Solving equations in a column. How to divide into a column? How to explain long division to a child? Division by single-digit, two-digit, three-digit numbers, division with a remainder

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.

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

At school these actions are studied from simple to complex. Therefore, it is imperative to thoroughly understand the algorithm for performing these operations on simple examples. So that later there will be no difficulties with division decimals in a column. After all, this is the most difficult version of such tasks.

This subject requires consistent study. Gaps in knowledge are unacceptable here. Every student should learn this principle already in the first grade. Therefore, if you miss several lessons in a row, you will have to master the material on your own. Otherwise, later problems will arise not only with mathematics, but also with other subjects related to it.

Second required condition Successful learning of mathematics - move on to examples of long division only after you have mastered addition, subtraction and multiplication.

It will be difficult for a child to divide if he has not learned the multiplication table. By the way, it is better to teach it using the Pythagorean table. There is nothing superfluous, and multiplication is easier to learn in this case.

How are natural numbers multiplied in a column?

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

1. Before multiplying two numbers, you need to look at them carefully. Choose the one with more digits (longer) and write it down first. Place the second one under it. Moreover, the numbers of the corresponding category must be under the same category. That is, the rightmost digit of the first number should be above the rightmost digit of the second.
2. Multiply the rightmost digit of the bottom number by each digit of the top number, starting from the right. Write the answer below the line so that its last digit is under the one you multiplied by.
3. Repeat the same with another digit of the lower number. But the result of multiplication must be shifted one digit to the left. In this case, its last digit will be under the one by which it was multiplied.

Continue this multiplication in a column until the numbers in the second factor run out. Now they need to be folded. This will be the answer you are looking for.

Algorithm for multiplying decimals

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

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

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

Where to start learning division?

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

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

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

Algorithm for dividing numbers into a column

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

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

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

The algorithm itself completely coincides with what was described above. The difference will be the number of digits in the incomplete dividend. Now there should be at least two of them, but if they turn out to be less than the divisor, then you have to work with the first three digits.

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

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

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

The answer in the example would be the number 14.

What if the dividend ends in zero?

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

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

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

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

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

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

Dividing two decimals

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

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

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

As an example: divide 28.4 by 3.2:

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

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

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

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

So, if you need to divide by 10, 100 or 1,000, then the decimal point is moved to the left by the same number of digits as there are zeros in the divisor. That is, when a number is divisible by 100, the decimal point must move to the left by two digits. If the dividend is a natural number, then it is assumed that the comma is at the end.

This action gives the same result as if the number were to be multiplied by 0.1, 0.01 or 0.001. In these examples, the comma is also moved to the left by a number of digits equal to the length of the fractional part.

When dividing by 0.1 (etc.) or multiplying by 10 (etc.), the decimal point should move to the right by one digit (or two, three, depending on the number of zeros or the length of the fractional part).

It is worth noting that the number of digits given in the dividend may not be sufficient. Then the missing zeros can be added to the left (in the whole part) or to the right (after the decimal point).

Division of periodic fractions

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

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

If the example contains different fractions...

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

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

Mathematical-Calculator-Online v.1.0

The calculator performs the following operations: addition, subtraction, multiplication, division, working with decimals, root extraction, exponentiation, percentage calculations and other operations.

Solution:

How to use a math calculator

Key	Designation	Explanation
5	numbers 0-9	Arabic numerals. Entering natural integers, zero. To get a negative integer, you must press the +/- key
.	semicolon)	Separator to indicate a decimal fraction. If there is no number before the point (comma), the calculator will automatically substitute a zero before the point. For example: .5 - 0.5 will be written
+	plus sign	Adding numbers (integers, decimals)
-	minus sign	Subtracting numbers (integers, decimals)
÷	division sign	Dividing numbers (integers, decimals)
X	multiplication sign	Multiplying numbers (integers, decimals)
√	root	Extracting the root of a number. When you press the “root” button again, the root of the result is calculated. For example: root of 16 = 4; root of 4 = 2
x 2	squaring	Squaring a number. When you press the "squaring" button again, the result is squared. For example: square 2 = 4; square 4 = 16
1/x	fraction	Output in decimal fractions. The numerator is 1, the denominator is the entered number
%	percent	Getting a percentage of a number. To work, you need to enter: the number from which the percentage will be calculated, the sign (plus, minus, divide, multiply), how many percent in numerical form, the "%" button
(	open parenthesis	An open parenthesis to specify the calculation priority. A closed parenthesis is required. Example: (2+3)*2=10
)	closed parenthesis	A closed parenthesis to specify the calculation priority. An open parenthesis is required
±	plus minus	Reverses sign
=	equals	Displays the result of the solution. Also above the calculator, in the “Solution” field, intermediate calculations and the result are displayed.
←	deleting a character	Removes the last character
WITH	reset	Reset button. Completely resets the calculator to position "0"

Algorithm of the online calculator using examples

Addition.

Addition of natural integers (5 + 7 = 12)

Addition of whole natural and negative numbers { 5 + (-2) = 3 }

Adding decimals fractional numbers { 0,3 + 5,2 = 5,5 }

Subtraction.

Subtracting natural integers ( 7 - 5 = 2 )

Subtracting natural and negative integers ( 5 - (-2) = 7 )

Subtracting decimal fractions (6.5 - 1.2 = 4.3)

Multiplication.

Product of natural integers (3 * 7 = 21)

Product of natural and negative integers ( 5 * (-3) = -15 )

Product of decimal fractions ( 0.5 * 0.6 = 0.3 )

Division.

Division of natural integers (27 / 3 = 9)

Division of natural and negative integers (15 / (-3) = -5)

Division of decimal fractions (6.2 / 2 = 3.1)

Extracting the root of a number.

Extracting the root of an integer ( root(9) = 3)

Extracting the root of decimal fractions (root(2.5) = 1.58)

Extracting the root of a sum of numbers ( root(56 + 25) = 9)

Extracting the root of the difference between numbers (root (32 – 7) = 5)

Squaring a number.

Squaring an integer ( (3) 2 = 9 )

Squaring decimals ((2,2)2 = 4.84)

Conversion to decimal fractions.

Calculating percentages of a number

Increase the number 230 by 15% ( 230 + 230 * 0.15 = 264.5 )

Reduce the number 510 by 35% ( 510 – 510 * 0.35 = 331.5 )

18% of the number 140 is (140 * 0.18 = 25.2)

Instructions

First, test your child's multiplication skills. If a child does not know the multiplication table firmly, then he may also have problems with division. Then, when explaining division, you can be allowed to peek at the cheat sheet, but you still have to learn the table.

Write the dividend and divisor using a vertical separator bar. Under the divisor you will write down the answer - the quotient, separating it with a horizontal line. Take the first digit of 372 and ask your child how many times the number six “fits” in three. That's right, not at all.

Then take two numbers - 37. For clarity, you can highlight them with a corner. Repeat the question again - how many times the number six is ​​contained in 37. To count quickly, it will come in handy. Put the answer together: 6*4 = 24 – not at all similar; 6*5 = 30 – close to 37. But 37-30 = 7 – six will “fit” again. Finally, 6*6 = 36, 37-36 = 1 – suitable. The first digit of the quotient found is 6. Write it under the divisor.

Write 36 under the number 37 and draw a line. For clarity, you can use the sign in the recording. Under the line, put the remainder - 1. Now “descend” the next digit of the number, two, to one - it turns out to be 12. Explain to the child that numbers always “descend” one at a time. Ask again how many “sixes” there are in 12. The answer is 2, this time without a remainder. Write the second digit of the quotient next to the first. The final result is 62.

Also consider the case of division in detail. For example, 167/6 = 27, remainder 5. Most likely, your child has not yet heard anything about simple fractions. But if he asks questions, the remainder can be explained using the example of apples. 167 apples were divided among six people. Everyone got 27 pieces, and five apples remained undivided. You can also divide them by cutting each into six slices and distributing them equally. Each person got one slice from each apple - 1/6. And since there were five apples, each one had five slices - 5/6. That is, the result can be written like this: 27 5/6.

To reinforce the information, look at three more examples of division:

1) The first digit of the dividend contains the divisor. For example, 693/3 = 231.
2) The dividend ends at zero. For example, 1240/4 = 310.
3) The number contains a zero in the middle. For example, 6808/8 = 851.

In the second case, children sometimes forget to add last digit the answer is 0. And in the third, it happens that they jump over zero.

Sources:

• division by column 3rd grade
• How to divide 927 into a column

Children learn concrete meanings much better than abstract ones. How to explain to kid, what is two thirds? Concept fractions requires special introduction. There are some methods that help you understand what a non-integer number is.

You will need

• - special lotto;
• - apple and candy;
• a cardboard circle consisting of several parts;
• - chalk.

Instructions

Try to interest. Play a special game of hopscotch while walking. If you are already tired of jumping into regular ones, but your child has mastered counting well, try this option. Draw hopscotch on the asphalt with chalk as shown in the picture and explain to the child that he can jump like this: 1 - 2 - 3..., or you can do it like this: 1 - 1.5 - 2 - 2.5... Children really like to play and so they are better because between the numbers there are still intermediate values ​​- parts. This is your next step towards learning fractional numbers. An excellent visual aid.

Take a whole apple and offer it to two people at the same time. They will immediately tell you that this is impossible. Then cut the apple and offer it to them again. Now everything is all right. everyone got the same half of an apple. These are parts of one whole.

Offer to split four with you in half. He will do it easily. Then take out another one and offer to do the same. It is clear that you cannot get the whole candy right away and to kid. The solution can be found by cutting the candy in half. Then everyone will get two whole candies and one half.

For older people, use a cutting circle. You can divide it into 2, 4, 6 or 8 parts. We invite the children to take a circle. Then we divide it into two halves. Two halves will make a perfect circle, even if you exchange half with your desk neighbor (the circles should be the same diameter). We divide each half of the loan into half. It turns out that the circle can consist of 4 parts. And each half comes from two halves. Then we write it on the board in the form fractions. Explaining what the numerator is (the parts taken) and the denominator (how many parts the total was divided into). This makes it easier for children to grasp a difficult concept - fractions.

Helpful advice

Be sure to apply visual aids in explaining an abstract concept.

The section "Multiplication and Division" is one of the most difficult in the mathematics course. primary classes. Children usually learn it at the age of 8-9 years. At this time, their mechanical memory is quite well developed, so memorization occurs quickly and without much effort.