2 more rules for dividing into a column:

1. If there are zeros in the dividend and divisor in the lower digits, then they can be reduced before dividing, for example:

How many zeros in the least significant digit of the dividend we remove, the same number of zeros we remove in the least significant digits of the divisor.

2. If zeros remain in the dividend after division, then they should be transferred to the quotient:

So, let's formulate a sequence of actions when dividing into a column.

1. We place the dividend on the left, the divisor on the right. Remember that we divide the dividend by bit by bit selecting incomplete dividends and dividing them sequentially by the divisor. The digits in the incomplete dividend are allocated from left to right from senior to junior.
2. If there are zeros in the dividend and divisor in the lower digits, then they can be reduced before dividing.
3. Determine the first incomplete divisor:

A) we allocate the most significant bit of the dividend into the incomplete divisor;

b) we compare the incomplete dividend with the divisor, if the divisor is greater, then go to the point (V), if less, then we have found an incomplete dividend and can proceed to the point 4 ;

V) add the next bit to the incomplete dividend and go to the point (b).

1. We determine how many digits there will be in the quotient, and put as many points in the place of the quotient (under the divisor) as there will be digits in it. One point (one digit) for the entire first incomplete dividend and the remaining points (digits) as many as the number of digits left in the dividend after the selection of the incomplete dividend.
2. We divide the incomplete dividend by the divisor, for this we find a number, when multiplied by the divisor, a number would be obtained that is either equal to the incomplete dividend or less than it.
3. We write the found number in place of the next digit of the quotient (points), and we write the result of multiplying it by the divisor under the incomplete dividend and find their difference.
4. If the found difference is less than or equal to the incomplete dividend, then we correctly divided the incomplete dividend by the divisor.
5. If there are still digits left in the dividend, then we continue the division, otherwise we go to the point 10 .
6. We lower the next digit of the dividend to the difference and get the next incomplete dividend:

a) compare the incomplete dividend with the divisor, if the divisor is greater, then go to step (b), if less, then we have found the incomplete dividend and can go to step 4;

b) we add the next bit of the dividend to the incomplete dividend, while writing 0 in the quotient in place of the next bit (point);

c) go to point (a).

10. If we performed division without a remainder and the last found difference is 0 , then we do the division correctly.

We talked about dividing a multi-digit number by a one-digit number. In the case when the divisor is larger, the division is performed in the same way:

Column division is an integral part of the school curriculum and necessary knowledge for the child. To avoid problems in the lessons and with their implementation, it is necessary to give the child basic knowledge from a young age.

It is much easier to explain certain things and processes to a child in a playful way, and not in the format of a standard lesson (although today there are quite a variety of teaching methods in different forms).

From this article you will learn

The principle of division for kids

Children constantly come across different mathematical terms, without even suspecting where they come from. Indeed, many mothers, in the form of a game, explain to the child that dads are more of a plate, go further to the kindergarten than to the store and other simple examples. All this gives the child an initial impression of mathematics, even before the child goes to first grade.

To teach a child to divide without a remainder, and later with a remainder, it is necessary to directly invite the child to play division games. Divide, for example, sweets among themselves, and then add the following participants in turn.

First, the child will share candy, giving each participant one. And at the end, draw a conclusion together. It should be clarified that “sharing” means the same number of candies for everyone.

If you need to explain this process using numbers, then you can give an example in the form of a game. We can say that the number is candy. It should be explained that the number of sweets to be divided between the participants is divisible. And the number of people into whom these sweets are divided is a divisor.

Then you should show it all clearly, give “live” examples in order to quickly teach the crumbs to divide. Playing, he will understand and learn everything much faster. While the algorithm will be difficult to explain, and now it is not necessary.

How to teach your baby to divide in a column

Explaining math to a little bit is a good preparation for going to class, especially math class. If you decide to move on to teaching your child to divide by a column, then he has already learned such actions as addition, subtraction, and what the multiplication table is.

If this still causes some difficulties for him, then all this knowledge needs to be tightened up. It is worth recalling the algorithm of actions of previous processes, teaching how to freely use your knowledge. Otherwise, the baby will simply get confused in all processes, and will cease to understand anything.

To make this easier to understand, there is now a division table for toddlers. The principle is the same as for multiplication tables. But is such a table already needed if the baby knows the multiplication table? It depends on the school and the teacher.

When forming the concept of "division", it is necessary to do everything in a playful way, give all examples on things and objects familiar to the child.

It is very important that all items be of an even number, so that it is clear to the baby that the result is equal parts. This will be correct, because it will allow the baby to realize that division is the reverse process of multiplication. If the items are an odd number, then the result will come out with the remainder and the baby will get confused.

Multiply and divide using a spreadsheet

When explaining to the baby the relationship between multiplication and division, it is necessary to clearly show all this using some example. For example: 5 x 3 = 15. Remember that the result of multiplication is the product of two numbers.

And only after that, explain that this is the reverse process to multiplication and demonstrate this clearly using a table.

Say that you need to divide the result “15” by one of the factors (“5” / “3”), and the result will be a constantly different factor that did not take part in the division.

It is also necessary to explain to the baby how the categories that perform division are correctly called: dividend, divisor, quotient. Again, use an example to show which of these is a particular category.

Dividing by a column is not a very complicated thing, it has its own easy algorithm that the baby needs to be taught. After fixing all these concepts and knowledge, you can proceed to further training.

In principle, parents should learn the multiplication table in reverse order with their beloved child, and remember it by heart, as this will be necessary when teaching division by a column.

This must be done before going to first grade, so that it is much easier for the child to get used to school and keep up with the school curriculum, and so that the class does not start teasing the child due to small failures. The multiplication table is both at school and in notebooks, so you don’t have to carry a separate table to school.

Divide with a column

Before starting the lesson, you need to remember the names of the numbers when dividing. What is a divisor, dividend and quotient. The child must divide these numbers into the correct categories without errors.

The most important thing when learning division by a column is to learn the algorithm, which, in general, is quite simple. But first, explain to the child the meaning of the word "algorithm" if he has forgotten it or has not studied it before.

In the event that the baby is well versed in the multiplication table and inverse division, he will not have any difficulties.

However, it is impossible to linger on the result obtained for a long time; it is necessary to regularly train the acquired skills and abilities. Move on as soon as it becomes clear that the baby understood the principle of the method.

It is necessary to teach the baby to divide in a column without a remainder and with a remainder, so that the child is not afraid that he failed to divide something correctly.

To make it easier to teach the baby the process of division, you must:

• in 2-3 years, understanding the whole-part relationship.
• at 6-7 years old, the baby should be able to freely perform addition, subtraction and be aware of the essence of multiplication and division.

It is necessary to encourage the child’s interest in mathematical processes so that this lesson at school brings him pleasure and a desire to learn, and not motivate him only in the classroom, but also in life.

The child should carry different tools for math lessons, learn how to use them. However, if it is difficult for a child to carry everything, then do not overload it.