We write down the line and multiply 1432. Column multiplication: a short guide to becoming a genius

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Learn multiplication tables - game

Try our tutorial electronic game. Using it, you will be able to decide tomorrow math problems in class at the blackboard without answers, without resorting to a tablet to multiply numbers. You just have to start playing, and within 40 minutes you will have an excellent result. And to consolidate the results, train several times, not forgetting about breaks. Ideally - every day (save the page so as not to lose it). Game form The exercise machine is suitable for both boys and girls.

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Multiplication directly on the site (online)

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Multiplication table (numbers from 1 to 20)

×	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
2	2	4	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
3	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60
4	4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
5	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
6	6	12	18	24	30	36	42	48	54	60	66	72	78	84	90	96	102	108	114	120
7	7	14	21	28	35	42	49	56	63	70	77	84	91	98	105	112	119	126	133	140
8	8	16	24	32	40	48	56	64	72	80	88	96	104	112	120	128	136	144	152	160
9	9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	153	162	171	180
10	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
11	11	22	33	44	55	66	77	88	99	110	121	132	143	154	165	176	187	198	209	220
12	12	24	36	48	60	72	84	96	108	120	132	144	156	168	180	192	204	216	228	240
13	13	26	39	52	65	78	91	104	117	130	143	156	169	182	195	208	221	234	247	260
14	14	28	42	56	70	84	98	112	126	140	154	168	182	196	210	224	238	252	266	280
15	15	30	45	60	75	90	105	120	135	150	165	180	195	210	225	240	255	270	285	300
16	16	32	48	64	80	96	112	128	144	160	176	192	208	224	240	256	272	288	304	320
17	17	34	51	68	85	102	119	136	153	170	187	204	221	238	255	272	289	306	323	340
18	18	36	54	72	90	108	126	144	162	180	198	216	234	252	270	288	306	324	342	360
19	19	38	57	76	95	114	133	152	171	190	209	228	247	266	285	304	323	342	361	380
20	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300	320	340	360	380	400

How to multiply numbers in a column (mathematics video)

To practice and learn quickly, you can also try multiplying numbers by column.

And multiplication. The multiplication operation will be discussed in this article.

Multiplying numbers

Multiplication of numbers is mastered by children in the second grade, and there is nothing complicated about it. Now we will look at multiplication with examples.

Example 2*5. This means either 2+2+2+2+2 or 5+5. Take 5 twice or 2 five times. The answer, accordingly, is 10.

Example 4*3. Likewise, 4+4+4 or 3+3+3+3. Three times 4 or four times 3. Answer 12.

Example 5*3. We do the same as the previous examples. 5+5+5 or 3+3+3+3+3. Answer 15.

Multiplication formulas

Multiplication is the sum of identical numbers, for example, 2 * 5 = 2 + 2 + 2 + 2 + 2 or 2 * 5 = 5 + 5. Multiplication formula:

Where, a is any number, n is the number of terms of a. Let's say a=2, then 2+2+2=6, then n=3 multiplying 3 by 2, we get 6. Let's look at it in reverse order. For example, given: 3 * 3, that is. 3 multiplied by 3 means that three must be taken 3 times: 3 + 3 + 3 = 9. 3 * 3=9.

Abbreviated multiplication

Abbreviated multiplication is a shortening of the multiplication operation in certain cases, and abbreviated multiplication formulas have been derived specifically for this purpose. Which will help make calculations the most rational and fastest:

Abbreviated multiplication formulas

Let a, b belong to R, then:

The square of the sum of two expressions is equal to the square of the first expression plus twice the product of the first expression and the second plus the square of the second expression. Formula: (a+b)^2 = a^2 + 2ab + b^2

The square of the difference of two expressions is equal to the square of the first expression minus twice the product of the first expression and the second plus the square of the second expression. Formula: (a-b)^2 = a^2 - 2ab + b^2

Difference of squares two expressions is equal to the product of the difference of these expressions and their sum. Formula: a^2 - b^2 = (a - b)(a + b)

Cube of sum two expressions is equal to the cube of the first expression plus triple the product of the square of the first expression and the second plus triple the product of the first expression and the square of the second plus the cube of the second expression. Formula: (a + b)^3 = a^3 + 3a(^2)b + 3ab^2 + b^3

Difference cube two expressions is equal to the cube of the first expression minus triple the product of the square of the first expression and the second plus triple the product of the first expression and the square of the second minus the cube of the second expression. Formula: (a-b)^3 = a^3 - 3a(^2)b + 3ab^2 - b^3

Sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Difference of cubes two expressions is equal to the product of the sum of the first and second expressions and the incomplete square of the difference of these expressions. Formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Sign up for the course "Speed ​​up mental arithmetic, NOT mental arithmetic"to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even take roots. In 30 days you will learn to use easy techniques to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Multiplying fractions

While looking at adding and subtracting fractions, the rule was brought up to bring fractions to a common denominator in order to complete the calculation. When multiplying this do No need! When multiplying two fractions, the denominator is multiplied by the denominator, and the numerator by the numerator.

For example, (2/5) * (3 * 4). Let's multiply two thirds by one quarter. We multiply the denominator by the denominator, and the numerator by the numerator: (2 * 3)/(5 * 4), then 6/20, make a reduction, we get 3/10.

Multiplication 2nd grade

The second grade is just the beginning of learning multiplication, so second graders solve simple problems to replace addition with multiplication, multiply numbers, and learn the multiplication table. Let's look at multiplication problems at the second grade level:

Oleg lives in a five-story building, on the top floor. The height of one floor is 2 meters. What is the height of the house?

The box contains 10 packages of cookies. There are 7 of them in each package. How many cookies are in the box?

Misha arranged his toy cars in a row. There are 7 of them in each row, but there are only 8 rows. How many cars does Misha have?

There are 6 tables in the dining room, and 5 chairs are pushed behind each table. How many chairs are there in the dining room?

Mom brought 3 bags of oranges from the store. The bags contain 22 oranges. How many oranges did mom bring?

There are 9 strawberry bushes in the garden, and each bush has 11 berries. How many berries grow on all the bushes?

Roma laid 8 pipe parts one after another, each of the same size, 2 meters each. What is the length of the complete pipe?

Parents brought their children to school on September 1st. 12 cars arrived, each with 2 children. How many children did their parents bring in these cars?

Multiplication 3rd grade

In third grade, more serious tasks are given. In addition to multiplication, Division will also be covered.

Among the multiplication tasks will be: multiplication double digit numbers, multiplication by column, replacing addition with multiplication and vice versa.

Column multiplication:

Column multiplication is the easiest way to multiply large numbers. Let's consider this method using the example of two numbers 427 * 36.

1 step. Let's write the numbers one below the other, so that 427 is at the top and 36 at the bottom, that is, 6 under 7, 3 under 2.

Step 2. We start multiplication with the rightmost digit of the bottom number. That is, the order of multiplication is: 6 * 7, 6 * 2, 6 * 4, then the same with three: 3 * 7, 3 * 2, 3 * 4.

So, first we multiply 6 by 7, answer: 42. We write it this way: since it turned out 42, then 4 are tens, and 2 are units, the recording is similar to addition, which means we write 2 under the six, and 4 we add the number 427 to the two.

Step 3. Then we do the same with 6 * 2. Answer: 12. The first ten, which is added to the four of the number 427, and the second - ones. We add the resulting two with the four from the previous multiplication.

Step 4. Multiply 6 by 4. The answer is 24 and add 1 from the previous multiplication. We get 25.

So, multiplying 427 by 6, the answer is 2562

REMEMBER! The result of the second multiplication should begin to be written under SECOND number of the first result!

Step 5. We commit similar actions with the number 3. We get the multiplication answer 427 * 3=1281

Step 6. Then we add up the obtained answers during multiplication and get the final multiplication answer 427 * 36. Answer: 15372.

Multiplication 4th grade

The fourth class is already the multiplication of large numbers only. The calculation is performed using the column multiplication method. The method is described above in accessible language.

For example, find the product of the following pairs of numbers:

1. 988 * 98 =
2. 99 * 114 =
3. 17 * 174 =
4. 164 * 19 =

Presentation on multiplication

Download a presentation on multiplication with simple tasks for second graders. The presentation will help children better navigate this operation, because it is written colorfully and in a playful style - in the best option for teaching a child!

Multiplication table

Every student in the second grade learns the multiplication table. Everyone should know it!

Sign up for the course "Speed ​​up mental arithmetic, NOT mental arithmetic" to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even extract roots. In 30 days, you'll learn how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Examples for multiplication

Multiplying by one digit

1. 9 * 5 =
2. 9 * 8 =
3. 8 * 4 =
4. 3 * 9 =
5. 7 * 4 =
6. 9 * 5 =
7. 8 * 8 =
8. 6 * 9 =
9. 6 * 7 =
10. 9 * 2 =
11. 8 * 5 =
12. 3 * 6 =

Multiplying by two digits

1. 4 * 16 =
2. 11 * 6 =
3. 24 * 3 =
4. 9 * 19 =
5. 16 * 8 =
6. 27 * 5 =
7. 4 * 31 =
8. 17 * 5 =
9. 28 * 2 =
10. 12 * 9 =

Multiplying two-digit by two-digit

1. 24 * 16 =
2. 14 * 17 =
3. 19 * 31 =
4. 18 * 18 =
5. 10 * 15 =
6. 15 * 40 =
7. 31 * 27 =
8. 23 * 25 =
9. 17 * 13 =

Multiplying three-digit numbers

1. 630 * 50 =
2. 123 * 8 =
3. 201 * 18 =
4. 282 * 72 =
5. 96 * 660 =
6. 910 * 7 =
7. 428 * 37 =
8. 920 * 14 =

Games for developing mental arithmetic

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

Game "Quick Count"

The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer “yes” or “no” to the question “are there 5 identical fruits?” Follow your goal, and this game will help you with this.

Game "Mathematical matrices"

"Mathematical Matrices" is great brain exercise for kids, which will help you develop his mental work, mental calculation, quick search for the necessary components, and attentiveness. The essence of the game is that the player has to find a pair from the proposed 16 numbers that will add up to a given number, for example in the picture below the given number is “29”, and the desired pair is “5” and “24”.

Game "Number Span"

The number span game will challenge your memory while practicing this exercise.

The essence of the game is to remember the number, which takes about three seconds to remember. Then you need to play it back. As you progress through the stages of the game, the number of numbers increases, starting with two and further.

Game "Guess the operation"

The game “Guess the Operation” develops thinking and memory. The main point game, you need to choose a mathematical sign for the equality to be true. There are examples on the screen, look carefully and put the right sign"+" or "-" so that the equality is true. The “+” and “-” signs are located at the bottom of the picture, select the desired sign and click on the desired button. If you answered correctly, you score points and continue playing.

Game "Simplification"

The game “Simplification” 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 operation is given; the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need using the mouse. If you answered correctly, you score points and continue playing.

Game "Quick addition"

The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers whose sum is equal to a given number. In this game, a matrix from one to sixteen is given. A given number is written above the matrix; you need to select the numbers in the matrix so that the sum of these digits is equal to the given number. If you answered correctly, you score points and continue playing.

Visual Geometry Game

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, you need to quickly count them, then they close. Below the table there are four numbers written, you need to select one correct number and click on it with the mouse. If you answered correctly, you score points and continue playing.

Game "Mathematical Comparisons"

The game "Mathematical Comparisons" develops thinking and memory. The main essence of the game is to compare numbers and mathematical operations. In this game you need to compare two numbers. At the top there is a question written, read it and answer the question correctly. You can answer using the buttons below. There are three buttons “left”, “equal” and “right”. If you answered correctly, you score points and continue playing.

Development of phenomenal mental arithmetic

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From the course you will not only learn dozens of techniques for simplified and quick multiplication, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games! Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.

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Development of memory and attention in a child 5-10 years old

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Why are there problems with money? In this course we will answer this question in detail, look deep into the problem, and consider our relationship with money from psychological, economic and emotional points of view. From the course you will learn what you need to do to solve all your financial problems, start saving money and invest it in the future.

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Multiplying large numbers by writing them into a string sooner or later becomes a rather complex and tedious process. It’s much easier to use a special algorithm for multiplying by column: you don’t have to keep the numbers in your head and remember anything. You can make notes above the column so you can always see how you need to move the numbers. If you are trying to teach a child this method, then it is very important that the multiplication table bounces off his teeth, otherwise the process will drag on for a long time, and the child himself will make many mistakes that will stretch in a string throughout the entire example. Read the article carefully and adopt this algorithm for yourself.

Write the example down on a line and see: which factor is smaller? The smaller one will appear lower in the column multiplication notation, and the larger factor will appear at the top.

Write down an example using the same principle as shown in the picture below.

• Write the larger number at the top.
• Place a multiplication sign in the form of a cross on the left.
• Write the smaller number below.
• Draw a straight line under the example.

If there is a multiplier in the example that ends in zero or more zeros, then it should be written like this:

• Zeros should be taken as an example.
• Write the numbers below the numbers.

In this case, you simply transfer this number of zeros directly to the answer. If both the first factor and the second have zeros, then add up their number and write down the answer.

Now start calculating according to this principle:

• You multiply the entire top number by the last digit of the bottom. Remember that the last zeros are not multiplied.
• To make it more convenient for you, write down the numbers that need to be transferred at the top of the entire example. You can simply erase them later, but you won't have to remember the carry numbers in the process.
• Once you have completed the calculation, write the resulting number below the line.

Once you multiply the top number by the last digit of the bottom and write down your answer, start multiplying the next one.

Using the same principle, multiply the entire top number by the second-to-last digit of the bottom one. Also write down the carry numbers, however, you should write the answer under the first solution, but moving the entry one cell to the left. You will end up with a column with a line protruding to the left.

As you may have guessed, you need to multiply the top number by all the digits of the bottom, starting from the end. Each time the answer entry is moved one cell to the left.

Multiply all the numbers together in this way. Now draw a line under the column again. Place an addition sign between all solutions.

Now all you have to do is do columnar addition, which you should already be able to do:

• Add all numbers that are on the same vertical line.
• If the number turns out to be two-digit, then you move the number of tens to the next vertical strip.

Under some numbers there will be no others at all - in this case, you simply write this number down as an answer. Don't forget to carry all the zeros that appear at the end of the factors into your answer.

Performing columnar multiplication is very convenient and fast, especially if you need to multiply large numbers. You can easily check if the multiplication is correct by simply dividing the answer by one of the factors. To do this, use a calculator or the corner division method. At first, such multiplication takes a significant amount of time, but with experience, the whole action takes place in just a couple of seconds.

To multiply by column, it is enough to know the multiplication table from 1 to 10 and a simple rule: multi-digit numbers can be multiplied by digits. Let's talk in more detail about the rules of multiplication by column.

How to multiply by column: basic rules

Let's take a simple example for mental counting.

First we multiply 16 by 1, we get 16. Then we multiply 16 by 20, we get 320. We add these two results:

This is multiplication by digits: the first multiplier is multiplied in turn by all the digits of the second multiplier, starting with the least significant digit, and then the results are added together.

If we write example 1 in a column, we get the following:

The most important thing here is accurate recording. The ones digits should be written under the ones, the tens digits under the tens, etc. Then there is addition by digits:

6 + 0 = 6; 1 + 2 = 3. There is nothing to add to the higher-order number 3, it remains a three.

It is not necessary to write 0 when multiplying by 20; you can simply multiply by 2, but shift the results to the left by 1 digit.

More complex example: 24 x 328. Larger number It is better to make it a multiplicand, and the smaller one - a multiplier: this way you will only need to add 2 numbers, not 3. Although it is possible the other way around, because Changing the places of terms or factors does not change the results. So:

Here the multiplication turned out to be more difficult. 8 x 4 = 32. We wrote down only 2, and keep 3 in mind: this three will need to be added to the result of multiplying tens.

Then we multiplied 4 x 2 = 8, yes 3 in our minds. We add up the tens, we get: 8 + 3 = 11. And again, we write only 1 in the tens category, and we keep the second unit, which will go into the hundreds category, in mind, and don’t forget.

4 x 3 = 12 and 1 in your head - a total of 13. Because. There are no more numbers to multiply, so we write this number down.

Now you need to multiply 328 in exactly the same way by 20 or 2 with the record shifted by 1 digit to the left. And add up the results.

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 dividing decimal fractions into a column. After all, this is the most difficult version of such tasks.

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

Second prerequisite successful study mathematics - move on to examples of long division only after addition, subtraction and multiplication have been mastered.

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

How are natural numbers multiplied in a column?

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

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

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

Algorithm for multiplying decimals

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

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

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

Where to start learning division?

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

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

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

Algorithm for dividing numbers into a column

First, let us present the procedure for natural numbers divisible by a single-digit number. They will also be the basis for multi-digit divisors or decimal fractions. Only then should you enter minor 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 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 divisor, then you should 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 division is carried out three digit numbers in 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 perform division in a column of fractions by natural number, it’s 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 prescribes replacing division with multiplication and divisor - reciprocal number. That is, the example comes down to multiplying 1/3 by 5/3. The answer will be 5/9.

If the example contains different fractions...

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

Secondly, every finite decimal can be written in ordinary form. 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.