Examples table for 2. Multiplication

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Learn multiplication tables - game

Try our educational e-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 in about 40 minutes it will be excellent result. And to consolidate the result, 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.

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

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

Dividing numbers

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

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

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

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

Division with remainder

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

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

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

Division by 3 and 9

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

Find the sum of the digits of the dividend.

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

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

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

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

Multiplication and division

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

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

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

Division 3 class

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

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

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

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

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

Division 4th grade

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

Column division

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

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

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

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

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

Step 3. Number 5 less number 8, which means it won’t be possible to divide. Therefore, we take another digit of the dividend:

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

Step 4. We put a dot under the divisor.

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

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

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

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

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

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

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

Division of three digits

Division three-digit numbers performed by the long division method, which was explained in the example above. An example of just a three-digit number.

Division of fractions

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

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

Dividing numbers into classes

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

Division of natural numbers

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

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 how to use easy techniques to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Division presentation

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

Examples for division

Easy level

Intermediate level

Difficult level

Games for developing mental arithmetic

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

Game "Guess the operation"

The game “Guess the Operation” develops thinking and memory. The main point games need to be selected mathematical sign so that the equality is 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"

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. Above the matrix it is written for given number, you need to select the numbers in the matrix so that the sum of these numbers is equal to the given number. If you answered correctly, you score points and continue playing.

Visual Geometry Game

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. There are four numbers written below the table, you need to choose one correct number and click on it with the mouse. If you answered correctly, you score points and continue playing.

Game "Piggy Bank"

The Piggy Bank game develops thinking and memory. The main point of the game is to choose which piggy bank to use more money.In this game there are four piggy banks, you need to count which piggy bank has the most money and show this piggy bank with the mouse. If you answered correctly, then you score points and continue playing.

Game "Fast addition reload"

The game “Fast addition reboot” develops thinking, memory and attention. The main point of the game is to choose the correct terms, the sum of which will be equal to the given number. In this game, three numbers are given on the screen and a task is given, add the number, the screen indicates which number needs to be added. You select the desired numbers from three numbers and press them. If you answered correctly, then you score points and continue playing.

Development of phenomenal mental arithmetic

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Super memory in 30 days

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Problems on the topic: "Multiplication of numbers. Multiplication table"

Additional materials
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Teaching aids and simulators in the Integral online store for grade 2
Mathematics, Russian, computer science for grades 1-4, educational simulators "MIR"
"Mathematics - a treasure trove of knowledge", teaching aid for elementary school

Multiplying numbers

1. Look at the pictures and make up examples of addition and multiplication.

2. Replace addition with multiplication and solve the examples.

5 + 5 + 5 =	6 + 6 =	8 + 8 + 8 + 8 =	3 + 3 + 3 =
4 + 4 + 4 =	5 + 5 + 5 + 5 + 5=	6 + 6 =	3 + 3 + 3 + 3 + 3 + 3=

3. Based on the drawing, make up word problem, which is solved by multiplication.

Problem solving

1. Mitya lives in a seven-story building. The height of each floor is three meters. Determine the height of the house in which Mitya lives, in meters.

2. The workers installed 6 fence posts. The distance between the pillars is four meters. What is the length of the fence?

3. One package contains 8 handkerchiefs. How many handkerchiefs are there in seven packages?

4. 9 cars arrived at the health camp. There were 4 children in each car. How many children were brought to the camp?

5. Raspberry bushes grow in the garden. They are planted in 8 rows of 5 bushes in each row. How many raspberry bushes are there in the garden?

6. There are 8 tables in the school canteen. There are 54 chairs around each table. How many chairs are there in the dining room?

7. There are 8 rows of cars parked in the car park. How many cars are there in the parking lot if 7 cars fit in one row?

8. A column of soldiers is marching across the square. The column consists of nine rows of eight soldiers in each row. How many soldiers are there in the column?

9. Kolya has 7 binders of the Murzilka magazine. Each binder contains 6 magazines. How many Murzilka magazines does Kolya have?

10. 7 years old Pasha collects ninja turtles. Every year he collects 5 collections. How many collections does Pasha have in total?

11. Dad brought 4 bags of apples from the market, each bag contains 11 apples. How many apples did dad bring?

Multiplication table

1. Do the multiplication.

9 * 2 =	7 * 4 =	8 * 6 =	3 * 9 =
6 * 5 =	6 * 7 =	7 * 4 =	8 * 2 =
5 * 9 =	8 * 8 =	7 * 7 =	8 * 3 =
8 * 5 =	4 * 4 =	6 * 3 =	5 * 4 =

2. Replace the product with a sum and solve the examples.

4 * 9 =	5 * 8 =	6 * 7 =	7 * 6 =
8 * 5 =	6 * 4 =	5 * 3 =	4 * 2 =
8 * 5 =	3 * 4 =	2 * 3 =	9 * 2 =

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 a sum 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. Consider 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 formulas for abbreviated multiplication were 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 equal to cube 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 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.

Multiplying fractions

Considering the addition and subtraction of fractions, the rule was raised for bringing fractions to common denominator to perform 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 placed 8 pipe parts one after another, 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.

Multiplication tasks will include: multiplying two-digit numbers, multiplying by columns, 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 to be 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 down SECOND number of the first result!

Step 5. We perform 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:

988 * 98 =
99 * 114 =
17 * 174 =
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!

Examples for multiplication

Multiplying by one digit

9 * 5 =
9 * 8 =
8 * 4 =
3 * 9 =
7 * 4 =
9 * 5 =
8 * 8 =
6 * 9 =
6 * 7 =
9 * 2 =
8 * 5 =
3 * 6 =

Multiplying by two digits

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

Multiplying two-digit by two-digit

24 * 16 =
14 * 17 =
19 * 31 =
18 * 18 =
10 * 15 =
15 * 40 =
31 * 27 =
23 * 25 =
17 * 13 =

Multiplying three-digit numbers

630 * 50 =
123 * 8 =
201 * 18 =
282 * 72 =
96 * 660 =
910 * 7 =
428 * 37 =
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 necessary components, care. 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"

Game " numerical coverage" will load 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.