Simulator flashcard subtraction from three-digit numbers. How to divide in a column? How to explain column division to a child? Divide by a single, two-digit, three-digit number, division with a remainder

11.10.2019

Online simulator "Addition by a column" is a free mathematical game that helps students of the second, third, fourth grades simply, easily and quickly master the addition of three-, four-, five-digit numbers ranging from 100 to 100,000.

How to learn to add numbers in a column? Algorithm

The game has three levels: adding numbers from 100 to 1,000 (three digits), adding numbers from 1000 to 10,000 (four digits), adding numbers from 10,000 to 100,000 (five digits). Choose one of the levels. The task of adding numbers will appear on the playing field. Drag the desired numbers with the mouse to get the correct amount.

Addition in a column is performed sequentially. Be sure to pay attention to the fact that the numbers of the same digit are always added together! First, the digits of the smallest digit of the number, units, are added to each other. Then tens are added, then hundreds, and so on. thus it becomes clear that the addition of numbers goes from right to left.

If, as a result of adding several digits, we get an amount equal to or greater than 10, then one is added to the next digit, and in place of the question mark, a figure should be written 10 less than the amount received. For example, we added 7 and 8. We got 15. We put the number 5 in place of the question, and add 1 to the sum of the numbers of the next (larger) category.

For each correct answer, 1 point is awarded. Incorrect - 3 points are deducted.

The regularity of classes is the most important thing in learning column addition. Therefore, it is very important to practice regularly! Best 6 days a week. Take care of it a little. You shouldn't overwork. Twice a day for 10-15 minutes will be enough. And after a week of such classes, your skills in adding numbers will be significantly improved. And after a while you will perfectly know and understand the addition of multi-digit numbers.

If you like this game, be sure to share it with your friends. After all, they might like it too :-)

This game is designed and extremely useful for boys and girls from 7 to 10 years old. It helps not only quickly and in a playful way to understand the addition of numbers, as it might seem at first. During the game, attention and memory of children also develop. And also the game-simulator "Column addition" develops fine motor skills and strengthens the muscles of the hand. Be sure to try dragging the numbers with a different hand than you usually do! If you constantly control the mouse with your right hand, then start dragging the numbers with your left hand in this game. And vice versa: if you almost always control the mouse with your left hand, drag the numbers with your right. This will do you good!

It is easy to teach a child to divide by a column. It is necessary to explain the algorithm of this action and consolidate the material covered.

According to the school curriculum, children begin to explain division by a column already in the third grade. Students who grasp everything “on the fly” quickly understand this topic
But, if the child fell ill and missed the lessons of mathematics, or he did not understand the topic, then the parents must explain the material to the child on their own. It is necessary to convey information to him as clearly as possible.
Moms and dads during the educational process of the child must be patient, showing tact in relation to their child. In no case should you yell at a child if something does not work out for him, because this way you can discourage him from all the desire to study

Important: In order for a child to understand the division of numbers, he must thoroughly know the multiplication table. If the kid does not know multiplication well, he will not understand division.

During home extra classes, cheat sheets can be used, but the child must learn the multiplication table before proceeding to the topic “Division”.

So how do you explain to a child column division:

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

Division is always given to children a little more difficult than multiplication. But diligent additional classes at home will help the baby understand the algorithm of this action and keep up with their peers at school.

Start simple - division by a single digit:

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

For example, 256 divided by 4:

Draw a vertical line on a sheet of paper and divide it in half on the right side. Write the first number on the left, and the second on the right above the line.
Ask the baby how many fours fit in a two - not at all
Then we take 25. For clarity, separate this number from above with a corner. Again ask the child 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 for the correct answer.
Write down the number 24 under 25, and underline to write down the answer - 1
Ask again: how many fours can fit in a unit - not at all. Then we demolish the number "6" to one
It turned out 16 - how many fours fit in this number? Correct - 4. We write down "4" next to "6" in the answer
Under 16 we write 16, underline 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 the division by a single number, you can move on. Written division by a two-digit number is a little more complicated, but if the baby 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 correctly select numbers and it will be easy for him to divide complex numbers.

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

First we divide 184 by 20, it turns out approximately 8. But we do not write the number 8 in the answer, since this is a trial number
Check if 8 fits or not. We multiply 8 by 23, it turns out 184 - this is exactly the number that we have in the divisor. The answer will be 8

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

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

Divide 768 by 24. Determine the first digit of the private - we divide 76 not by 24, but by 20, it turns out 3. We write 3 in response under the line to the right
Under 76 we write down 72 and draw a line, write down the difference - it turned out 4. Is this figure divisible by 24? No - we demolish 8, it turns out 48
Is 48 divisible by 24? That's right - yes. It turns out 2, we write this figure in response
It turned out 32. Now you can check whether we performed the division action correctly. Multiply 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 you need 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 instance:

Divide 146064 by 716. First we take 146 - ask the child if this number is divisible by 716 or not. That's right - no, then we take 1460
How many times will the number 716 fit in the number 1460? Correct - 2, so we write this figure in the answer
We multiply 2 by 716, it turns out 1432. We write this figure under 1460. It turns out the difference is 28, we write under the line
Demolition 6. Ask the child - 286 is divisible by 716? That's right - no, so we write 0 in the answer next to 2. We demolish another number 4
We divide 2864 by 716. We take 3 each - a little, 5 each - a lot, which means we get 4. We multiply 4 by 716, we get 2864
Write 2864 under 2864 for a difference of 0. Answer 204

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

It's time for the child to explain 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 with a simple example: 35:8=4 (remainder 3):

How many eights fit in 35? Correct - 4. Remains 3
Is this number divisible by 8? That's right - no. So the remainder is 3.

After that, the child should learn that you can continue the division by adding 0 to the number 3:

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

Tip: If the child does not understand something, do not be angry. Let a couple of days go by and try to explain the material again.

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

The algorithm for dividing numbers is as follows:

Make an estimate of the number that will be in the answer
Find the first incomplete dividend
Determine the number of digits in a quotient
Find the digits in each digit of the quotient
Find the remainder (if any)

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 studying with a child, often ask him examples for making an estimate. He must quickly calculate the answer in his mind. For instance:

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 should be with the correct answer.

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

Video: Arithmetic game for kids addition subtraction division multiplication

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

Tasks on the topic: "Subtraction of three-digit numbers in a column. Examples"

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Teaching aids and simulators in the online store "Integral" for grade 3
L.G. Peterson M.I. Moro T.E. Demidova

Subtraction of two digit numbers (repetition)

1.1. Subtract 49 from 78.
1.2. Subtract 63 from 92.
1.3. Subtract 38 from 49.

2. Solve examples.

Subtraction of three-digit numbers

1. Write the given sentences in the form of numerical expressions and solve them.

1.1. Subtract 647 from 798.
1.2. Subtract 412 from 458.
1.3. Subtract 241 from 599.

2. Solve examples.

936 - 287 =	745 - 293 =	366 - 182 =	959 - 235 =
862 - 192 =	779 - 503 =	848 - 472 =	729 - 531 =
374 - 233 =	852 - 634 =	773 - 117 =	892 - 442 =

Solving word problems for subtraction

1. The school has 670 students, 370 of them are boys. How many girls are in school?

2. 690 bags of sugar were brought to the warehouse. On the first day, 130 bags were taken away, and on the second day, another 357 bags were taken away. How many bags of sugar are left in the warehouse after the second day?

3. 702 books were brought to the library, of which 268 books were distributed to the 3rd grade and 211 books to the 1st grade. How many books are left in the library for grade 2?

4. 869 liters of gasoline were poured into the tank, 347 liters of gasoline were used up. How many liters of gasoline are left in the tank?

Tabular Subtraction and Addition Subtraction Test

1. Subtract and check the result.

385 - 247 =	164 - 95 =	548 - 118 =	338 - 144 =
436 - 147 =	235 - 215 =	696 - 23 =	985 - 566 =
757 - 664 =	347 - 164 =	654 - 147 =	179 - 155 =

2. Write the given sentences in the form of numerical expressions, solve them and check the result.

2.1. Subtract 18 from 564.
2.2. Subtract 676 from 851.
2.3. Subtract 213 from 352.
2.4. Subtract three hundred thirty-five from four hundred and sixteen.

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

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

Although the program and the load on students often change, division into a column of numbers with a different number of digits remains an impregnable top for many of them from the first entry. Therefore, training at home with parents is often indispensable.

In order not to waste time and prevent the formation of a coma that is incomprehensible to a child in mathematics, brush up on your knowledge of dividing numbers by a column. The article will help you with this.

How to divide numbers in a column correctly: division algorithm

To divide numbers by a column, follow these steps:

write down the action of division on paper correctly. Choose the upper right corner of the notebook/sheet. If you are just learning how to perform the division in a column, take paper in a cage. This way you keep the visual consistency of the solution,
line the space between the dividend and the divisor.
The diagram below will help you.

plan space for division into a column. The longer the number to be divided, and the greater the divisor, the lower the decision will go down on the page,
perform the first division action with the number of digits of the dividend, which is equal to the divisor. For example, if you have a one-digit number to the right of the dividing line, then consider the first one in the dividend, if two-digit - then 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 step,
complete the action by subtracting and determining 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 the solution,
the last division step is when you get 0 from subtracting or a number less than the divisor. In the second case, your answer will be with a remainder, for example, 17 and 3 in the remainder.

How to explain division to a child and teach division by a column?

First, consider a number of input factors:

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

play with the multiplication table. Put it in front of the child and use examples to show the ease of use when dividing,
explain the location of the dividend, divisor, quotient, remainder. Have your child repeat these categories,
turn the process into a game, come up with a story about numbers and division,
prepare visual objects for teaching. Counting sticks, apples, coins, toys, peeled mixing or an orange will do. Offer to distribute them among a different number of people, for example, between mom, dad and child,
first show the child actions with even numbers so that he sees the result of division, a multiple of two.

The process of mastering division by a column:

write down the numbers, separating them with borders. Repeat with the child the arrangement of division categories,
invite him to analyze the numbers of the dividend for the “greater-less” divisor. Help with the question - how many times one number is placed in the second. As a result, the child should highlight the number / numbers that he will use to perform the first action,
Podskajite algorithm for determining the capacity of the private. It is convenient to depict it with dots, which then turn into numbers,
help to correctly determine and write the first number into a quotient, multiply it by a divisor, write the result under the dividend, perform a subtraction. 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 action recording,
continue until the difference is zero. This is relevant only for dividing numbers without a remainder,
reinforce the knowledge of the child with a few more examples. Make sure that he is not tired, otherwise give a break.

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

Let's start a step-by-step analysis of examples for dividing into a column.

Perform an action on the numbers 25 and 2:

write them 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 steps for multiplication and subtraction.

A partially completed task for 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 by a column is possible in one step.

Second example. Divide 87 by 26 in a column.

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

To make it easier for a child who is just learning the basics of division, invite him to focus on the first digits of the dividend and divisor. For example, 8:2=4. Let the child substitute this number under the line and do the multiplication. He needs to see with his own eyes that 4 is a lot and needs to try with a 3.

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

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

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

How to divide a three-digit number into a one-digit, two-digit and three-digit number in a column: 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 one-digit number, the algorithm of action 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, select a number with the child that corresponds to the number of holdings of the second in the first part of the first or as a whole. That is, consider first 2 digits of the three-digit dividend, if they are less than the divisor, then all three.

When the child has just begun mastering division by a column, tell him to perform actions with single-digit numbers. That is, with the first in the dividend and divisor. Let the kid make a mistake that will lead to a negative subtraction value and return to selecting a number under the line, which will get confused with the action immediately for a 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 intimidating for a child. Calm him down by explaining that the principle of operation is identical, as in the division of prime numbers.

The method of enumerating one digit will help the baby deal with each number separately. Only the amount of time for this action will take him more than in the previous examples. For better visual perception, combine with arcs the number of digits that will participate in the first action.

Dividing a 3-digit number by a 3-digit number.

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

In the case of dividing a four-digit number by any one that contains up to 4 orders 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 "private" column, and in the example 8956:1243 - a one-digit integer,
the appearance of zeros in the quotient. When, in the course of solving, when transferring the next number of the dividend, the result is less than the divisor,
checking the result obtained by performing the 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 once again divide the numbers into a column.

Below is an example solution.

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

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

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

Detailed solution examples below.

When performing the division action on polynomials, draw the attention of children 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 action, add the missing degrees of the function, multiplied by zero, to the polynomial,
perform polynomial transformation by extracting repeated two-/polynomials. Then cut them down and you get the result without a trace.

Below are a number of detailed examples with solutions.

How to divide in a column with a remainder?

The algorithm for dividing into a column with a remainder is similar to the classical one. The only difference is the appearance of the remainder, which is less than the divisor. So 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
words, for example, 73 integers and 6 remainder

How to divide decimal fractions with a comma by a column?

There are several features in such a division. If you are doing an action with:

decimal fraction-divisible and integer-divisor, then proceed according to the usual algorithm until the digits of the dividend before the decimal point run out. Then put it in private and continue to carry 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 the number of digits equal to the number of zeros of the divisor. For example, 749.5:100=7.495,
decimal fractions both in the divisor and in the dividend, 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 characters that are separated by the divisor. For example, convert 416.788:5.3 to 4167.88:53 and do the usual long division.

How to divide a smaller number by a larger one?

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

In order for the child to better learn such a division and not get confused in the number of zeros, the place where the comma is placed in the private, give him the following example:

carry out the first subtraction action with zeros written one at a time under the divisor and in the “quotient” column,
put a comma in the quotient, and the remainder after the difference, add zero and continue the usual division in a column,
when the remainder of the subtraction is again less than the divisor, add zero to the first and continue the action. The final result is getting 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 infinitely repeating number / numbers.

Below is an example.

How to divide a column of numbers with zeros?

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

Of the nuances, we note:

if there are zeros at the end of the divisor and the dividend, feel free to abbreviate them. Invite the child to cross them out with a pencil and continue the division as usual. For example, in the situation 1200:400, the child can remove both zeros from both numbers, but in the situation 15600:560, only one extreme,
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 ended before you used them all, then transfer them to the quotient after the numbers that were formed before. Example, 1000:2=500 - you moved the last two zeros.

So, we examined the main situations of dividing numbers of different numbers of bit depth into a column, determined the algorithm of action and accents for teaching a child.

Practice what you've learned and help your child learn math.