How to divide a six-digit number by a two-digit number. How to learn to divide by column: examples and solutions

Algorithm for dividing numbers into a column, teaching a child. Features of dividing multi-digit numbers and polynomials.

School gives the child not only discipline, development of talents and communication skills, but also knowledge of fundamental sciences. One of them is mathematics.

Although the program and workload for students often change, dividing numbers with different numbers of digits into a column remains an unapproachable peak for many of them from the first attempt. Therefore, it is often impossible to do without training at home with your parents.

In order not to waste time and prevent your child from forming a lump of incomprehensibility in mathematics, refresh your memory of your knowledge of dividing numbers in a column. This article will help you with this.

How to correctly divide numbers into a column: division algorithm

To divide numbers in a column, follow these steps:

• Write down the division action correctly on paper. Select the upper right corner of the notebook/sheet. If you are just learning to do long division, use squared paper. This way you will maintain the visual consistency of the solution,
• Line the space between the dividend and the divisor.
  The diagram below will help you.

• plan space for dividing into columns. The longer the number that is to be divided, and the larger the divisor, the lower the solution goes down on the page,
• Perform the first division operation with the number of digits of the dividend that is equal to the divisor. For example, if you have a single-digit number to the right of the dividing line, then consider the first one of the dividend; if it’s a two-digit number, then consider the first 2,
• multiply the numbers below and above the line and write the result under the numbers of the dividend that you indicated for the first action,
• complete the activity by subtracting and finding the remainder. Draw a horizontal line above it to separate the first step of the solution,
• add the next digit of the dividend to the remainder and continue solving,
• The last step of division is when you get 0 or a number less than the divisor from subtraction. In the second case, your answer will have a remainder, for example, 17 and 3 as a remainder.

How to explain division to a child and teach how to divide using a column?

First, consider a number of input factors:

• the child knows the multiplication table
• is well versed and able to apply in practice the operations of subtraction and addition
• understands the difference between the whole and its constituent elements

• play with the multiplication table. Place it in front of the child and show with examples how easy it is to use when dividing,
• explain the location of the dividend, divisor, quotient, remainder. Invite your child to repeat these categories,
• turn the process into a game, come up with a story about numbers and division,
• Prepare visual aids for teaching. Counting sticks, apples, coins, toys, peeled notes or oranges will do. Offer to distribute them among different numbers of people, for example, between mom, dad and child,
• Be the first to show your child operations with even numbers so that he can see the result of division, a multiple of two.

The process of mastering long division:

• write down the numbers, separating them with boundaries. Repeat with your child the location of division categories,
• Invite him to analyze the digits of the dividend into the “greater-than-less” divisor. Help with a question - how many times one number is placed in the second. As a result, the child should select the number/numbers that he will use to perform the first action,
• Tell me the algorithm for determining the bit depth of a quotient. It is convenient to depict it with dots, which will then turn into numbers,
• help correctly identify and write the first number as a quotient, multiply it by the divisor, write the result under the dividend, and subtract. Explain that the result of a subtraction must always be less than the divisor. Otherwise, the action was performed with an error and should be redone,
• the next step is to analyze the situation with adding the second number from the dividend and determining the number of times the divisor is repeated in it,
• again help with recording the action,
• continue until the result of the difference is zero. This is only relevant for dividing numbers without a remainder,
• Reinforce your child’s knowledge with a few more examples. Make sure he doesn't get tired, otherwise give him a break.

How to divide a two-digit number into a single-digit and two-digit number in writing: examples, explanation

Let's start with a step-by-step analysis of examples of long division.

Perform the action on the numbers 25 and 2:

• write them down side by side and separate them with border lines,
• determine the required number of digits of the dividend for the first action,
• write the value under the divisor and the result of the multiplication under the dividend,
• do the subtraction,
• Add the second digit of the dividend and repeat the multiplication and subtraction steps.

For a partially completed task on dividing a two-digit number by a single-digit number by a column, see below:

Please note that dividing a two-digit number by a single-digit number with a column is possible in one step.

Second example. Divide 87 by 26 in a column.

The algorithm is similar to that discussed above with the only difference that you need to take into account 2 numbers of the divisor at once when determining the number of times the dividend is repeated.

To make the task easier for a child who is just learning the basics of division, ask him to focus on the first digits of the dividend and divisor. For example, 8:2=4. Have your child put this number under the line and do the multiplication. He needs to see with his own eyes that 4 is a lot and he needs to try with three.

Below is an example of a column dividing a two-digit number by a two-digit number with a remainder.

Third example. How to divide a number into a column with a zero in the answer.

First, we divide 15 by 15, the remainder is 0, the answer is 1. We take away 6, but it is not divisible by 15, so we put 0 in the answer. Next, 15 multiplied by 0 will be zero and subtract it from 6. We take away zero, which is at the end of the number, we get 60, which is divided by 15 and put 4 in response.

How to divide a three-digit number into a single-digit, two-digit and three-digit number: examples, explanation

Let's continue the analysis of the action of division by a column using examples with a three-digit dividend.

When the divisor is a single-digit number, the operation algorithm is similar to those discussed above.

Schematically it looks like this:

In the case of dividing a three-digit dividend by a two-digit divisor, choose with your child a number corresponding to the number of spaces of the second in the first part of the first or in general. That is, consider first the 2 digits of the three-digit dividend; if they are less than the divisor, then all three.

When your child has just begun to master long division, tell him how to perform actions with single-digit numbers. That is, with the first ones in the dividend and divisor. Let the kid make a mistake that will lead to a negative subtraction value and return to the selection of the number under the line, thereby getting confused with the action immediately for the two-digit divisor.

The scheme for dividing a three-digit number by a two-digit number is as follows:

Three-digit values ​​in the divisor and dividend look cumbersome and scary for a child. Reassure him by explaining that the principle of operation is identical to that of dividing prime numbers.

The method of enumerating one digit at a time will help your child figure out each number separately. Only he will need more time for this action than in previous examples. For better visual perception, combine with arcs the number of numbers that will participate in the first action.

Diagram for dividing a three-digit number by a three-digit number.

How to divide four-digit, multi-digit large numbers, polynomials into polynomials: examples, explanation

In the case of dividing a four-digit number by any number that contains up to 4 orders of magnitude at the same time, pay the child’s attention to the nuances:

• Determining the correct number of orders after the division action. For example, in the example 6734:56 you should get a two-digit integer in the “quotient” column, and in the example 8956:1243 - a single-digit integer,
• the appearance of zeros in the quotient. When, during the solution, when carrying over the next number of the dividend, the result turns out to be less than the divisor,
• checking the result obtained by performing a multiplication operation. This nuance is relevant for dividing large numbers without a remainder. If the latter is present, then advise the child to check himself and divide the numbers into a column again.

Below is an example solution.

For large multi-digit numbers that are divisible into specific values ​​less than or equal to them in the number of digits, all the algorithms discussed above are relevant.

The child should be especially careful in such cases and correctly determine:

• the number of characters of the quotient, that is, the result
• digits of the dividend for the first action
• correctness of transfer of remaining numbers

Examples of detailed solutions are below.

When performing division operations on polynomials, draw children's attention to a number of features:

• an action may or may not have a remainder. In the first case, write it in the numerator and the divisor in the denominator,
• to perform the subtraction operation, add the missing powers of the function multiplied by zero to the polynomial,
• transform polynomials by isolating repeating bi-/polynomials. Then reduce them and you will get the result without a trace.

Below are a number of detailed examples with solutions.

How to divide with a remainder?

The algorithm for long division with a remainder is similar to the classic one. The only difference is the appearance of a remainder, which is less than the divisor. This means that the first one remains unchanged.

Write it down in your answer either:

• like a fraction, where the numerator is the remainder and the denominator is the divisor
• in words, for example, 73 whole and 6 remainder

How to divide decimal fractions with a comma?

There are several features of this division. If you perform an action with:

• a decimal fraction-dividend and an integer divisor, then proceed according to the usual algorithm until the dividend runs out of digits before the decimal point. Then put it in the quotient and continue moving the numbers until the end of the division,
• a number that is divisible by 10, 100, 100, etc., then move the comma in the dividend to the left by a number of digits equal to the number of zeros of the divisor. For example, 749.5:100=7.495,
• decimal fractions in both the divisor and the dividend at the same time, then first get rid of the comma from the second element. To do this, move it to the right in both fractional numbers by the number of digits that are separated from the divisor. For example, convert 416.788:5.3 to 4167.88:53 and do normal long division.

How to divide a smaller number by a larger number using a column?

With this division, your quotient will start at 0 and have a comma after it.

To help your child better understand this division and not get confused about the number of zeros and where the comma is placed in the quotient, give him the following example:

• carry out the first subtraction operation with zeros, written one at a time under the divisor and in the “quotient” column,
• put a comma in the quotient, and add a zero for the remainder after the difference and continue the usual long division,
• when the remainder of the subtraction is again less than the divisor, add a zero to the first and continue the action. The final result is getting a zero from the difference between the upper and lower numbers or repeating the remainder. IN the latter case there is a value in the period, that is, an endlessly repeating number/numbers.

Below is an example.

How to divide numbers with zeros using a column?

The sequence and algorithm of actions is similar to the classic one discussed in the first section.

Among the nuances we note:

• If there are zeros at the end of the divisor and dividend, feel free to reduce them. Invite your child to cross them out with a pencil and continue dividing as usual. For example, in a situation of 1200:400, a child can remove both zeros from both numbers, but in a situation of 15600:560 - only one extreme one,
• if zero is only in the divisor, then select the first digit for the action, focusing on the number in front of it. For example, in the example 6537:70, put 9 in the quotient as the first number. For this example, multiply by both digits of the divisor and sign them under the three of the dividend.

When the dividend has a lot of zeros and the division process is over before you have used them all, then move them to the quotient after the numbers that were formed before. Example, 1000:2=500 - you moved the last two zeros.

So, we have examined the basic situations of dividing numbers of different numbers of digits into a column, determined the algorithm of action and emphasis for teaching a child.

Practice the knowledge you have acquired and help your child master mathematics.

Video: how to correctly divide numbers into a column?

Let's first look at simple cases of division, when the quotient results in a single-digit number.

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

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

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

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

The quotient will be a single digit number.

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

The value of the quotient of 184 and 23 is 8.

Let's consider more complex cases of division. Let's find the value of the quotient of 768 and 24.

The first incomplete dividend is 76 tens. This means that the quotient will have 2 digits.

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

Let's continue the division. The next partial dividend is 48 units. Let's divide 48 by 24. To make it easier to choose the quotient, let's divide 48 not by 24, but by 20. That is, if we divide 48 by 10, there will be 4 (the remainder is 8). And we divide 4 by 2, it becomes 2. This is the test digit of the quotient. We must first check if it will fit. Let's multiply. We see that the number 2 fits and, therefore, we can write it in place of the units of the quotient.

The meaning of the quotient of 768 and 24 is 32.

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

The first incomplete dividend is 153 hundreds, which means that the quotient will have three digits.

Let's determine the first digit of the quotient. Let's divide 153 by 56. To make it easier to find the quotient, let's divide 153 not by 56, but by 50. To do this, divide 153 by 10, the result will be 15 (remainder 3). And divide 15 by 5, it becomes 3. 3 is the test digit of the quotient. Remember: you cannot immediately write it down in private, but you must first check whether it is suitable. Let's multiply. And 168 is greater than 153. This means that the quotient will be less than 3. Let's check if the number 2 is suitable. Let's multiply. A . The remainder is less than the divisor, which means that the number 2 is suitable, it can be written in the place of hundreds in the quotient.

Let us form the following incomplete dividend. That's 414 tens. Let's divide 414 by 56. To make it more convenient to choose the quotient number, let's divide 414 not by 56, but by 50. . . Remember: 8 is a test number. Let's check it out. . And 448 is greater than 414, which means that the quotient 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. This means that the number fits and in the quotient we can write 7 in place of tens.

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

The value of the quotient of 15,344 and 56 is 274.

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

Bibliography

1. Mathematics. Textbook for 4th grade. beginning school At 2 o'clock/M.I. Moreau, M.A. Bantova - M.: Education, 2010.
2. Uzorova O.V., Nefedova E.A. Large math problem book. 4th grade. - M.: 2013. - 256 p.
3. Mathematics: textbook. for 4th grade. general education institutions with Russian language training. At 2 p.m. Part 1 / T.M. Chebotarevskaya, V.L. Drozd, A.A. Carpenter; lane with white language L.A. Bondareva. - 3rd ed., revised. - Minsk: Nar. Asveta, 2008. - 134 p.: ill.
4. Mathematics. 4th grade. Textbook. At 2 o'clock/Geidman B.P. and others - 2010. - 120 p., 128 p.

1. Ppt4web.ru ().
2. Myshared.ru ().
3. Viki.rdf.ru ​​().

Homework

Perform division

At school these actions are studied from simple to complex. Therefore, it is imperative to thoroughly understand the algorithm for performing these 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. Every student should learn this principle already in the first grade. Therefore, if you miss several lessons in a row, you will have to master the material on your own. Otherwise, later problems will arise not only with mathematics, but also with other subjects related to it.

The second prerequisite for successfully studying mathematics is to move on to examples of long division 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 teach it using the Pythagorean table. There is nothing superfluous, and multiplication is easier to learn in this case.

How are natural numbers multiplied in a column?

If difficulty arises in solving examples in a column for division and multiplication, then you should begin to solve the problem with multiplication. Since division is the inverse operation of multiplication:

1. Before multiplying two numbers, you need to look at them carefully. Choose the one with more digits (longer) and write it down first. Place the second one under it. Moreover, the numbers of the corresponding category must be under the same category. That is, the rightmost digit of the first number should 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 below the line so that its last digit is under the one you multiplied by.
3. Repeat the same with another digit of the lower number. But the result of 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 factor run out. Now they need to be folded. This will be the answer you are looking for.

Algorithm for multiplying decimals

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

The difference begins when the answer is written down. At this moment, it is necessary to count all the numbers that appear after the decimal points in both fractions. This is exactly how many of them need to be counted from the end of the answer and put a comma there.

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

Where to start learning division?

Before solving long division examples, you need to remember the names of the numbers that appear in the long division example. The first of them (the one that is divided) is divisible. The second (divided by) is the divisor. The answer is private.

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

After this, you can become familiar with the division rules and master them using specific examples. First simple ones, and then move on to more and more complex ones.

Algorithm for dividing numbers into a column

First, let us present the procedure for natural numbers divisible by a single-digit number. They will also be the basis for multi-digit divisors or decimal fractions. Only then should you make small changes, but more on that later:

• Before doing long division, you need to figure out where the dividend and divisor are.
• Write down the dividend. To the right of it is the divider.
• Draw a corner on the left and bottom near the last corner.
• Determine the incomplete dividend, that is, the number that will be minimal for division. Usually it consists of one digit, maximum of two.
• Choose the number that will be written first in the answer. It should be the number of times the divisor fits into the dividend.
• Write down the result of multiplying this number by the divisor.
• Write it under the incomplete dividend. Perform subtraction.
• Add to the remainder the first digit after the part that has already been divided.
• Choose the number for 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: remove the number, pick up the number, multiply, subtract.

How to solve long division if the divisor has more than one digit?

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 you have to work with the first three digits.

There is one more nuance in this division. The fact is that the remainder and the number added to it are sometimes not divisible by the divisor. Then you have to add another number in order. But the answer must be zero. If you are dividing three-digit numbers into a column, you may need to remove more than two digits. Then a rule is introduced: there should be one less zero in the answer than the number of digits removed.

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

• The incomplete dividend in it turns out to be the number 1208. The number 863 is placed in it only once. Therefore, the answer is supposed to be 1, and under 1208 write 863.
• After subtraction, the remainder is 345.
• You need to add the number 2 to it.
• The number 3452 contains 863 four times.
• Four must be written down as an answer. Moreover, when multiplied by 4, this is exactly the number obtained.
• The remainder after subtraction is zero. That is, the division is completed.

The answer in the example would be the number 14.

What if the dividend ends in zero?

Or a few zeros? In this case, the remainder is zero, but the dividend still contains zeros. There is no need to despair, everything is simpler than it might seem. It is enough to simply add to the answer all the zeros that remain undivided.

For example, you need to divide 400 by 5. The incomplete dividend is 40. Five fits into it 8 times. This means that the answer should be written as 8. When subtracting, there is no remainder left. That is, the division is completed, but a zero remains in the dividend. It will have to be added to the answer. Thus, dividing 400 by 5 equals 80.

What to do if you need to divide a decimal fraction?

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

The only difference will be the semicolon. It is supposed to be put in the answer as soon as the first digit from the fractional part is removed. Another way to say this is this: if you have finished dividing the whole part, put a comma and continue the solution further.

When solving examples of long division with decimal fractions, you need to remember that any number of zeros can be added to the part after the decimal point. Sometimes this is necessary in order to complete the numbers.

Dividing two decimals

It may seem complicated. But only at the beginning. After all, how to divide a column of fractions by a natural number is already clear. This means that we need to reduce this example to an already familiar form.

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

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

As an example: divide 28.4 by 3.2:

• They must first be multiplied by 10, since the second number has only one digit after the decimal point. Multiplying will give 284 and 32.
• They are supposed to be separated. Moreover, the whole number is 284 by 32.
• The first number chosen for the answer is 8. Multiplying it gives 256. The remainder is 28.
• The division of the whole part has ended, and a comma is required in the answer.
• Remove to remainder 0.
• Take 8 again.
• Remainder: 24. Add another 0 to it.
• Now you need to take 7.
• The result of multiplication is 224, the remainder is 16.
• Take down another 0. Take 5 each and you get exactly 160. The remainder is 0.

The division is complete. The result of example 28.4:3.2 is 8.875.

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

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

So, if you need to divide by 10, 100 or 1,000, then the decimal point is moved to the left by the same number of digits as there are zeros in the divisor. That is, when a number is divisible by 100, the decimal point must 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.

This action gives 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 decimal point 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 added to the left (in the whole part) or to the right (after the decimal point).

Division of periodic fractions

In this case, it will not be possible to obtain an accurate answer when dividing into a column. How to solve an example if you encounter a fraction with a period? Here we need to move on to ordinary fractions. And then divide them according to the previously learned rules.

For example, you need to divide 0.(3) by 0.6. The first fraction is periodic. It converts to the fraction 3/9, which when reduced gives 1/3. The second fraction is the final decimal. It’s even easier to write it down as usual: 6/10, which is equal to 3/5. The rule for dividing ordinary fractions requires replacing division with multiplication and divisor with the reciprocal. That is, the example comes down to multiplying 1/3 by 5/3. The answer will be 5/9.

If the example contains different fractions...

Then several solutions are possible. Firstly, you can try to convert a common fraction to a decimal. Then divide two decimals using the above algorithm.

Secondly, every final decimal fraction can be written as a common fraction. But this is not always convenient. Most often, such fractions turn out to be huge. And the answers are cumbersome. Therefore, the first approach is considered more preferable.

Teaching your child long division is easy. It is necessary to explain the algorithm of this action and consolidate the material covered.

• According to the school curriculum, division by columns begins to be explained to children in the third grade. Students who grasp everything on the fly quickly understand this topic
• But, if the child got sick and missed math lessons, or he did not understand the topic, then the parents must explain the material to the child themselves. It is necessary to convey information to him as clearly as possible
• Moms and dads must be patient during the child’s educational process, showing tact towards their child. Under no circumstances should you yell at your child if he doesn’t succeed in something, because this can discourage him from doing anything.

Important: In order for a child to understand the division of numbers, he must thoroughly know the multiplication table. If your child doesn't know multiplication well, he won't understand division.

During extracurricular activities at home, you can use cheat sheets, but the child must learn the multiplication table before starting the topic “Division.”

So, how to explain to a child division by column:

• Try to explain in small numbers first. Take counting sticks, for example 8 pieces
• Ask your child how many pairs are there in this row of sticks? Correct - 4. So, if you divide 8 by 2, you get 4, and when you divide 8 by 4, you get 2
• Let the child divide another number himself, for example, a more complex one: 24:4
• When the baby has mastered dividing prime numbers, then you can move on to dividing three-digit numbers into single-digit numbers.

Division is always a little more difficult for children than multiplication. But diligent additional studies at home will help the child understand the algorithm of this action and keep up with his peers at school.

Start with something simple—dividing by a single digit number:

Important: Calculate in your head so that the division comes out without a remainder, otherwise the child may get confused.

For example, 256 divided by 4:

• Draw a vertical line on a piece of paper and divide it in half from the right side. Write the first number on the left and the second number on the right above the line.
• Ask your child how many fours fit in a two - not at all
• Then we take 25. For clarity, separate this number from above with a corner. Ask the child again how many fours fit in twenty-five? That's right - six. We write the number “6” in the lower right corner under the line. The child must use the multiplication table to get the correct answer.
• Write down the number 24 under 25 and underline it to write down the answer - 1
• Ask again: how many fours can fit in a unit - not at all. Then we bring down the number “6” to one
• It turned out 16 - how many fours fit in this number? Correct - 4. Write “4” next to “6” in the answer
• Under 16 we write 16, underline it and it turns out “0”, which means we divided correctly and the answer turned out to be “64”

Written division by two digits

When the child has mastered division by a single digit number, you can move on. Written division by a two-digit number is a little more difficult, but if the child understands how this action is performed, then it will not be difficult for him to solve such examples.

Important: Again, start explaining with simple steps. The child will learn to select numbers correctly and it will be easy for him to divide complex numbers.

Do this simple action together: 184:23 - how to explain:

• Let's first divide 184 by 20, it turns out to be approximately 8. But we do not write the number 8 in the answer, since this is a test number
• Let's check if 8 is suitable or not. We multiply 8 by 23, we get 184 - this is exactly the number that is in our divisor. The answer will be 8

Important: For your child to understand, try taking 9 instead of 8, let him multiply 9 by 23, it turns out 207 - this is more than what we have in the divisor. The number 9 does not suit us.

So gradually the baby will understand division, and it will be easy for him to divide more complex numbers:

• Divide 768 by 24. Determine the first digit of the quotient - divide 76 not by 24, but by 20, we get 3. Write 3 in the answer under the line on the right
• Under 76 we write 72 and draw a line, write down the difference - it turns out 4. Is this number divisible by 24? No - we take down 8, it turns out 48
• Is 48 divisible by 24? That's right - yes. It turns out 2, write this number as the answer
• The result is 32. Now we can check whether we performed the division operation correctly. Do the multiplication in a column: 24x32, it turns out 768, then everything is correct

If the child has learned to divide by a two-digit number, then it is necessary to move on to the next topic. The algorithm for dividing by a three-digit number is the same as the algorithm for dividing by a two-digit number.

For example:

• Let's divide 146064 by 716. Take 146 first - ask your child whether this number is divisible by 716 or not. That's right - no, then we take 1460
• How many times can the number 716 fit in the number 1460? Correct - 2, so we write this number in the answer
• We multiply 2 by 716, we get 1432. We write this figure under 1460. The difference is 28, we write it under the line
• Let's take down 6. Ask your child - is 286 divisible by 716? That's right - no, so we write 0 in the answer next to 2. We also remove the number 4
• Divide 2864 by 716. Take 3 - a little, 5 - a lot, which means you get 4. Multiply 4 by 716, you get 2864
• Write 2864 under 2864, the difference is 0. Answer 204

Important: To check the correctness of division, multiply together with your child in a column - 204x716 = 146064. The division is done correctly.

The time has come to explain to the child that division can be not only whole, but also with a remainder. The remainder is always less than or equal to the divisor.

Division with a remainder should be explained using a simple example: 35:8=4 (remainder 3):

• How many eights fit in 35? Correct - 4. 3 left
• Is this number divisible by 8? That's right - no. It turns out the remainder is 3

After this, the child should learn that division can be continued by adding 0 to the number 3:

• The answer contains the number 4. After it we write a comma, since adding a zero indicates that the number will be a fraction
• It turns out 30. Divide 30 by 8, it turns out 3. Write it down, and under 30 we write 24, underline it and write 6
• We add the number 0 to number 6. Divide 60 by 8. Take 7 each, it turns out 56. Write under 60 and write down the difference 4
• To the number 4 we add 0 and divide by 8, we get 5 - write it down as the answer
• Subtract 40 from 40, we get 0. So, the answer is: 35:8 = 4.375

Advice: If your child doesn’t understand something, don’t get angry. Let a couple of days pass and try again to explain the material.

Mathematics lessons at school will also reinforce knowledge. Time will pass and the child will quickly and easily solve any division problems.

The algorithm for dividing numbers is as follows:

• Make an estimate of the number that will appear in the answer
• Find the first incomplete dividend
• Determine the number of digits in the quotient
• Find the numbers in each digit of the quotient
• Find the remainder (if there is one)

According to this algorithm, division is performed both by single-digit numbers and by any multi-digit number (two-digit, three-digit, four-digit, and so on).

When working with your child, often give him examples of how to perform the estimate. He must quickly calculate the answer in his head. For example:

• 1428:42
• 2924:68
• 30296:56
• 136576:64
• 16514:718

To consolidate the result, you can use the following division games:

• "Puzzle". Write five examples on a piece of paper. Only one of them must have the correct answer.

Condition for the child: Among several examples, only one was solved correctly. Find him in a minute.

Video: Arithmetic game for children addition, subtraction, division, multiplication

Video: Educational cartoon Mathematics Learning by heart the multiplication and division tables by 2

Division multi-digit or multi-digit numbers are convenient to produce in writing in a column. Let's figure out how to do this. Let's start by dividing a multi-digit number by a single-digit number, and gradually increase the digit of the dividend.

So let's divide 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 the quotient will be written under the divisor.

Now we begin to divide the dividend by the divisor bitwise 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 it with the divisor.

3 more 2 , Means 3 and there is an incomplete dividend. We put a dot in the quotient and determine how many more digits will be in the quotient - the same number as remained in the dividend after selecting the incomplete dividend. In our case, the quotient has the same number of digits as the dividend, that is, the most significant digit will be hundreds:

In order to 3 divide by 2 remember the multiplication table by 2 and find the number, when multiplied by 2 we get the greatest product, which is less than 3.

2 × 1 = 2 (2< 3)

2 × 2 = 4 (4 > 3)

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

Let's write it down 1 to the quotient in place of the first point (in the hundreds place), and write the found product under the dividend:

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

The resulting value is compared with the divisor. 15 more 2 , which means we have found the second incomplete dividend. To find the result of division 15 on 2 again remember the multiplication table 2 and find the greatest product that is less 15 :

2 × 7 = 14 (14< 15)

2 × 8 = 16 (16 > 15)

The required multiplier 7 , we write it as 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 quotient and divisor:

We continue the division, why we find third incomplete dividend. We lower the next digit of the dividend:

We divide the incomplete dividend by 2, putting the resulting value in the category of units of the quotient. Let's check the correctness of the division:

2 × 7 = 14

We write the result of dividing the third incomplete dividend by the divisor into the quotient and find the difference:

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

Let's complicate the problem 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.

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

10 – 10 = 0

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

We compare the second incomplete dividend with the divisor.

2 < 5

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

20 ÷ 5 = 4

We write the answer in the category of units of the quotient 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 the dividend and divisor have zeros in the low-order digits, then before dividing they can be reduced, for example:

As many zeros in the low-order digit of the dividend we remove, we remove the same number of zeros in the low-order digits of the divisor.

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

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

1. Place the dividend on the left and the divisor on the right. We remember that we divide the dividend by isolating incomplete dividends bit by bit and dividing them sequentially by the divisor. The digits in the incomplete dividend are allocated from left to right from high to low.
2. If the dividend and divisor have zeros in the lower digits, then they can be reduced before dividing.
3. We determine the first incomplete divisor:

A) allocate the highest digit of the dividend into the incomplete divisor;

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

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

1. We determine how many digits there will be in the quotient, and put as many dots in 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) are the same as the number of digits left in the dividend after selecting the incomplete dividend.
2. We divide the incomplete dividend by the divisor; to do this, we find a number that, when multiplied by the divisor, would result in a number either equal to or less than the incomplete dividend.
3. We write the found number in place of the next quotient digit (dot), and write the result of multiplying it by the divisor under the incomplete dividend and find their difference.
4. If the difference found is less than or equal to the incomplete dividend, then we have correctly divided the incomplete dividend by the divisor.
5. If there are still digits left in the dividend, then we continue division, otherwise we go to 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 point (b), if less, then we have found the incomplete dividend and can move on to point 4;

b) add the next digit of the dividend to the incomplete dividend, and write 0 in the place of the next digit (dot) in the quotient;

c) go to point (a).

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

We talked about dividing a multi-digit number by a single-digit number. In the case where the divider is larger, division is performed in the same way: