Multiplication table on fingers. Multiplication on fingers

Preparation
Each finger on the left and right hand is assigned a specific number:
little finger - 6,
ring finger - 7,
average - 8,
index - 9
and the big one - 10.
At the beginning of mastering the method, these numbers can be drawn on your fingertips. When multiplying, the hands are positioned naturally, palms facing you.

Methodology
1. Multiply 7 by 8. Turn your hands with your palms facing you and touch ring finger(7) left hand middle finger (8) right (see figure).

Let's pay attention to the fingers that are above the touching fingers 7 and 8. On the left hand there are three fingers above 7 (middle, index and thumb), on the right hand above 8 there are two fingers (index and thumb).
We will call these fingers (three on the left hand and two on the right) upper. We will call the remaining fingers (little and ring fingers on the left hand and little, ring and middle fingers on the right) lower. In this case (7 x 8) there are 5 upper fingers and 5 lower ones.
Now let’s find the product 7 x 8. To do this:
1) multiply the number of lower fingers by 10, we get 5 x 10 = 50;
2) multiply the number of upper fingers on the left and right hands, we get 3 x 2 = 6;
3) finally, add these two numbers, we get the final answer: 50 + 6 = 56.
We got that 7 x 8 = 56.

2. Multiply 6 by 6. Turn your hands with your palms facing you and touch your left hand with your little finger (6) to your right hand (6).


Now there are 4 upper fingers on the left and right hands.
Let's find the product 6 x 6:
1) multiply the number of lower fingers by 10: 2 x 10 = 20;
2) multiply the number of upper fingers on the left and right hands: 4 x 4 = 16;
3) add these two numbers: 20 + 16 = 36.
We got that 6 x 6 = 36.

3. Multiply 7 by 10. This will test the rule of multiplication by 10. Touch the ring finger (6) of your left hand thumb(10) right. There are 3 upper fingers on the left hand, and 0 on the right (see figure).


Let's find the product 7 x 10:
1) multiply the number of lower fingers by 10: 7 x 10 = 70;
2) multiply the number of upper fingers on the left and right hands: 3 x 0 = 0;
3) add these two numbers: 70 + 0 = 70.
We got that 7 x 10 = 70.
http://www.baby.ru/blogs/post/202133846-69131/

Multiply by 9
To do this, place your hands palms down next to each other, fingers straight. Now, to multiply any number by 9, simply bend your finger under the number of this number (counting from the left). The number of fingers before the curved one will be tens of the answer, and after - units.

http://4brain.ru/memory/_kak-vyuchit-tablicu-umnozhenija.php

Today in the lesson we will literally learn to multiply numbers with our fingers. When you don’t have a notebook and calculator at hand, pay attention to the hand itself - it has fingers. My grandmother showed me this method of multiplication, and I decided, since I myself will never become a grandmother, it’s time to tell you about the capabilities 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:
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. Multiply 6x6. Bend one finger on both hands.
We multiply the unbent fingers by each other. 4x4=16. We take the bent ones as tens and add them up. This is 20. 20+16=36. Total 6x6=36
Let's multiply. 6x7.
We multiply the unbent fingers by each other. 4x3=12. We take the bent ones as tens and add them up. This is 30. 30+12=42. Total 6x7=42
Multiply 7x7
We multiply the unbent fingers by each other. 3x3=9. We take the bent ones as tens and add them up. This is 40. 40+9=49. Total 7x7=49
Multiply 7x8
We multiply the unbent fingers by each other. 3x2=6. We take the bent ones as tens and add them up. This is 50. 50+6=56. Total 7x8=56
Multiply 8x8
We multiply the unbent fingers by each other. 2x2=4. We take the bent ones as tens and add them up. This is 60. 60+4=42. Total 8x8=64
Multiply 8x9
We multiply the unbent fingers by each other. 2x1=2. We take the bent ones as tens and add them up. This is 70. 70+2=72. Total 8x9=72
And multiply 9x9

In life, people who are able to do mental calculations look like “super smart people,” although there is nothing complicated about it. A calculator is a calculator, but counting in your head is useful!

How to help your child learn the multiplication tables?

Below are some simple techniques

Multiplying by 2 or doubling.

Doubling is quite easy, just add something to yourself. First, I showed one, two, three, four, five fingers on my left and right hand at the same time - this is how we got 2, 4, 6, 8, 10.

Together with my student's fingers, we reached twenty, and then I pointed to different things in the room, and suggested that they count and double - the number of letters in a poster, the number of symbols on a clock dial, count the number of spokes on one side of a bicycle wheel, and check if it fits whether total number with doubled and so on.

Multiplying by 4 and 8, 3 and 6

When you know how to multiply by two, this is mere nonsense. Multiplying by four is the same as doubling the answer for something that has already been doubled, for example, 7x4 is 7x2x2, and we already remembered well that 7x2 is 14 in the previous lesson about doubling, so turn 14 itself into 28 will not be difficult. Once you've figured out the four, it's not so difficult to figure out the large numbers eights. Along the way we noticed that, for example, 16 is both 2x8 and 4x4. So we learned that there are numbers consisting entirely of twos: 2, 4, 8, 16, 32, 64.

By multiplying by 3 and 6, we learned the old pirate method of "dividing by three."

If you add the digits of a number multiplied by 3, 6, or any other number that is divisible by three, then the result of adding the digits of the answer is always a multiple of three. For example, 3x5 = 15, 1+5 = 6. Or 6x8 = 48, and 4+8 = 12, a multiple of three. And you can add the numbers into 12, you also get 3, so if you get to the end like this, you always get one of three numbers: 3, 6 or 9.

So we turned it into another game. I would ask a number, even a three- or four-digit one, and ask if it was divisible by 3. To answer, just add the numbers, which is quite simple. If the number was divisible by 3, then I asked - “and by 6?” – and then you just had to see if it was even. And then (in the special case of small numbers from the table) sometimes I also wanted to find out what would happen when dividing by 3 or 6. It was a very fun activity.

Multiplying by 5 and 7, prime numbers

And now we are left with multiplication by five, seven, and nine. This means that we learned how to multiply them by many other numbers - by 1, 2, 3, 4, 6, 8 and 10. We figured out five very quickly - it’s easy to remember: at the end there is either a zero or five, just the same as a number to be multiplied: either even or odd.

A clock dial is a great object to use with A's; you can come up with a lot of problems about traveling in time and space. At the same time, I explained why there are sixty minutes in an hour, and we understood why this is convenient.

We saw that it is convenient to divide 60 by 1, 2, 3, 4, 5, 6, but it is inconvenient to divide by 7. So it was time to take a closer look at this number. From multiplication by seven, the only things left to remember were 7×7 and 7×9. Now we knew almost everything we needed. I explained that seven is simply a very proud number - such numbers are called prime, they are divisible only by 1 and themselves.

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 an interesting method of multiplication on our fingers. We figured it out. Arina is delighted, and I’m also somewhat surprised why they didn’t know about this at school! I'm sharing.

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

Now let's try to multiply, for example, 7x8. To do this, connect finger No. 7 on your left hand with finger No. 8 on your right.

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

And we multiply the fingers of the left hand remaining on top 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 greater than 9. In such cases, you need to add both results into a column.

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

3 (tens)
+
12 (units)
________
42

Multiply by 9

Turn your hands again with your palms facing you, but now the numbering of your 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 No. 2 is tens (that is, 1 in this case). And all that remains after finger No. 2 is units (that is, 8). As a result we get 18.

Multiplying by 1 and 10

It’s worth starting with this to reassure the child: multiplying by one is the number itself, and multiplying by 10 is the number and zero after it. Now he already knows the answers to the first and last examples in all columns.

Multiply by 2

Multiplying a number by two means adding two identical numbers.

Multiply by 3

To remember this column, mnemonic techniques are suitable, for example, short poems. You can come up with them together with your child or look for “ready-made” ones on the Internet:

Come on, my friend, look,

What is three times three?

There is nothing to do!

Well, of course, nine!

All the boys need to know

What is three times five?

And don't make mistakes!

Three times five is fifteen!

If you are not strong in poetry, come up with prose stories, the heroes of which will be two - a swan, three - a snake, four - an overturned chair, eight - glasses, and so on - the children themselves will tell you who they think the numbers look like .

Stories and poems can be invented not only for the three, but also for any column of the Pythagorean table.

Multiply by 4

Multiplying by 4 can be represented as multiplying by 2 and again by 2. This column will not cause any difficulties for students who have mastered multiplication by two.

Multiply by 5

This is the easiest column to remember. All values ​​of this column are located 5 units apart. Moreover, if multiplied by 5 even number, the product will end in 0, and if odd, it will end in 5.

Multiplying by 6, 7, 8

These columns, as well as the column of multiplication by 9, traditionally cause difficulties for schoolchildren. You can reassure students by explaining that they have already learned most of the examples from these columns and the daunting 8x3 is the same as the already learned 3x8. By swapping the factors, you can remember what the product is equal to.

This means that children will only have to remember 6 “unfamiliar” examples:

These examples can be written on cards, hung on the wall, and memorized mechanically. You can learn to count on your fingers:

You can also multiply 7 by 8 or 8 by 9 in the same way.

You can see the process of such multiplication with your own eyes in the video (note: in the video, numbering is done in a similar way, but starting with the thumbs):

Multiply by 9

To begin with, you can remember that in the multiplication table by nine, the sum of tens and ones in the answer is always equal to 9. Namely: 9×2=18 (add the numbers of the answer: 1+8=9), the same in other examples: 9 ×6=54 (5+4=9).

In this case, the ten digit in the answer is always one less than the second factor in the example. In practice: 9×7=63 (the second factor is 7, which means there are 6 tens in the answer. If we now remember the first rule, that the sum of tens and ones in the answer should be equal to 9, we get the answer 63).

And one more “secret”: if you have paper and a pencil at hand, you can quickly write down the numbers from 0 to 9 in a column (these will be tens), and next to a second column from 9 to 0, you will get the answers to the multiplication table by 9.

You can quickly check multiplication by 9 on your fingers:

Place your hands palms down on the table;

Mentally number your fingers from the little finger of your left hand to the little finger of your right (little finger of the left hand - 1, ring finger of the left hand - 2 and so on to the little finger right hand, which, accordingly, will be 10):

Name the number you want to multiply nine by. Let's say this number is 3:

Bend the finger that was assigned serial number 3 (this will be the middle finger of the left hand);

The fingers that remain to the left of the curved one represent tens (for us it is the little finger and the ring finger - two fingers, i.e. 2 tens, the number 20);

The fingers that remain to the right of the bent one are units. We have 2 fingers of the left hand left on the right + all 5 fingers of the right hand - a total of 7 fingers, 7 units;

2 tens (20) + 7 units (7) = 27. This is the product of 9 and 3.

You can also multiply 9 by 7 or 9 by 10 in the same way.

Studying the multiplication table will require perseverance and patience from any student, but counting on fingers, rhymes, and cards with examples will help facilitate memorization and make it interesting and quick.