Calculator division into a column of integers. Long division

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 the 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 to know 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:

1. Numbers.
2. Signs of arithmetic operations.
3. 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

1. It helps the student not only to quickly get the correct result of mathematical calculations, but also to understand the very principle of calculation.
2. Very simple, intuitive interface for every user.
3. You can install the application even on the most budget Android device with operating system 2.2 and later.
4. 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 the principle of calculating in a column to elementary school students, 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.

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

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

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

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

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

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

2 × 1 = 2 (2< 3)

2 × 2 = 4 (4 > 3)

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

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

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

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

2 × 7 = 14 (14< 15)

2 x 8 = 16 (16 > 15)

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

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

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

2 x 7 = 14

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

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

Let's complicate the task and give another example:

1020 ÷ 5

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

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

1 < 5

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

10 > 5 We have found an incomplete dividend.

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

10 – 10 = 0

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

Compare the second incomplete dividend with the divisor.

2 < 5

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

20 ÷ 5 = 4

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

And 2 more rules for dividing into a column:

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

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

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

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

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

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

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

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

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

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

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

c) go to point (a).

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

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

How to divide decimal fractions by natural numbers? Consider the rule and its application with examples.

To divide a decimal by a natural number, you need:

1) divide the decimal fraction by the number, ignoring the comma;

2) when the division of the integer part is over, put a comma in the private part.

Examples.

Split decimals:

To divide a decimal by a natural number, divide without paying attention to the comma. 5 is not divisible by 6, so we put zero in the quotient. The division of the integer part is over, in the private we put a comma. We take zero. Divide 50 by 6. Take 8 each. 6∙8=48. From 50 we subtract 48, in the remainder we get 2. We demolish 4. We divide 24 by 6. We get 4. The remainder is zero, which means the division is over: 5.04: 6 = 0.84.

2) 19,26: 18

We divide the decimal fraction by a natural number, ignoring the comma. We divide 19 by 18. We take 1 each. The division of the integer part is over, in the private we put a comma. We subtract 18 from 19. The remainder is 1. We demolish 2. 12 is not divisible by 18, in private we write zero. We demolish 6. 126 divided by 18, we get 7. The division is over: 19.26: 18 = 1.07.

Divide 86 by 25. Take 3 each. 25∙3=75. We subtract 75 from 86. The remainder is 11. The division of the integer part is over, in the private we put a comma. Demolish 5. Take 4 each. 25∙4=100. Subtract 100 from 115. The remainder is 15. We demolish zero. We divide 150 by 25. We get 6. The division is over: 86.5: 25 = 3.46.

4) 0,1547: 17

Zero is not divisible by 17, we write zero in private. The division of the integer part is over, in the private we put a comma. We demolish 1. 1 is not divisible by 17, we write zero in private. We demolish 5. 15 is not divisible by 17, in private we write zero. Demolish 4. Divide 154 by 17. Take 9 each. 17∙9=153. We subtract 153 from 154. The remainder is 1. We take down 7. We divide 17 by 17. We get 1. The division is over: 0.1547: 17 = 0.0091.

5) A decimal fraction can also be obtained by dividing two natural numbers.

When dividing 17 by 4, we take 4 each. The division of the integer part is over, in the private we put a comma. 4∙4=16. We subtract 16 from 17. The remainder is 1. We demolish zero. Divide 10 by 4. Take 2 each. 4∙2=8. We subtract 8 from 10. The remainder is 2. We demolish zero. We divide 20 by 4. We take 5 each. The division is over: 17: 4 \u003d 4.25.

And a couple more examples for division decimal fractions for natural numbers:

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 will hand over the money with a whole class (25 people) and buy a gift for the teacher, but you will not spend everything, there will be change. So you will have to share the change among all. The division operation comes into play to help you solve this problem.

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

Number division

So, a little theory, and then practice! What is division? Division is breaking something into equal parts. That is, it can be a package of sweets that needs to be divided into equal parts. For example, there are 9 sweets in a bag, and the person who wants to receive them has three. Then you need to divide these 9 sweets into 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 numbers three contained in the number 9. The reverse action, the test, will be multiplication. 3*3=9. Right? Absolutely.

So, consider the example of 12:6. First, let's name each component of the example. 12 - divisible, that is. number that is divisible. 6 - divisor, this is the number of parts into which the dividend is divided. And the result will be a number called "private".

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 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, the answer is 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. Then the answer 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 will be division by the number 3 and the number 9. If you want to know 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 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 a trace.

For example, the number 63. The sum of the digits 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 if it is divisible with the remainder 3 or 9 or not.

Multiplication and division

Multiplication and division are opposite operations. Multiplication can be used as a division test, and division as a multiplication test. You can learn more about multiplication and master the operation in our article about multiplication. In which multiplication is described in detail and how to perform 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 an example is 6*4. Answer: 24. Then let's check the answer by division: 24:4=6, 24:6=4. Decided right. In this case, the check is made by dividing the answer by one of the factors.

Or an example is given for dividing 56:8. Answer: 7. Then the test will be 8*7=56. Right? Yes. AT this case the check is made by multiplying the answer by the divisor.

Division 3 class

In the third grade, division is just beginning to pass. Therefore, third-graders solve the simplest problems:

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

Task 2. On New Year's Eve, the school gave out 75 sweets to children in a class of 15 students. How many candies should each child get?

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

Task 4. Four friends bought 58 cookies. But then they realized that they could not divide them equally. How many cookies do you need to buy for each child to get 15 cookies?

Division 4 class

Division in the fourth grade is more serious than in the third. All calculations are carried out by dividing into a column, and the numbers that participate in the division are not small. What is division into a column? You can find the answer below:

Long division

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

Consider the example, 512:8.

1 step. We write the dividend and the divisor as follows:

The quotient will be written as a result under the divisor, and the calculations under the dividend.

2 step. The division starts from left to right. Let's take number 5 first.

3 step. Number 5 less than a number 8, which means that it will not be possible to divide. Therefore, we take one more digit of the dividend:

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

4 step. We put a dot under the divider.

5 step. After 51 there is another number 2, which means that the answer will have one more number, that is. private - two-digit number. We put the second point:

6 step. We begin the division operation. Largest number, divisible without a remainder by 8 to 51 - 48. Dividing 48 by 8, we get 6. We write the number 6 instead of the first point under the divisor:

7 step. Then we write the number exactly under the number 51 and put the "-" sign:

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

* 9 step*. We demolish the number 2 and write next to the number 3:

10 step The resulting number 32 is divided by 8 and we get the second digit of the answer - 4.

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

Three-digit division

Division three-digit numbers is performed by the division into a column method, which was explained in the example above. An example of just the same 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 division method is quite simple. 2/3 is the dividend, 1/4 is the divisor. You can replace the division sign (:) with multiplication ( ), but for 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 a better understanding. Consider fractions (4/7):(2/5):

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

Dividing a Number into Classes

Let's imagine the number 148951784296, and divide it by 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 category. 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 units, 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 both with a remainder and without a remainder. The divisor and dividend can be any non-fractional, whole numbers.

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division presentation

The presentation is another way to visually show the topic of division. Below we will find a link to an excellent presentation that explains well how to divide, what division is, what is dividend, divisor and quotient. Don't waste your time and consolidate your knowledge!

Division examples

Easy level

Average level

Difficult level

Games for the development of mental counting

Special educational games developed with the participation of Russian scientists from Skolkovo will help improve oral counting skills in an interesting game form.

Game "Guess the operation"

The game "Guess the operation" develops thinking and memory. The main essence of the game must be chosen mathematical sign for the equality to be true. Examples are given on the screen, look carefully and put the desired “+” or “-” sign so that the equality is true. The sign "+" and "-" are located at the bottom of the picture, select the desired sign and click on the desired button. If you answer correctly, you score points and continue playing.

Game "Simplify"

The game "Simplify" develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and continue playing.

Game "Fast Addition"

The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers, the sum of which is equal to a given number. This game is given a matrix from one to sixteen. A given number is written above the matrix, you must select the numbers in the matrix so that the sum of these numbers is equal to the given number. If you answer correctly, you score points and continue playing.

Game "Visual Geometry"

The game "Visual Geometry" develops thinking and memory. The main essence of the game is to quickly count the number of shaded objects and select it from the list of answers. In this game, blue squares are shown on the screen for a few seconds, they must be quickly counted, then they close. Four numbers are written below the table, you must select one correct number and click on it with the mouse. If you answer correctly, you score points and continue playing.

Piggy bank game

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Game "Fast addition reload"

The game "Fast Addition Reboot" develops thinking, memory and attention. The main essence of the game is to choose the correct terms, the sum of which will be equal to a given number. In this game, three numbers are given on the screen and the task is given, add the number, the screen indicates which number to add. You select the desired numbers from the three numbers and press them. If you answer correctly, then you score points and continue to play further.

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One of milestones in teaching a child mathematical operations - learning the operation of division prime numbers. How to explain division to a child, when can you start mastering this topic?

In order to teach a child division, it is necessary that by the time of learning he has already mastered such mathematical operations as addition, subtraction, and also has a clear understanding of the very essence of the operations of multiplication and division. That is, he must understand that division is the division of something into equal parts. It is also necessary to teach multiplication operations and learn the multiplication table.

I already wrote about how this article can be useful for you.

We master the operation of division (division) into parts in a playful way

At this stage, it is necessary to form in the child the understanding that division is the division of something into equal parts. The easiest way to teach a child to do this is to invite him to share a certain number of items among his friends or family members.

For example, take 8 identical cubes and invite the child to divide into two equal parts - for him and another person. Vary and complicate the task, invite the child to divide 8 cubes not into two, but into four people. Analyze the result with him. Change the components, try with a different number of objects and people into which these objects need to be divided.

Important: Make sure that at first the child operates with an even number of objects, so that the result of division is the same number of parts. This will be useful in the next step, when the child needs to understand that division is the inverse of multiplication.

Multiply and divide using the multiplication table

Explain to your child that, in mathematics, the opposite of multiplication is called division. Using the multiplication table, demonstrate to the student, using any example, the relationship between multiplication and division.

Example: 4x2=8. Remind your child that the result of multiplication is the product of two numbers. Then explain that division is the inverse of multiplication and illustrate this clearly.

Divide the resulting product "8" from the example - by any of the factors - "2" or "4", and the result will always be another factor that was not used in the operation.

You also need to teach the young student how the categories that describe the operation of division are called - “divisible”, “divisor” and “quotient”. Use an example to show which numbers are divisible, divisor and quotient. Consolidate this knowledge, they are necessary for further learning!

In fact, you need to teach your child the multiplication table “in reverse”, and you need to memorize it as well as the multiplication table itself, because this will be necessary when you start teaching long division.

Divide by a column - give an example

Before starting the lesson, remember with your child how the numbers are called during the division operation. What is a "divisor", "divisible", "quotient"? Learn to accurately and quickly identify these categories. This will be very useful while teaching the child to divide prime numbers.

We explain clearly

Let's divide 938 by 7. In this example, 938 is the dividend, 7 is the divisor. The result will be a quotient, and then you need to calculate it.

Step 1. We write down the numbers, dividing them with a "corner".

Step 2 Show the student the number of divisible and invite him to choose from them that smallest number, which is greater than the divisor. Of the three numbers 9, 3 and 8, this number will be 9. Invite the child to analyze how many times the number 7 can be contained in the number 9? That's right, just once. Therefore, the first result we write down will be 1.

Step 3 Let's move on to the design of the division by a column:

We multiply the divisor 7x1 and get 7. We write the result obtained under the first number of our dividend 938 and subtract, as usual, in a column. That is, we subtract 7 from 9 and get 2.

We write down the result.

Step 4 The number we see less divisor, so it needs to be increased. To do this, we combine it with the next unused number of our dividend - it will be 3. We attribute 3 to the resulting number 2.

Step 5 Next, we act according to the already known algorithm. Let's analyze how many times our divisor 7 is contained in the resulting number 23? That's right, three times. We fix the number 3 in the quotient. And the result of the product - 21 (7 * 3) is written below under the number 23 in a column.

Step.6 Now it remains to find the last number of our quotient. Using the already familiar algorithm, we continue to do calculations in a column. By subtracting in the column (23-21) we get the difference. It equals 2.

Of the dividend, we have one number left unused - 8. We combine it with the number 2 obtained as a result of subtraction, we get - 28.

Step 7 Let's analyze how many times our divisor 7 is contained in the resulting number? That's right, 4 times. We write the resulting figure in the result. So, we have the quotient obtained as a result of division by a column = 134.

How to teach a child to divide - we consolidate the skill

The main reason why many students have a problem with mathematics is the inability to quickly do simple arithmetic calculations. And on this basis, all mathematics is built in primary school. Especially often the problem is in multiplication and division.
In order for a child to learn how to quickly and efficiently carry out division calculations in the mind, the correct teaching methodology and consolidation of the skill are necessary. To do this, we advise you to use the currently popular aids in mastering the division skill. Some are designed for children to work with their parents, others for independent work.

1. "Division. Level 3 Workbook» from the largest international center additional education Kumon
2. "Division. Level 4 Workbook by Kumon
3. “Not mental arithmetic. A system for teaching a child rapid multiplication and division. For 21 days. Notepad simulator.» from Sh. Akhmadulin - the author of best-selling educational books

The most important thing when you teach a child to divide in a column is to master the algorithm, which, in general, is quite simple.

If the child operates well with the multiplication table and "reverse" division, he will not have difficulties. Nevertheless, it is very important to constantly train the acquired skill. Don't stop there as soon as you realize that the child has grasped the essence of the method.

In order to easily teach a child the operation of division, you need:

• So that at the age of two or three years he mastered the relationship "whole - part". He should develop an understanding of the whole as an inseparable category and the perception of a separate part of the whole as an independent object. For example, a toy truck is a whole, and its body, wheels, doors are parts of this whole.
• To in junior school age the child freely operated on addition and subtraction of numbers, understood the essence of the processes of multiplication and division.

In order for the child to enjoy mathematics, it is necessary to arouse his interest in mathematics and mathematical actions, not only during training, but also in everyday situations.

Therefore, encourage and develop observation in the child, draw analogies with mathematical operations (operations on counting and division, analysis of part-whole relationships, etc.) during construction, games and observations of nature.

Lecturer, child development center specialist
Druzhinina Elena
site specially for the project

Video plot for parents, how to correctly explain the division into a column to the child: