Long division with remainder 3. Division with remainder. Dividing natural numbers with a remainder. Checking the result

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

• According to school curriculum, division by column begins to be explained to children already 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 during educational process children must be patient, 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 classes at home will help your 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 baby 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

What does 3rd grade do in math? Division with a remainder, examples and problems - this is what is studied in the lessons. Division with a remainder and the algorithm for such calculations will be discussed in the article.

Peculiarities

Let's look at the topics included in the program that 3rd grade is studying. Division with a remainder is included in a special section of mathematics. What is it about? If the dividend is not evenly divisible by the divisor, then a remainder remains. For example, we divide 21 by 6. It turns out 3, but the remainder remains 3.

In cases where, when dividing natural numbers, the remainder is zero, it is said that a complete division has been performed. For example, if 25 is divided by 5, the result is 5. The remainder is zero.

Solving Examples

In order to perform division with a remainder, a specific notation is used.

Let's give examples in mathematics (3rd grade). Division with a remainder need not be written in a column. It is enough to write in the line: 13:4=3 (remainder 1) or 17:5=3 (remainder 2).

Let's look at everything in more detail. For example, dividing 17 by three gives the integer five and also leaves a remainder of two. What is the procedure for solving this example for division with a remainder? First you need to find the maximum number up to 17, which can be divided without a remainder by three. The largest would be 15.

Next, divide 15 by the number three, the result of the action will be the number five. Now we subtract the number we found from the dividend, that is, from 17 we subtract 15, we get two. A mandatory action is to reconcile the divisor and remainder. After verification, the response of the completed action must be recorded. 17:3=15 (remainder 2).

If the remainder is greater than the divisor, the action was performed incorrectly. This is the algorithm used to perform class 3 division with a remainder. The examples are first analyzed by the teacher on the board, then the children are asked to test their knowledge by doing independent work.

Example with multiplication

One of the most difficult topics that 3rd grade faces is division with a remainder. The examples can be complex, especially when additional calculations are required, recorded in a column.

Let's say you need to divide the number 190 by 27 to obtain the minimum remainder. Let's try to solve the problem using multiplication.

Let's select a number that, when multiplied, will give a figure as close as possible to the number 190. If we multiply 27 by 6, we get the number 162. Subtract the number 162 from 190, the remainder will be 28. It turns out to be greater than the original divisor. Therefore, the number six is ​​not suitable as a multiplier for our example. Let's continue solving the example, taking the number 7 for multiplication.

Multiplying 27 by 7, we get the product 189. Next, we will check the correctness of the solution, to do this, subtract the result obtained from 190, that is, subtract the number 189. The remainder will be 1, which is clearly less than 27. This is how they are solved complex expressions at school (3rd grade, division with remainder). Examples always include recording a response. The entire mathematical expression can be written as follows: 190:27 = 7 (remainder 1). Similar calculations can be made in a column.

This is exactly how grade 3 does division with a remainder. The examples given above will help you understand the algorithm for solving such problems.

Conclusion

In order for students primary classes If correct computational skills have been developed, the teacher, during mathematics classes, must pay attention to explaining the algorithm of the child’s actions when solving problems involving division with a remainder.

According to the new federal state educational standards special attention is paid individual approach to learning. The teacher must select tasks for each child taking into account his individual abilities. At each stage of teaching the rules of division with a remainder, the teacher must carry out intermediate control. It allows him to identify the main problems that arise with the assimilation of the material for each student, timely correct knowledge and skills, eliminate emerging problems, and obtain the desired result.

Division is one of the four basic mathematical operations (addition, subtraction, multiplication). Division, like other operations, is important not only in mathematics, but also in Everyday life. For example, you as a whole class (25 people) donate money and buy a gift for the teacher, but you don’t spend it all, there will be change left over. So you will need to divide the change among everyone. The division operation comes into play to help you solve this problem.

Division is an interesting operation, as we will see in this article!

Dividing numbers

So, a little theory, and then practice! What is division? Division is breaking something into equal parts. That is, it could be a bag of sweets that needs to be divided into equal parts. For example, there are 9 candies in a bag, and the person who wants to receive them is three. Then you need to divide these 9 candies among three people.

It is written like this: 9:3, the answer will be the number 3. That is, dividing the number 9 by the number 3 shows the number of three numbers contained in the number 9. The reverse action, a check, will be multiplication. 3*3=9. Right? Absolutely.

So let's look at example 12:6. First, let's name each component of the example. 12 – dividend, that is. a number that can be divided into parts. 6 is a divisor, this is the number of parts into which the dividend is divided. And the result will be a number called “quotient”.

Let's divide 12 by 6, the answer will be the number 2. You can check the solution by multiplying: 2*6=12. It turns out that the number 6 is contained 2 times in the number 12.

Division with remainder

What is division with a remainder? This is the same division, only the result is not an even number, as shown above.

For example, let's divide 17 by 5. Since the largest number divisible by 5 to 17 is 15, then the answer will be 3 and the remainder is 2, and is written like this: 17:5 = 3(2).

For example, 22:7. In the same way, we determine the maximum number divisible by 7 to 22. This number is 21. The answer then will be: 3 and the remainder 1. And it is written: 22:7 = 3 (1).

Division by 3 and 9

A special case of division would be division by the number 3 and the number 9. If you want to find out whether a number is divisible by 3 or 9 without a remainder, then you will need:

Find the sum of the digits of the dividend.

Divide by 3 or 9 (depending on what you need).

If the answer is obtained without a remainder, then the number will be divided without a remainder.

For example, the number 18. The sum of the digits is 1+8 = 9. The sum of the digits is divisible by both 3 and 9. The number 18:9=2, 18:3=6. Divided without remainder.

For example, the number 63. The sum of the digits is 6+3 = 9. Divisible by both 9 and 3. 63:9 = 7, and 63:3 = 21. Such operations are carried out with any number to find out whether it is divisible with the remainder by 3 or 9, or not.

Multiplication and division

Multiplication and division are opposite operations. Multiplication can be used as a test for division, and division can be used as a test for multiplication. You can learn more about multiplication and master the operation in our article about multiplication. Which describes multiplication in detail and how to do it correctly. There you will also find the multiplication table and examples for training.

Here is an example of checking division and multiplication. Let's say the example is 6*4. Answer: 24. Then let's check the answer by division: 24:4=6, 24:6=4. It was decided correctly. In this case, the check is performed by dividing the answer by one of the factors.

Or an example is given for the division 56:8. Answer: 7. Then the test will be 8*7=56. Right? Yes. IN in this case verification is done by multiplying the answer by the divisor.

Division 3 class

In third grade they are just starting to go through division. Therefore, third graders solve the simplest problems:

Problem 1. A factory worker was given the task of putting 56 cakes into 8 packages. How many cakes should be put in each package to make the same amount in each?

Problem 2. On New Year's Eve at school, children in a class of 15 students were given 75 candies. How many candies should each child receive?

Problem 3. Roma, Sasha and Misha picked 27 apples from the apple tree. How many apples will each person get if they need to be divided equally?

Problem 4. Four friends bought 58 cookies. But then they realized that they could not divide them equally. How many additional cookies do the kids need to buy so that each gets 15?

Division 4th grade

The division in the fourth grade is more serious than in the third. All calculations are carried out using the column division method, and the numbers involved in the division are not small. What is long division? You can find the answer below:

Column division

What is long division? This is a method that allows you to find the answer to dividing large numbers. If prime numbers like 16 and 4 can be divided, and the answer is clear - 4. Then 512:8 is not easy for a child in his mind. And it’s our task to talk about the technique for solving such examples.

Let's look at an example, 512:8.

1 step. Let's write the dividend and divisor as follows:

The quotient will ultimately be written under the divisor, and the calculations under the dividend.

Step 2. We start dividing from left to right. First we take the number 5:

Step 3. The number 5 is less than the number 8, which means it will not be possible to divide. Therefore, we take another digit of the dividend:

Now 51 is greater than 8. This is an incomplete quotient.

Step 4. We put a dot under the divisor.

Step 5. After 51 there is another number 2, which means there will be one more number in the answer, that is. quotient is a two-digit number. Let's put the second point:

Step 6. We begin the division operation. Largest number, divisible by 8 without a remainder to 51 – 48. Dividing 48 by 8, we get 6. Write the number 6 instead of the first dot under the divisor:

Step 7. Then write the number exactly below the number 51 and put a “-” sign:

Step 8. Then we subtract 48 from 51 and get the answer 3.

* 9 step*. We take down the number 2 and write it next to the number 3:

Step 10 We divide the resulting number 32 by 8 and get the second digit of the answer – 4.

So the answer is 64, without remainder. If we divided the number 513, then the remainder would be one.

Division of three digits

Dividing three-digit numbers is done using the long division method, which was explained in the example above. An example of just a three-digit number.

Division of fractions

Dividing fractions is not as difficult as it seems at first glance. For example, (2/3):(1/4). The method of this division is quite simple. 2/3 is the dividend, 1/4 is the divisor. You can replace the division sign (:) with multiplication ( ), but to do this you need to swap the numerator and denominator of the divisor. That is, we get: (2/3)(4/1), (2/3)*4, this is equal to 8/3 or 2 integers and 2/3. Let's give another example, with an illustration for better understanding. Consider the fractions (4/7):(2/5):

As in the previous example, we reverse the 2/5 divisor and get 5/2, replacing division with multiplication. We then get (4/7)*(5/2). We make a reduction and answer: 10/7, then take out the whole part: 1 whole and 3/7.

Dividing numbers into classes

Let's imagine the number 148951784296, and divide it into three digits: 148,951,784,296. So, from right to left: 296 is the class of units, 784 is the class of thousands, 951 is the class of millions, 148 is the class of billions. In turn, in each class 3 digits have their own digit. From right to left: the first digit is units, the second digit is tens, the third is hundreds. For example, the class of units is 296, 6 is ones, 9 is tens, 2 is hundreds.

Division of natural numbers

Division of natural numbers is the simplest division described in this article. It can be either with or without a remainder. The divisor and dividend can be any non-fractional, integer numbers.

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Division presentation

Presentation is another way to visualize the topic of division. Below we will find a link to an excellent presentation that does a good job of explaining how to divide, what division is, what dividend, divisor and quotient are. Don’t waste your time, but consolidate your knowledge!

Examples for division

Easy level

Average level

Difficult level

Games for developing mental arithmetic

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Game "Simplification"

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The easiest way to divide multi-digit numbers is with a column. Column division is also called corner division.

Before we begin to perform division by a column, we will consider in detail the very form of recording division by a column. First, write down the dividend and put a vertical line to the right of it:

Behind the vertical line, opposite the dividend, write the divisor and draw a horizontal line under it:

Under the horizontal line, the resulting quotient will be written step by step:

Intermediate calculations will be written under the dividend:

The full form of writing division by column is as follows:

How to divide by column

Let's say we need to divide 780 by 12, write the action in a column and proceed to division:

Column division is performed in stages. The first thing we need to do is determine the incomplete dividend. We look at the first digit of the dividend:

this number is 7, since it is less than the divisor, we cannot start division from it, which means we need to take another digit from the dividend, the number 78 is greater than the divisor, so we start division from it:

In our case the number 78 will be incomplete divisible, it is called incomplete because it is only a part of the divisible.

Having determined the incomplete dividend, we can find out how many digits will be in the quotient, for this we need to calculate how many digits are left in the dividend after the incomplete dividend, in our case there is only one digit - 0, this means that the quotient will consist of 2 digits.

Having found out the number of digits that should be in the quotient, you can put dots in its place. If, when completing the division, the number of digits turns out to be more or less than the indicated points, then an error was made somewhere:

Let's start dividing. We need to determine how many times 12 is contained in the number 78. To do this, we sequentially multiply the divisor by the natural numbers 1, 2, 3, ... until we get a number as close as possible to the incomplete dividend or equal to it, but not exceeding it. Thus, we get the number 6, write it under the divisor, and from 78 (according to the rules of column subtraction) we subtract 72 (12 6 = 72). After we subtract 72 from 78, the remainder is 6:

Please note that the remainder of the division shows us whether we have chosen the number correctly. If the remainder is equal to or greater than the divisor, then we did not choose the number correctly and we need to take a larger number.

To the resulting remainder - 6, add the next digit of the dividend - 0. As a result, we get an incomplete dividend - 60. Determine how many times 12 is contained in the number 60. We get the number 5, write it in the quotient after the number 6, and subtract 60 from 60 ( 12 5 = 60). The remainder is zero:

Since there are no more digits left in the dividend, it means 780 is divided by 12 completely. As a result of performing long division, we found the quotient - it is written under the divisor:

Let's consider an example when the quotient turns out to be zeros. Let's say we need to divide 9027 by 9.

We determine the incomplete dividend - this is the number 9. We write 1 into the quotient and subtract 9 from 9. The remainder is zero. Usually, if in intermediate calculations the remainder is zero, it is not written down:

We take down the next digit of the dividend - 0. We remember that when dividing zero by any number there will be zero. We write zero into the quotient (0: 9 = 0) and subtract 0 from 0 in intermediate calculations. Usually, in order not to clutter up intermediate calculations, calculations with zero are not written:

We take down the next digit of the dividend - 2. In intermediate calculations it turned out that the incomplete dividend (2) is less than the divisor (9). In this case, write zero to the quotient and remove the next digit of the dividend:

We determine how many times 9 is contained in the number 27. We get the number 3, write it as a quotient, and subtract 27 from 27. The remainder is zero:

Since there are no more digits left in the dividend, it means that the number 9027 is divided by 9 completely:

Let's consider an example when the dividend ends in zeros. Let's say we need to divide 3000 by 6.

We determine the incomplete dividend - this is the number 30. We write 5 into the quotient and subtract 30 from 30. The remainder is zero. As already mentioned, it is not necessary to write zero in the remainder in intermediate calculations:

We take down the next digit of the dividend - 0. Since dividing zero by any number will result in zero, we write zero in the quotient and subtract 0 from 0 in intermediate calculations:

We take down the next digit of the dividend - 0. We write another zero into the quotient and subtract 0 from 0 in intermediate calculations. Since in intermediate calculations the calculation with zero is usually not written down, the entry can be shortened, leaving only the remainder - 0. Zero in the remainder in at the very end of the calculation is usually written to show that the division is complete:

Since there are no more digits left in the dividend, it means 3000 is divided by 6 completely:

Column division with remainder

Let's say we need to divide 1340 by 23.

We determine the incomplete dividend - this is the number 134. We write 5 into the quotient and subtract 115 from 134. The remainder is 19:

We take down the next digit of the dividend - 0. We determine how many times 23 is contained in the number 190. We get the number 8, write it into the quotient, and subtract 184 from 190. We get the remainder 6:

Since there are no more digits left in the dividend, the division is over. The result is an incomplete quotient of 58 and a remainder of 6:

1340: 23 = 58 (remainder 6)

It remains to consider an example of division with a remainder, when the dividend is less than the divisor. Let us need to divide 3 by 10. We see that 10 is never contained in the number 3, so we write 0 as a quotient and subtract 0 from 3 (10 · 0 = 0). Draw a horizontal line and write down the remainder - 3:

3: 10 = 0 (remainder 3)

Long division calculator

This calculator will help you perform long division. Simply enter the dividend and divisor and click the Calculate button.

How to teach a child division? The simplest method is learn long division. This is much easier than carrying out calculations in your head; it helps you avoid getting confused, not “losing” the numbers, and developing a mental scheme that will work automatically in the future.

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How is it carried out?

Division with a remainder is a method in which a number cannot be divided into exactly several parts. As a result of this mathematical operation, in addition to the whole part, an indivisible piece remains.

Let's give a simple example how to divide with remainder:

There is a jar for 5 liters of water and 2 jars of 2 liters each. When water is poured from a five-liter jar into two-liter jars, 1 liter of unused water will remain in the five-liter jar. This is the remainder. In digital form it looks like this:

5:2=2 rest (1). Where is 1 from? 2x2=4, 5-4=1.

Now let's look at the order of division into a column with a remainder. This visually simplifies the calculation process and helps not to lose numbers.

The algorithm determines the location of all elements and the sequence of actions by which the calculation is performed. As an example, let's divide 17 by 5.

Main stages:

1. Correct entry. Dividend (17) – located according to left side. To the right of the dividend, write the divisor (5). A vertical line is drawn between them (indicating the division sign), and then, from this line, a horizontal line is drawn, emphasizing the divisor. The main features are indicated in orange.
2. Search for the whole. Next, the first and simplest calculation is carried out - how many divisors fit into the dividend. Let's use the multiplication table and check in order: 5*1=5 - fits, 5*2=10 - fits, 5*3=15 - fits, 5*4=20 - doesn't fit. Five times four is more than seventeen, which means the fourth five does not fit. Let's go back to three. A 17 liter jar will fit 3 five liter jars. We write the result in the form: 3 is written under the line, under the divisor. 3 is an incomplete quotient.
3. Definition of remainder. 3*5=15. We write 15 under the dividend. We draw a line (indicated by the “=” sign). Subtract the resulting number from the dividend: 17-15=2. We write the result below the line - in a column (hence the name of the algorithm). 2 is the remainder.

Note! When dividing in this way, the remainder must always be less than the divisor.

When the divisor is greater than the dividend

Difficulty arises when the divisor is larger than the dividend. Decimals they are not yet studied in the 3rd grade curriculum, but, following the logic, the answer should be written in the form of a fraction - at best a decimal, at worst - a simple one. But (!) in addition to the program, the calculation method limited by the task: it is necessary not to divide, but to find the remainder! some of them are not! How to solve such a problem?

Note! There is a rule for cases when the divisor is greater than the dividend: the partial quotient is equal to 0, the remainder is equal to the dividend.

How to divide the number 5 by the number 6, highlighting the remainder? How many 6-liter cans will fit into a 5-liter jar? , because 6 is greater than 5.

The assignment requires filling 5 liters - not a single one has been filled. This means that all 5 remain. Answer: partial quotient = 0, remainder = 5.

Division begins to be studied in the third grade of school. By this time, students should already be able to do the division of two-digit numbers by single-digit numbers.

Solve the problem: 18 sweets need to be distributed to five children. How many candies will be left?

Examples:

We find the incomplete quotient: 3*1=3, 3*2=6, 3*3=9, 3*4=12, 3*5=15. 5 – overkill. Let's go back to 4.

Remainder: 3*4=12, 14-12=2.

Answer: incomplete quotient 4, 2 left.

You may ask why when divided by 2, the remainder is either 1 or 0. According to the multiplication table, between digits that are multiples of two there is a difference of one.

Another task: 3 pies must be divided into two.

Divide 4 pies between two.

Divide 5 pies between two.

Working with multi-digit numbers

The 4th grade program offers more difficult process carrying out division with increasing calculated numbers. If in the third grade calculations were carried out on the basis of a basic multiplication table ranging from 1 to 10, then fourth graders carry out calculations with multi-digit numbers over 100.

It is most convenient to perform this action in a column, since the incomplete quotient will also be a two-digit number (in most cases), and the column algorithm simplifies the calculations and makes them more visual.

Let's divide multi-digit numbers to double digits: 386:25

This example differs from the previous ones in the number of calculation levels, although the calculations are carried out according to the same principle as before. Let's take a closer look:

386 is the dividend, 25 is the divisor. It is necessary to find the incomplete quotient and select the remainder.

First level

The divisor is a two-digit number. The dividend is three-digit. We select the first two left digits of the dividend - this is 38. We compare them with the divisor. Is 38 more than 25? Yes, that means 38 can be divided by 25. How many whole 25 are in 38?

25*1=25, 25*2=50. 50 is more than 38, let's go back one step.

Answer - 1. Write the unit to the zone not completely private.

38-25=13. Write the number 13 below the line.

Second level

Is 13 more than 25? No - that means you can “lower” the number 6 down by adding it next to 13, on the right. It turned out to be 136. Is 136 more than 25? Yes - that means you can subtract it. How many times can 25 fit into 136?

25*1=25, 25*2=50, 25*3=75, 25*4=100, 25*5=125, 256*=150. 150 is more than 136 – we go back one step. We write the number 5 in the incomplete quotient zone, to the right of one.

Calculate the remainder:

136-125=11. Write it below the line. Is 11 more than 25? No - division cannot be carried out. Does the dividend have digits left? No - there is nothing more to share. The calculations are completed.

Answer: the partial quotient is 15, the remainder is 11.

What if such a division is proposed, when the two-digit divisor is greater than the first two digits of the multi-digit dividend? In this case, the third (fourth, fifth and subsequent) digit of the dividend takes part in the calculations immediately.

Let's give examples for division with three- and four-digit numbers:

75 is a two-digit number. 386 – three-digit. Compare the first two digits on the left with the divisor. 38 is more than 75? No - division cannot be carried out. We take all 3 numbers. Is 386 more than 75? Yes, division can be done. We carry out calculations.

75*1=75, 75*2=150, 75*3=225, 75*4=300, 75*5= 375, 75*6=450. 450 is more than 386 – we go back a step. We write 5 in the incomplete quotient zone.

Find the remainder: 386-375=11. Is 11 more than 75? No. Are there any digits left for the dividend? No. The calculations are completed.

Answer: partial quotient = 5, remainder - 11.

Let's check: is 11 more than 35? No - division cannot be carried out. Let's substitute the third number - 119 is more than 35? Yes, we can carry out the action.

35*1=35, 35*2=70, 35*3=105, 35*4=140. 140 is more than 119 – we go back one step. We write 3 in the incomplete balance zone.

Find the remainder: 119-105=14. Is 14 over 35? No. Are there any digits left for the dividend? No. The calculations are completed.

Answer: incomplete quotient = 3, 14 left.

Let's check: is 11 greater than 99? No, we substitute another number. Is 119 more than 99? Yes - let's start the calculations.

11<99, 119>99.

99*1=99, 99*2=198 – overkill. We write 1 in the incomplete quotient.

Find the remainder: 119-99=20. 20<99. Опускаем 5. 205>99. Let's calculate.

99*1=99, 99*2=198, 99*3=297. Too much. We write 2 in the incomplete quotient.

Find the remainder: 205-198=7.

Answer: partial quotient = 12, remainder - 7.

Division with remainder - examples

Learning to divide by column with a remainder

Conclusion

This is how calculations are carried out. If you are careful and follow the rules, then there will be nothing complicated here. Every student can learn to count with a column, because it is fast and convenient.