Today in the lesson we will literally learn how to multiply numbers on our fingers. When you don’t have a notebook and a calculator at hand, pay attention to the hand itself - it has fingers on it. This multiplication method was shown to me by my grandmother, and I decided, since I myself will never become a grandmother, it's time to tell you about the possibilities of our fingers.
I hasten to warn you that the method talks about multiplying the numbers 6, 7, 8, 9. By default, it is assumed that you know how to multiply up to five.
So the counting rules are:
One bent finger is the number 6, two fingers is the number 7, three fingers is the number 8, four fingers is the number 9.
Example. We multiply 6x6. We bend the finger on both hands.
We multiply unbent fingers on each other. 4x4=16. We take the bent ones for tens, and add them up. This is 20. 20+16=36. Total 6x6=36
We multiply. 6x7.
We multiply unbent fingers on each other. 4x3=12. We take the bent ones for tens, and add them up. This is 30. 30+12=42. Total 6x7=42
Multiply 7x7
We multiply unbent fingers on each other. 3x3=9. We take the bent ones for tens, and add them up. This is 40. 40+9=49. Total 7x7=49
Multiply 7x8
We multiply unbent fingers on each other. 3x2=6. We take the bent ones for tens, and add them up. This is 50. 50+6=56. Total 7x8=56
Multiply 8x8
We multiply unbent fingers on each other. 2x2=4. We take the bent ones for tens, and add them up. This is 60. 60+4=42. Total 8x8=64
Multiply 8x9
We multiply unbent fingers on each other. 2x1=2. We take the bent ones for tens, and add them up. This is 70. 70+2=72. Total 8x9=72
And multiply 9x9

This method is often referred to as the granny method. It should be said right away that this is the worst of the proposed ways to study multiplication - it leads to a dead end, and the technique below is recommended more for familiarization than for practical use.

Finger multiplication technique.

Description and preparation.

The child is required to be able to add, know the multiplication table from 1 to 5 and be able to multiply by 10. To multiply by 6, 7, 8, 9 and 10, use the fingers of both hands.

First you need to place both hands with your palms facing you, sequentially number all fingers from 6 to 10. The numbering of the fingers is as follows:

Little finger - 6,

Nameless - 7,

Medium - 8,

Index - 9,

Large - 10.

At the initial stage, the fingers can be numbered with a pen. In the process of multiplication, you will need to touch the right fingers of both hands. More details on the examples.

Example 7 * 6.

First you need to touch the ring finger of your left hand (number 7) to the little finger right hand(number 6). This matches the numbers in the example.

Multiply 7 by 6

The touching fingers and the fingers below them are called the lower ones, the fingers above are called the upper ones.

To multiply 7 * 6, first calculate the sum of the lower fingers. In our case, this is 3. Then multiply by 10, we get 30.

Now add 30 and 12 and get the answer 42.

Example 8 * 9.

First you need to touch the middle finger of the left hand (number 8) to the index finger of the right hand (number 9).

Multiply 8 by 9

First, let's calculate the sum of the lower fingers. In this case, it's 7. Then multiply by 10, we get 70.

Adding 70 and 2, we get the answer 72.

Advantages of the method

• Pretty easy to use.

Cons of the method

• Dead end method. Multiplication on the fingers will not allow you to count anything more than the multiplication table, that is, you still have to relearn how to multiply normally.
• Inferior. Requires basic knowledge of multiplication.
• Uncomfortable. Requires the use of both hands.
• Not practical. It is unlikely to be able to pass the multiplication table, counting on the fingers in front of the teacher.
• Not serious. A child, counting on his fingers, can become the object of ridicule of classmates.

In the summer, Arina must learn the multiplication table. She already knows up to 5, and then the set of numbers is a little more complicated. Today we discovered a curious method of multiplication on the fingers. Understood. Arina is delighted, and I am somewhat surprised why the school did not know about this! I share.

Turn your hands with your palms facing you and assign the numbers 6 to 10 to each finger, starting with the little finger.

Now let's try to multiply, for example, 7x8. To do this, connect the number 7 finger on the left hand with the number 8 finger on the right.

And now we count the fingers: the number of fingers under the connected ones is tens.

And the fingers of the left hand, remaining on top, are multiplied by the fingers of the right - these will be our units (3x2 = 6). The total is 56.

Sometimes it happens that when multiplying “units”, the result is more than 9. In such cases, you need to add both results in a column.

For example, 7x6. In this case, it turns out that the "units" are equal to 12 (3x4). Tens equals 3.

3 (tens)
+
12 (units)
________
42

Multiply by 9

Again turn the palms towards you, but now the numbering of the fingers will go in order from left to right, that is, from 1 to 10.

Now we multiply, for example, 2x9. Everything that goes up to finger number 2 is tens (that is, 1 in this case). And all that remains after finger number 2 is units (that is, 8). As a result, we get 18.

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Learn multiplication table - game

Try our educational e-game. Using it, you will be able to decide tomorrow math problems in class at the blackboard with no answers, without resorting to the tablet to multiply the numbers. One has only to start playing, and after 40 minutes there will be an excellent result. And to consolidate the result, train several times, not forgetting the breaks. Ideally, every day (save the page so you don't lose it). The game form of the simulator is suitable for both boys and girls.

See the full cheat sheet below.

Multiplication directly on the site (online)

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Multiplication table (numbers 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 by a column (mathematics video)

To practice and learn quickly, you can also try to multiply numbers by a column.

Not everyone needs higher mathematics in life. But if a child has mastered the multiplication table, then it simply cannot happen that it will not come in handy sometime and somewhere. Though in early years, at least later, but he will definitely need such knowledge. They may be required at any time at home when solving household problems, while going to shops and the market, when paying for utilities and other services. Whoever a child becomes when he turns into an adult: a laborer, a businessman, a production worker, a scientist, a minister, without such knowledge it is simply impossible to imagine the work process. And it is not always and everywhere convenient to carry a calculator with you. But how easy is it to remember the multiplication table for little man, and adults - to help him with this? Some fun tricks and exciting games allow you to optimize the process.

Cut the work in half

Everyone knows how to find the result according to the table, where the vertical left edge and the topmost line are cells filled with numbers from 1 to 10. And children learn to use it usually easily and without difficulty. For example, if we need to find out how much seven eight will be, we must first find 7 in the left vertical column and draw in our mind a horizontal imaginary line from it to the right. Next, you need to find 8 in the top row and lower the perpendicular down from it. At the intersection of such lines, the result will be visible. It is easy to verify that it is equal to 56, which is true. These tables are used frequently. They are convenient in that they allow you to compactly write down the multiplication table and easily find the result from it. This system of numbers is well known to schoolchildren. lower grades and studied by them in the classroom.

Carefully considering the multiplication table of numbers from 1 to 10, given above, one can notice one interesting thing. It is a square, and if you draw an imaginary line from the left extreme corner at the top to the right extreme bottom, that is, the diagonal, then the numbers will be displayed into each other through it, as in a mirror. This shows very important property multiplications: when the factors are swapped, the result of the calculation never changes. For example: 4 x 8 = 24, and also 8 x 4 = 24.

From this we conclude: how to remember the multiplication table quickly and easily? It is possible to halve the effort by memorizing the numbers of only the upper of the formed triangles. And the rest of the data is reproduced by changing the multipliers in places.

It will be easier for the child to find the result when multiplying numbers up to 10, if the smaller of them is put in the first place. This is usually taught in Japanese schools. It is believed that 4 times 8 is much easier to calculate than taking 8 times 4.

Sometimes it's better to start from the end

Children usually have no problems multiplying a number by 1, because the result will necessarily be the number itself. But when the child learns this simple rule, you should immediately explain to him that he cannot have difficulties with multiplying by 10 either, because it is almost as easy to do. When making these calculations, you simply need to attribute 0 to the number itself in your mind or on paper.

This convenience can be used a little later, helping to easily remember the multiplication table for 9. How to do this? We assign zero to the original number and subtract this number from the resulting number.

Let's give an example by multiplying 6 by 9. We add zero to the six and get 60. Then we subtract 6 - and 54 comes out. And so with all the other numbers.

Multiply by 9 with your fingers

Fingers help to master this science without difficulty. Starting a story about how easy it is to remember the multiplication table, namely that one difficult part, when we are talking about multiplying by 9, let's spread both hands in front of us on the table with palms to its surface. And let's number the fingers from left to right, assigning them numbers from 1 to 10.

Now imagine that you need to multiply 4 by 9. To do this, we bend the one of the fingers that has the fourth number, that is, the index on the left hand. This process is illustrated in the picture. To find the desired result, let's pay attention to the fact that three fingers remained uncurved on the left. These will be the tens of our number. And on the right we see six fingers. This will become the units of the desired result. In total, we get the number 36. As you know, 4 x 9 will be exactly the same.

It can be verified that this technique works in all other cases as well. That is, when multiplying 1 by 9, there will be no bent fingers on the left, and nine of them will remain on the right. This means that the desired number will be 9 (0 tens and 9 units), which for all mathematical laws right.

And one more example. Multiply 6 by 9. Bend the sixth finger on the left. This will be the thumb of the right hand. There are five tens on the left and four ones on the right. So our number will be 54. And this is the correct answer.

Here is a way to make it easier to remember the multiplication table for a child with such a large and uncomfortable number 9.

Number squares

Considering the table given at the beginning of the article, let's pay special attention to its elements marked in red. They are arranged diagonally from left to right. These numbers are the result of multiplying by themselves the numbers from 1 to 10.

And this is expressed by all known equalities:

1 x 1 = 1; 2 x 2 = 4; 3 x 3 = 9; 4 x 4 = 16; 5 x 5 = 25; 6 x 6 = 36; 7 x 7 = 49; 8 x 8 = 64; 9 x 9 = 81; 10 x 10 = 100.

Children in primary school do not yet know that such an action is tantamount to squaring. But if at this stage of training attention is paid to this circumstance, then later it will be more convenient for them to learn it.

How easy is it to remember the multiplication table in such a case? Let's explain this clearly for the multiplication of 7 x 7.

You should draw a rectangle, the length and width of which are seven cells, and number each of them. It is quite clear that a square will turn out, and the number of cells will be its area. In life, it is measured in square centimeters, meters, kilometers, and so on, that is, also in a kind of squares, but of a different and different size. And the desired result of the action, that is, 7 x 7, will be written in the very last, lower right cell. It reflects the number of cells and is simultaneously shown by the area of ​​the drawn square.

Series of differences of squares

What is the best way to memorize square numbers? Note that the results of multiplying numbers by themselves, given above, differ from each other in the following way.

4 - 1 = 3; 9 - 4 = 5; 16 - 9 = 7; 25 - 16 = 9; 36 - 25 = 11; 49 - 36 = 13; 64 - 49 = 15; 81 - 64 = 17; 100 - 91 = 19.

Total, there is a sequence of numbers: 3; five; 7; nine; eleven; 13; 15; 17; 19.

We have found the differences, and they are members of the resulting series. In such a sequence, each subsequent number differs from the previous one by 2. This means that the square of each next number increases compared to the square of the number that is one less, by a certain difference. And it, in turn, changes in each subsequent case by two, becoming larger.

If you point the child to such a property, this will be another way of how to remember the multiplication table quickly and easily. Numbers have interesting patterns, and knowing such interesting tricks in learning gives a result much better than stupid memorization of logically unrelated numbers. This can be presented to a child in the form of a game, which, by the way, can not only be exciting, but will help to practice mental counting.

small numbers

How easy is it to remember the multiplication table for 2 and 3? This is usually easy to achieve when working with a child. Small numbers, as a rule, do not cause difficulties for children. When multiplying two by factors from 1 to 10, you still won’t get more than 20. And here you just need to learn how to double. This can be achieved by sitting next to the child and counting using the fingers of two pairs of hands. Here's how easy it is to memorize the multiplication table by 2.

In the same way, you should train with tripling the numbers, connecting one more of the family members, as well as friends of the son or daughter, to a similar game.

Multiplying by five, it is most convenient and most correct to also resort to the same kind of trick. And in this case, the process is facilitated by the fact that a person has five fingers on each of the hands. And this is convenient when calculating and forming the result in the student's memory. Explaining this to a child, it is very appropriate here to delve into the history of mathematics. You can talk about how the decimal system of calculus arose in ancient times. And that this is due to the number of human fingers counted on one and two hands.

Prime Factors and Divisibility Tests

The child should pay special attention to the fact that when multiplying by 5 any of the numbers, even if it is much more than 10, you always get a product that ends in 0 or 5 in its writing. This will later help the little student to learn the signs of divisibility by 5.

It is useful to do the same with the numbers 2 and 3. How easy is it to remember the multiplication table for these numbers? Constantly pointing out that when any number is doubled, the result of the calculation always ends with the number 2; 4; 6; 8; 0. And when tripled, a product comes out, the constituent figures of which in the sum are always divisible by three.

Then you can start multiplying by 6, proving to the child in practice that when performing this action, you first need to triple the original number, and then double it (or vice versa), because the number 6 itself is made up of factors 2 and 3.

How easy is it to memorize the multiplication table for 8? Here it is convenient to show that the correct answer is obtained by doubling any given number three times. Similarly, multiplying by four, doubling the original should be twice.

prime number 7

Among the numbers from 1 to 10, seven turns out to be unexpectedly difficult for many children, precisely because it is a prime number. Although such a statement seems like a pun. Yes, from the point of view of mathematics, seven is prime, like all other numbers that, apart from themselves and one, have no divisors. And, of course, in view of this, it is difficult to multiply it. After all, the principles that have just been applied to 6 and 8 are not suitable for 7.

But given what was said about the number 7, how easy is it to remember the multiplication table? The game will help the child cope with the recalcitrant number. But what is needed for this?

Consider a very interesting thing - dice. It has six faces and is endowed with a remarkable property: the number of points on its opposite sides, when added, always gives seven. Therefore, to calculate the sum of the numbers marked on all faces, 3 x 7 is enough. This will be 21. If you take several dice, to calculate the number of points on its sides in the sum, it will be enough to multiply 21 by the number of these playing devices.

When working with a child, you should collect as many of these items as possible. When throwing dice, you must first offer the little student to count the numbers that fell on their upper and lower faces, adding them up. Then on the sides, all sides, and so on, comparing the results of each other during the game. At the same time, of course, in adults who know the secret of these mysterious objects, the calculations will be surprisingly fast, and the calculation of the answer will occur at magical speed. At the end of the competition, the secret should be revealed to the child, who will no doubt be surprised by such abilities. And explain at the same time how the calculation is made, inviting him to try it himself. That's what it is easy way memorize the multiplication table when it comes to a complex number like 7.

Multiplication by numbers greater than 5

Special difficulties in children younger age, of course, cause numbers greater than 5 and their multiplication with each other. But to easily cope with this task, fingers can again come to the rescue. It should be assured that there are ways to always find the answer to any question posed, solve examples and accurately find out the product of two indicated numbers, starting from 6 and ending with 10.

So how easy is it to remember the multiplication table on your fingers? They should be numbered again, but in a different way, not as in the application of the technique of multiplying only by 9, which was discussed earlier. Here, the thumbs on both hands are assigned the number 6, the index fingers - 7, the middle fingers following them - 8, the ring fingers - 9, and the little fingers - 10. The numbering scheme is shown in the picture below.

To find the product, fingers with the numbers of the desired numbers are connected. The number indicating the tens of the desired number is calculated as follows: two connected fingers plus the lower ones from them. And the units are found by multiplying the upper ones.

In the illustration below, you can see in more detail: how to multiply 8 by 9. Fingers with the corresponding numbers are connected. Next, the number of tens is counted, there are seven of them. Units are found by multiplying the number of upper fingers. So: 2 x 1 \u003d 2. In total, the number 72 comes out in the answer, which is correct.

There are also more difficult cases. For example, let's try to calculate 6 x 6. In this case, you have to connect your thumbs, and the number of tens seems to be 2, although this is not true. But the main difficulties in counting immediately become apparent when you have to determine the units and multiply the numbers of the upper fingers of both hands. Here 4 x 4 = 16, which is no longer a number, but a two-digit number. To get the correct answer, add two tens and the number 16. As a result, we get 36, which is the correct answer. This should be done every time when multiplying the upper fingers turns out to be a number greater than 9.

If the child learns the techniques described, he will immediately understand how easy it is to memorize the multiplication table.

We write mathematical poems

All children are known to be different. And they all have their own abilities. Some of them perfectly operate with numbers and learn their laws. Others are lyricists by nature. And no matter how much you explain the logic of multiplying numbers to them, they are little able to understand and remember. Therefore, there are small students for whom it is easy to remember the multiplication table in verse. How to do it better?

First of all, the child's attention should be drawn to the fact that some problems with multiplication and the answers to them rhyme on their own.

Here are some examples of this:

five five - twenty five;

six six - thirty six;

seven five - thirty five;

nine five - forty five.

But even if the tasks do not immediately add up to rhymes, then you can add them, that is, add phrases, thereby creating a poem out of them.

Here, as an example, consider the multiplication table for 7. And the rhyme can be like this:

Family two - fourteen, I want to become a scientist;

A family of three - twenty-one, we will sit stubbornly;

Family four - twenty-eight, we will decide for ourselves, we will not ask anyone;

A family of five - thirty-five, a hundred times I will repeat again;

A family of six - forty-two, help me learn words;

Family seven - forty nine, the main thing is to do the work;

Seven eight - fifty-six, I'm sure it is;

Seven nine - sixty three, and that's right, whatever you say.

The most important thing in implementing this method for parents is to understand that children should not be offered ready-made rhymed lines, forcing them to mindlessly memorize them. It is better to try to compose your own poems together and pick up good rhymes. Only then can we talk about the confidence that the child will perfectly memorize the multiplication table and remember it for the rest of his life.