Solution of long examples in a column. How to divide in a column? How to explain column division to a child? Divide by a single, two-digit, three-digit number, division with a remainder

A column calculator for Android devices will be a great helper for modern schoolchildren. The program not only gives the correct answer to a mathematical action, but also clearly demonstrates its step-by-step solution. If you need more complex calculators, you can look at or advanced engineering calculator.

Peculiarities

The main feature of the program is the uniqueness of the calculation of mathematical operations. Displaying the calculation process in a column allows students to get acquainted with it in more detail, understand the solution algorithm, and not just get the finished result and rewrite it in a notebook. This feature has a huge advantage over other calculators. quite often at school, teachers require intermediate calculations to be written down to make sure that the student does them in his mind and really understands the algorithm for solving problems. By the way, we have another program of a similar kind - .

To start using the program, you need to download a calculator in a column on Android. You can do this on our website absolutely free of charge without additional registrations and SMS. After installation will open main page in the form of a notebook sheet in a cell, on which, in fact, the results of calculations and their detailed solution will be displayed. At the bottom there is a panel with buttons:

Numbers.
Signs of arithmetic operations.
Delete previously entered characters.

Input is carried out according to the same principle as on. All the difference is only in the interface of the application - all mathematical calculations and their results are displayed in a virtual student notebook.

The application allows you to quickly and correctly perform standard mathematical calculations for a student in a column:

multiplication;
division;
addition;
subtraction.

A nice addition to the app is the daily reminder function. homework mathematics. If you want, do your homework. To enable it, go to the settings (press the button in the form of a gear) and check the reminder box.

Advantages and disadvantages

It helps the student not only to quickly get the correct result of mathematical calculations, but also to understand the very principle of calculation.
Very simple, intuitive interface for every user.
You can install the application even on the most budget Android device with operating system 2.2 and later.
The calculator saves a history of mathematical calculations, which can be cleared at any time.

The calculator is limited in mathematical operations, so it will not work for complex calculations that an engineering calculator could handle. However, given the purpose of the application itself - to clearly demonstrate to elementary school students the principle of calculating in a column, this should not be considered a disadvantage.

The application will also be an excellent assistant not only for schoolchildren, but also for parents who want to get their child interested in mathematics and teach him how to correctly and consistently perform calculations. If you have already used the Stacked Calculator app, leave your impressions below in the comments.

At school, these actions are studied from simple to complex. Therefore, it is absolutely necessary to master well the algorithm for performing these operations on 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.

Second required condition successful study mathematics - move on to examples for 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:

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.
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.
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 in 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 on concrete examples. Simple ones at first, and then moving on to more and more complex ones.

Algorithm for dividing numbers into a column

First, let's take a look at the procedure for natural numbers divisible by single digit. 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.
Again choose the number for the answer.
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. There should now be at least two of them, but if they turn out to be less 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 division is made three-digit numbers in a column, you may need to demolish more than two digits. 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 the number of digits, equal to the length 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. Firstly, common fraction You can try to convert to decimal. Then divide already two decimals according to the above algorithm.

Secondly, each finite decimal can be written in the form of an ordinary 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.

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 typical examples dividing by a column of natural numbers with detailed explanations of the solution and illustrations.

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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 doing so, the following rule should be followed: more 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.

Solution.

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. In this case, the record will take next view:

The final stage of dividing single-digit natural numbers by a column remains. Under the number written under the dividend, you need to spend horizontal line, and subtract numbers over 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.

Solution.

On 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.

Solution.

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 .

Solution.

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.

Solution.

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:

Maths. Any textbooks for grades 1, 2, 3, 4 of educational institutions.
Maths. Any textbooks for 5 classes of educational institutions.

Children in grades 2-3 learn a new mathematical action - division. It is not easy for a schoolchild to understand the essence of this mathematical action, so he needs the help of his parents. Parents need to understand how to present new information to the child. TOP 10 examples will tell parents how to teach children to divide numbers by a column.

Learning to divide in a column in the form of a game

Children get tired at school, they get tired of textbooks. Therefore, parents need to abandon textbooks. Present information in the form of an exciting game.

You can set tasks like this:

1 Give your child a place to learn in the form of a game. Plant his toys in a circle, and give the child pears or sweets. Have the student share 4 candies between 2 or 3 dolls. To gain understanding from the child, gradually add the number of sweets up to 8 and 10. Even if the baby will act for a long time, do not press or yell at him. You will need patience. If a child does something wrong, correct him calmly. Then, as he completes the first action of dividing candies between the participants in the game, ask him to calculate how many candies each toy got. Now the conclusion. If there were 8 candies and 4 toys, then each got 2 candies. Let your child understand that sharing means distributing an equal amount of candy to all the toys.

2 You can teach mathematical action with the help of numbers. Let the student understand that numbers can be qualified like pears or candies. Say that the number of pears to be divided is divisible. And the number of toys that contain sweets is a divisor.

3 Give the child 6 pears. Set a task for him: to divide the number of pears between grandfather, dog and dad. Then ask him to share 6 pears between grandpa and dad. Explain to the child the reason why the result was not the same when dividing.

4 Tell the student about division with a remainder. Give the child 5 candies and ask him to distribute them equally between the cat and dad. The child will have 1 candy left. Tell your child why it happened the way it did. This mathematical operation should be considered separately, as it can cause difficulties.

Learning in a playful way can help the child quickly understand the whole process of dividing numbers. He will be able to learn that the largest number is divisible by the smallest, or vice versa. That is, the largest number is sweets, and the smallest is the participants. In column 1, the number will be the number of sweets, and 2 will be the number of participants.

Do not overload your child with new knowledge. You need to learn gradually. You need to move on to a new material when the previous material is fixed.

Teaching long division using the multiplication table

Students up to grade 5 will be able to figure out division faster if they know multiplication well.

Parents need to explain that division is similar to the multiplication table. Only the actions are opposite. To illustrate, here is an example:

Tell the student to randomly multiply the values 6 and 5. The answer is 30.
Tell the student that the number 30 is the result of a mathematical operation with two numbers: 6 and 5. Namely, the result of multiplication.
Divide 30 by 6. As a result of the mathematical operation, you get 5. The student will be able to make sure that division is the same as multiplication, but vice versa.

You can use the multiplication table for clarity of division, if the child has learned it well.

Learning to divide in a column in a notebook

You need to start training when the student understands the material about division in practice, using the game and the multiplication table.

One must begin to divide in this way, using simple examples. So, dividing 105 by 5.

You need to explain the mathematical operation in detail:

Write an example in your notebook: 105 divided by 5.
Write it down as you would for long division.
Explain that 105 is the dividend and 5 is the divisor.
With a student, identify 1 number that can be divided. The value of the dividend is 1, this figure is not divisible by 5. But the second number is 0. The result will be 10, this value can be divided by this example. The number 5 goes into the number 10 twice.
In the division column, under the number 5, write the number 2.
Ask the child to multiply the number 5 by 2. The result of the multiplication will be 10. This value must be written under the number 10. Next, you need to write the subtraction sign in the column. From 10 you need to subtract 10. You get 0.
Write in the column the number resulting from the subtraction - 0. 105 has a number left that did not participate in the division - 5. This number must be written down.
The result is 5. This value must be divided by 5. The result is the number 1. This number must be written under 5. The result of the division is 21.

Parents need to explain that this division has no remainder.

You can start division with numbers 6,8,9, then go to 22, 44, 66 , and after to 232, 342, 345 , etc.

Learning to divide with a remainder

When the child learns the material about division, you can complicate the task. Division with a remainder is the next step in learning. Explain with available examples:

Invite the child to divide 35 by 8. Write the task in a column.
To make it as clear as possible to the child, you can show him the multiplication table. The table clearly shows that the number 35 includes 4 times the number 8.
Write under the number 35 the number 32.
The child needs to subtract 32 from 35. It turns out 3. The number 3 is the remainder.

Simple examples for a child

You can continue with this example:

When dividing 35 by 8, the remainder is 3. You need to add 0 to the remainder. In this case, after the number 4 in the column, you need to put a comma. Now the result will be fractional.
When dividing 30 by 8, you get 3. This figure must be written after the decimal point.
Now you need to write 24 under the value 30 (the result of multiplying 8 by 3). The result will be 6. You also need to add zero to the number 6. Get 60.
The number 8 is placed in the number 60 7 times. That is, it turns out 56.
When subtracting 60 from 56, you get 4. You also need to sign 0 to this figure. It turns out 40. In the multiplication table, the child can see that 40 is the result of multiplying 8 by 5. That is, the number 8 is included in the number 40 5 times. There is no rest. The answer looks like this - 4.375.

This example may seem complicated to a child. Therefore, you need to divide the values \u200b\u200bmany times, which will have a remainder.

Learning division through games

Parents can use division games for student learning. You can give your child coloring pages in which you need to determine the color of the pencil by dividing. You need to choose coloring pages with easy examples so that the child can solve the examples in his mind.

The picture will be divided into parts, which will contain the results of division. And the colors to be used will be examples. For example, the red color is marked with an example: Divide 15 by 3 to get 5. You need to find a part of the picture under this number and color it. Math coloring pages captivate children. Therefore, parents should try this method of education.

Learning to divide the column of the smallest number by the largest

Division by this method assumes that the quotient will begin with 0, and after it there will be a comma.

In order for the student to correctly assimilate the information received, he needs to give an example of such a plan.