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What is the name for counting large numbers in your head? Subtract three-digit numbers in your head. Effective mental arithmetic or brain exercise

One of the main reasons for poor results in mathematics on the Unified State Exam or Unified State Exam is the inability to count. Many schoolchildren find it difficult to solve an example even on a piece of paper, not to mention quickly counting in their heads. But some parts of the brain atrophy if a person does not use mental skills. Therefore, it is important to develop mental abilities to their full potential.

The basis for developing mental arithmetic skills

Some parents believe that teaching a child to quickly count examples in his head is not necessary: ​​he will not need it in the future, because he can always use a calculator. But at the same time, they forget that such training is simply necessary for brain development: any learned method (technique) of counting is a new neural chain (connection), the more such chains there are, the smarter the student. Therefore, the main benefit of the quick counting skill is the development of the brain and intelligence.

It is impossible to learn to work with numbers in your head if you have a weak understanding of them and actions with them.

Counting skills develop gradually from a visual representation of numbers and actions with them to an abstract logical one:

  1. First, the child learns to count straight and reverse order with the help of rhymes, nursery rhymes, practical exercises while walking, eating games (counting how many objects are on the table, cars in the garage, birds in the tree). Gets acquainted with numbers, learns what they mean, learns to correlate numbers and quantities.
  2. Then he masters the concepts of “more - less”, “equally”, learns to compare the number of objects, sizes.
  3. After this, he gets acquainted with addition and subtraction and learns the meaning of these actions. All examples are illustrative (the child moves 2 more apples to two apples and counts how many they get).
  4. Learns to count objects with his eyes, first pronounces out loud the actions and the result of the actions, and then in a whisper: if you add 2 more cars to 4, you get 6.
  5. Repeated repetition of actions will lead to the fact that the baby will learn to recognize examples that he has already worked with and say the result out loud, bypassing the stage of pronunciation.

At the stage of learning to count, it is important to interest the child, support him in case of failure and rejoice with him in victories, even small ones. When, the skill will need to be developed by introducing the student to various techniques and techniques.

Development of mental arithmetic skills

  • Improving the ability to work with numbers in your head.
  • Acquaintance with new techniques and techniques.
  • Training the ability to select the optimal solution algorithm in each specific case.

Ability to work with numbers

The following exercises will help you develop this skill:

  • “Name the numbers in which...” - indicates the range and condition, for example, “Name the numbers from 5 to 50 that contain the digit 3” or “Name all two-digit numbers that contain the digit 0.” By doing this exercise It is important to immediately work through all the mistakes made by the student. If he missed a number or said the wrong one, he starts over.
  • "Maintaining progression" (range and arithmetic operations depend on age and development of counting skills). For example, “Go from 5 in steps of 3” or “Go backwards from 30 in steps of 4” - for children primary school. For those who have already learned the multiplication table, you can give tasks for multiplication and division: “Go from 2, multiplying all numbers by 3.”
  • “Find the numbers from 1 to...” - children need to find and name in order all the numbers in the table.
  • “Compare the numbers” - children determine which one is larger (smaller), by how much;
  • “Examples” - schoolchildren are asked to solve examples in their minds, first the simplest ones (with small numbers), after working out the numbers are gradually increased. You should not introduce your child to two- or three-digit numbers if he does not know how to perform operations with numbers up to 5 perfectly.

Techniques for quickly counting numbers

Unfortunately, there is simply no single - universal - method that allows you to solve all examples equally quickly. Therefore, it is important to know and be able to put into practice several methods, from which you can then choose the most appropriate one.

Useful algorithms for solving some examples:

  • To quickly subtract 7, 8 or 9 from a number, you must first subtract 10 and then add 3,2 or 1, respectively. For example: 45-9=45-10+1=36, or 36-8=36-10+2=28.
  • You can also quickly multiply by 4, 8 and 16. To do this, you must first remember that 4=2*2, 8=2*2*2, 16=2*2*2*2. Then simply multiply the number by 2 several times: 6*16=6*2*2*2*2=96.
  • To multiply a number by 9, it is first increased 10 times, and then the first factor is subtracted from the resulting one: 27*9=27*10-27=243. This technique will allow you to very quickly find the result of multiplying by 9, if you do not use a calculator.
  • When multiplying by 2, it is more convenient to round non-round numbers, and then subtract or add (depending on which direction you rounded) the product of the remaining or missing number by 2: 132*2=130*2+2*2=264, or 138* 2=140*2-2*2=276.
  • Similarly, numbers are divided by 2: 156/2=150/2+6/2=78, or 156/2=160/2-4/2=78.
  • To multiply by 5, the number is divided by 2 and then increased by 10 times (the operation can be done the other way around): 27*5=27/2*10 or 27*10/2=135.
  • Similar actions are performed when multiplying by 25: first divide by 4, and then increase by 100 times (simply add two zeros): 16*25=16/4*100=400. Of course, it is more convenient to use this method when the first factor is divisible by 4 without a remainder. Determining whether a number is divisible by 4 without a remainder is not difficult (non-tabular cases): a number consisting of its last two digits must be divisible by 4. For example, the number 124 is divisible by 4 (24/4=6), but 526 is not (26 is not divisible by 4 without a remainder).

And another way to multiply a multi-digit number by a single-digit number is to multiply bit terms by the second factor and add the results. For example, 424*5=400*5+20*5+4*5=2000+100+20=2120.

In order not to make mistakes in calculations, it is important to be able to predict the future result, and several statements will help here:

  • When multiplying single-digit numbers, the result does not exceed 81: 9*9=81.
  • Similarly, 99*99=9801, so the result of multiplying two-digit numbers should not be greater than this number, and when multiplying three-digit numbers, the maximum number is 998001.

Practicing mental arithmetic skills

The above algorithms are the basis for developing mental counting skills. Learn to count complex examples It is possible only with regular training, bringing the use of the skill to automaticity.

The effectiveness of work in this direction can be increased if during classes:

  1. Create a game situation , transforming the ordinary educational process into an interesting and unusual process.
  2. Keep your child engaged interesting material constant change of activity.
  3. Create a spirit of competition – the awareness that someone can do better will make you strive for new achievements; such classes will be more effective than memorizing “alone.”
  4. Record personal achievements , set new goals to achieve new heights.

The ability to concentrate on solving a problem in any situation (even when others are in the way) also contributes to the development of counting skills (and not only). You can train this ability by solving examples with music on or while in a noisy company.

To prevent your child from becoming bored, it is important to learn how to deal with this feeling. Psychologists recommend using any action for this: for example, looking at what is happening outside the window, or observing the movement of the clock hands. If a child learns to cope with boredom and direct his energy in the right direction, then in class he will be able to absorb a greater amount of information, which will have a positive impact on his academic performance. .

Quick counting techniques: magic accessible to everyone

In order to understand what role numbers play in our lives, perform a simple experiment. Try to do without them for a while. Without numbers, without calculations, without measurements... You will find yourself in strange world, where you will feel absolutely helpless, tied hand and foot. How to make it to a meeting on time? Can you tell one bus from another? Make a phone call? Buy bread, sausage, tea? Cook soup or potatoes? Without numbers, and therefore without counting, life is impossible. But how difficult this science is sometimes! Try quickly multiplying 65 by 23? Does not work? The hand itself reaches for a mobile phone with a calculator. Meanwhile, semi-literate Russian peasants 200 years ago calmly did this, using only the first column of the multiplication table - multiplication by two. Don't believe me? But in vain. This is reality.

Stone Age "computer"

Even without knowing the numbers, people were already trying to count. If our ancestors, who lived in caves and wore skins, needed to exchange something with a neighboring tribe, they did it simply: they cleared the area and laid out, for example, an arrowhead. A fish or a handful of nuts lay nearby. And so on until one of the exchanged goods ran out, or the head of the “trade mission” decided that enough was enough. It’s primitive, but very convenient in its own way: you won’t get confused and won’t be deceived.

With the development of cattle breeding, the tasks became more complicated. Big herd it was necessary to somehow count in order to know whether all the goats or cows were there. The “calculating machine” of the illiterate but smart shepherds was a hollowed-out pumpkin with pebbles. As soon as the animal left the pen, the shepherd placed a pebble in the pumpkin. In the evening the herd returned, and the shepherd took out a pebble with each animal that entered the pen. If the pumpkin was empty, he knew that the herd was all right. If there were stones left, he went to look for the loss.

When the numbers came in, things got better. Although for a long time our ancestors had only three numerals in use: “one”, “pair” and “many”.

Is it possible to count faster than a computer?

Overtake a device performing hundreds of millions of operations per second? Impossible... But the one who says this is cruelly disingenuous, or simply deliberately overlooks something. A computer is just a set of chips in plastic; it does not count on its own.

Let's pose the question differently: can a person, counting in his head, outperform someone who does calculations on a computer? And here the answer is yes. After all, in order to receive a response from the “black suitcase”, the data must first be entered into it. This will be done by a person using his fingers or voice. And all these actions have time limits. Insurmountable restrictions. Nature itself supplied them to the human body. Everything - except one organ. Brain!

The calculator can perform only two operations: addition and subtraction. For him, multiplication is multiple addition, and division is multiple subtraction.

Our brains act differently.

The class where the future king of mathematics, Carl Gauss, studied, once received a task: add all the numbers from 1 to 100. Carl wrote the absolutely correct answer on his board as soon as the teacher finished explaining the task. He did not diligently add the numbers in order, as any self-respecting computer would do. He applied the formula he himself discovered: 101 x 50 = 5050. And this is far from the only technique that speeds up mental calculations.

The simplest techniques for quick counting

They are studied at school. The simplest thing: if you need to add 9 to any number, add 10 and subtract 1 if 8 (+ 10 - 2), 7 (+ 10 - 3), etc.

54 + 9 = 54 + 10 - 1 = 63. Fast and convenient.

Two-digit numbers add just as easily. If the last digit in the second term is greater than five, the number is rounded to the next ten, and then the “extra” is subtracted. 22 + 47 = 22 + 50 - 3 = 69. If the key number is less than five, then you need to add the tens first, then the ones: 27 + 51 = 20 + 50 + 7 + 1 = 78.

With three-digit numbers, no difficulties arise in the same way. We add them up as we read, from left to right: 321 + 543 = 300 + 500 + 20 + 40 + 1 + 3 = 864. Much easier than in a column. And much faster.

What about subtraction? The principle is the same: we round what is subtracted to a whole number and add what is missing: 57 - 8 = 57 - 10 + 2 = 49; 43 - 27 = 43 - 30 + 3 = 16. Faster than using a calculator - and no complaints from the teacher, even during the test!

Do I need to learn the multiplication table?

Children, as a rule, cannot stand this. And they do it right. There's no point in teaching her! But don’t rush to be indignant. No one is saying that you don't need to know the table.

Its invention is attributed to Pythagoras, but, most likely, the great mathematician only gave a complete, laconic form to what was already known. At the excavations of ancient Mesopotamia, archaeologists found clay tablets with the sacramental: “2 x 2”. People have been using this for a long time highest degree convenient system of calculations and discovered many ways that help to comprehend the internal logic and beauty of the table, to understand - and not to stupidly, mechanically memorize.

IN ancient China We started learning the table by multiplying by 9. It’s easier this way, not least because you can multiply by 9 “on your fingers.”

Place both hands on the table, palms down. The first finger on the left is 1, the second is 2, etc. Let's say you need to solve the example 6 x 9. Raise your sixth finger. The fingers on the left will show tens, on the right - ones. Answer 54.

Example: 8 x 7. Left hand- the first multiplier, the right one - the second. There are five fingers on the hand, but we need 8 and 7. We bend three fingers on the left hand (5 + 3 = 8), on the right hand 2 (5 + 2 = 7). We have five bent fingers, which means five dozen. Now let's multiply the remaining ones: 2 x 3 = 6. These are units. Total 56.

This is just one of the simplest “finger” multiplication techniques. There are many of them. You can operate with numbers up to 10,000 on your fingers!

The “finger” system has a bonus: the child perceives it as fun game. He studies willingly, experiences a lot of positive emotions and, as a result, very soon begins to perform all operations in his mind, without the help of his fingers.

You can also divide using your fingers, but it is a little more difficult. Programmers still use their hands to convert numbers from decimal to binary - it is more convenient and much faster than on a computer. But within school curriculum You can learn to quickly divide even without fingers, in your mind.

Let's say we need to solve example 91: 13. Column? There is no need to dirty the paper. The dividend ends in one. And the divisor is by three. What is the very first thing in the multiplication table that involves a three and ends with a one? 3 x 7 = 21. Seven! That's it, we caught her. You need 84: 14. Remember the table: 6 x 4 = 24. The answer is 6. Simple? Still would!

The magic of numbers

Most fast counting techniques are similar to magic tricks. Take at least famous example multiplying by 11. To, for example, 32 x 11, you need to write 3 and 2 at the edges, and put their sum in the middle: 352.

To multiply a two-digit number by 101, you simply write the number twice. 34 x 101 = 3434.

To multiply a number by 4, you need to multiply it by 2 twice. To divide, divide it by 2 twice.

Many witty and, most importantly, quick techniques help raise a number to a power, extract Square root. The famous "30 techniques of Perelman" for mathematical thinking people will cooler show Copperfield, because they also UNDERSTAND what is happening and how it is happening. Well, the rest can just enjoy the beautiful focus. For example, you need to multiply 45 by 37. Write the numbers on a sheet of paper and divide them with a vertical line. Divide the left number by 2, discarding the remainder until we get one. Right - multiply until the number of lines in the column is equal. Then we cross out from the RIGHT column all those numbers opposite which in the LEFT column we got an even result. We add up the remaining numbers from the right column. The result is 1665. Multiply the numbers in the usual way. The answer will fit.

"Charge" for the mind

Quick counting techniques can greatly make life easier for a child at school, for a mother in a store or in the kitchen, and for a father at work or in the office. But we prefer a calculator. Why? We don't like to strain ourselves. It's hard for us to keep numbers, even two-digit ones, in our heads. For some reason they don't hold up.

Try going to the middle of the room and doing the splits. For some reason it doesn’t “plant”, right? And the gymnast does it completely calmly, without straining. Need to train!

The easiest way to train and, at the same time, warm up the brain: mentally count out loud (required!) through numbers to one hundred and back. In the morning, while standing in the shower, or while preparing breakfast, count: 2.. 4.. 6.. 100... 98.. 96. You can count in three, in eight - the main thing is to do it out loud. In just a couple of weeks regular classes you'll be surprised how much EASIER it becomes to handle numbers.

Mental counting, like everything else, has its own tricks, and in order to learn to count faster you need to know these tricks and be able to apply them in practice.

Today we will do just that!

1. How to quickly add and subtract numbers

Let's look at three random examples:

  1. 25 – 7 =
  2. 34 – 8 =
  3. 77 – 9 =

Like 25 – 7 = (20 + 5) – (5- 2) = 20 – 2 = (10 + 10) – 2 = 10 + 8 = 18

Agree that such operations are difficult to carry out in your head.

But there is an easier way:

25 – 7 = 25 – 10 + 3, since -7 = -10 + 3

It is much easier to subtract 10 from a number and add 3 than to make complex calculations.

Let's return to our examples:

  1. 25 – 7 =
  2. 34 – 8 =
  3. 77 – 9 =

Let's optimize the subtracted numbers:

  1. Subtract 7 = subtract 10 add 3
  2. Subtract 8 = subtract 10 add 2
  3. Subtract 9 = subtract 10 add 1

In total we get:

  1. 25 – 10 + 3 =
  2. 34 – 10 + 2 =
  3. 77 – 10 + 1 =

Now it’s much more interesting and easier!

Now calculate the examples below in this way:

  1. 91 – 7 =
  2. 23 – 6 =
  3. 24 – 5 =
  4. 46 – 8 =
  5. 13 – 7 =
  6. 64 – 6 =
  7. 72 – 19 =
  8. 83 – 56 =
  9. 47 – 29 =

2. How to quickly multiply by 4, 8 and 16

In the case of multiplication, we also break numbers into simpler ones, for example:

If you remember the multiplication table, then everything is simple. And if not?

Then you need to simplify the operation:

We put the largest number first, and decompose the second into simpler ones:

8 * 4 = 8 * 2 * 2 = ?

Doubling numbers is much easier than quadrupling or octupling them.

We get:

8 * 4 = 8 * 2 * 2 = 16 * 2 = 32

Examples of decomposing numbers into simpler ones:

  1. 4 = 2*2
  2. 8 = 2*2 *2
  3. 16 = 22 * 2 2

Practice this method using the following examples:

  1. 3 * 8 =
  2. 6 * 4 =
  3. 5 * 16 =
  4. 7 * 8 =
  5. 9 * 4 =
  6. 8 * 16 =

3. Dividing a number by 5

Let's take the following examples:

  1. 780 / 5 = ?
  2. 565 / 5 = ?
  3. 235 / 5 = ?

Dividing and multiplying with the number 5 is always very simple and enjoyable, because five is half of ten.

And how to solve them quickly?

  1. 780 / 10 * 2 = 78 * 2 = 156
  2. 565 /10 * 2 = 56,5 * 2 = 113
  3. 235 / 10 * 2 = 23,5 *2 = 47

To work through this method, solve the following examples:

  1. 300 / 5 =
  2. 120 / 5 =
  3. 495 / 5 =
  4. 145 / 5 =
  5. 990 / 5 =
  6. 555 / 5 =
  7. 350 / 5 =
  8. 760 / 5 =
  9. 865 / 5 =
  10. 1270 / 5 =
  11. 2425 / 5 =
  12. 9425 / 5 =

4. Multiplying by single digits

Multiplication is a little more difficult, but not much, how would you solve the following examples?

  1. 56 * 3 = ?
  2. 122 * 7 = ?
  3. 523 * 6 = ?

Without special counters, solving them is not very pleasant, but thanks to the “Divide and Conquer” method we can count them much faster:

  1. 56 * 3 = (50 + 6)3 = 50 3 + 6*3 = ?
  2. 122 * 7 = (100 + 20 + 2)7 = 100 7 + 207 + 2 7 = ?
  3. 523 * 6 = (500 + 20 + 3)6 = 500 6 + 206 + 3 6 =?

All we have to do is multiply single digit numbers, some of which contain zeros, and add the results.

To work through this technique, solve the following examples:

  1. 123 * 4 =
  2. 236 * 3 =
  3. 154 * 4 =
  4. 490 * 2 =
  5. 145 * 5 =
  6. 990 * 3 =
  7. 555 * 5 =
  8. 433 * 7 =
  9. 132 * 9 =
  10. 766 * 2 =
  11. 865 * 5 =
  12. 1270 * 4 =
  13. 2425 * 3 =

    14. Divisibility of a number by 2, 3, 4, 5, 6 and 9

Check the numbers: 523, 221, 232

A number is divisible by 3 if the sum of its digits is divisible by 3.

For example, take the number 732, represent it as 7 + 3 + 2 = 12. 12 is divisible by 3, which means the number 372 is divisible by 3.

Check which of the following numbers are divisible by 3:

12, 24, 71, 63, 234, 124, 123, 444, 2422, 4243, 53253, 4234, 657, 9754

A number is divisible by 4 if the number consisting of its last two digits is divisible by 4.

For example, 1729. The last two digits form 20, which is divisible by 4.

Check which of the following numbers are divisible by 4:

20, 24, 16, 34, 54, 45, 64, 124, 2024, 3056, 5432, 6872, 9865, 1242, 2354

A number is divisible by 5 if its last digit is 0 or 5.

Check which of the following numbers are divisible by 5 (the easiest exercise):

3, 5, 10, 15, 21, 23, 56, 25, 40, 655, 720, 4032, 14340, 42343, 2340, 243240

A number is divisible by 6 if it is divisible by both 2 and 3.

Check which of the following numbers are divisible by 6:

22, 36, 72, 12, 34, 24, 16, 26, 122, 76, 86, 56, 46, 126, 124

A number is divisible by 9 if the sum of its digits is divisible by 9.

For example, take the number 6732, represent it as 6 + 7 + 3 + 2 = 18. 18 is divisible by 9, which means the number 6732 is divisible by 9.

Check which of the following numbers are divisible by 9:

9, 16, 18, 21, 26, 29, 81, 63, 45, 27, 127, 99, 399, 699, 299, 49

Game "Quick addition"

  1. Speeds up mental counting
  2. Trains attention
  3. Develops creative thinking

An excellent simulator for developing fast counting. A 4x4 table is given on the screen, and numbers are shown above it. The most big number need to be collected in a table. To do this, click on two numbers whose sum is equal to this number. For example, 15+10 = 25.

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 "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.

Today's task

Solve all examples and practice for at least 10 minutes in the game Quick Addition.

It is very important to work through all the tasks in this lesson. The better you complete the tasks, the more benefits you will receive. If you feel that you don’t have enough tasks, you can create examples for yourself and solve them and practice mathematical educational games.

Lesson taken from the course "Mal Calculus in 30 Days"

Learn to quickly and correctly add, subtract, multiply, divide, square numbers, and even take roots. I will teach you how to use easy techniques to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

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Knowledge of the psychology of money and how to work with it makes a person a millionaire. 80% of people take out more loans as their income increases, becoming even poorer. On the other hand, self-made millionaires will earn millions again in 3-5 years if they start from scratch. This course teaches you how to properly distribute income and reduce expenses, motivates you to study and achieve goals, teaches you how to invest money and recognize a scam.

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Why do we need mental arithmetic if this is the 21st century, and all sorts of gadgets are capable of performing any arithmetic operations almost at lightning speed? You don’t even have to point your finger at your smartphone, but give a voice command and immediately receive the correct answer. Nowadays even schoolchildren do this successfully. junior classes who are too lazy to divide, multiply, add and subtract on their own.

But this medal also has back side: scientists warn that if you don’t train, don’t load him with work and make his tasks easier, he begins to be lazy and his performance declines. In the same way, without physical training, our muscles weaken.

Mikhail Vasilyevich Lomonosov also spoke about the benefits of mathematics, calling it the most beautiful of sciences: “You have to love mathematics because it puts your mind in order.”

Oral arithmetic develops attention and reaction speed. It is not for nothing that more and more new methods of rapid mental calculation are appearing, intended for both children and adults. One of them is the Japanese mental counting system, which uses the ancient Japanese soroban abacus. The methodology itself was developed in Japan 25 years ago, and now it is successfully used in some of our mental counting schools. It uses visual images, each of which corresponds to a specific number. Such training develops the right hemisphere of the brain, which is responsible for spatial thinking, constructing analogies, etc.

It is curious that in just two years, students of such schools (they accept children aged 4–11 years) learn to perform arithmetic operations with 2-digit and even 3-digit numbers. Kids who don't know multiplication tables can multiply here. They add and subtract large numbers without writing them down. But, of course, the goal of training is the balanced development of the right and left.

You can also master mental arithmetic with the help of the problem book “1001 problems for mental arithmetic at school,” compiled back in the 19th century by a rural teacher and famous educator Sergei Aleksandrovich Rachinsky. This problem book is supported by the fact that it went through several editions. This book can be found and downloaded on the Internet.

People who practice quick counting recommend Yakov Trachtenberg’s book “The Quick Counting System.” The history of the creation of this system is very unusual. To survive the concentration camp where he was sent by the Nazis in 1941, and not lose his mental clarity, a Zurich mathematics professor began developing algorithms for mathematical operations that allow him to quickly count in his head. And after the war, he wrote a book in which the quick counting system is presented so clearly and accessiblely that it is still in demand.

There are also good reviews about Yakov Perelman’s book “Quick Counting. Thirty simple examples oral counting." The chapters of this book are devoted to multiplying by single-digit and two-digit numbers, in particular multiplying by 4 and 8, 5 and 25, by 11/2, 11/4, *, dividing by 15, squaring, and formula calculations.

The simplest methods of mental counting

People who have certain abilities will master this skill faster, namely: the ability to logical thinking, the ability to concentrate and store several images in short-term memory at the same time.

No less important is knowledge of special action algorithms and some mathematical laws that allow, as well as the ability to choose the most effective one for a given situation.

And, of course, you can’t do without regular training!

Some of the most common quick counting techniques are:

1. Multiplying a two-digit number by a one-digit number

The easiest way to multiply a two-digit number by a single-digit number is to split it into two components. For example, 45 - by 40 and 5. Next, we multiply each component by the required number, for example, by 7, separately. We get: 40 × 7 = 280; 5 × 7 = 35. Then we add the resulting results: 280 + 35 = 315.

2. Multiplying a three-digit number

Multiplying a three-digit number in your head is also much easier if you break it down into its components, but present the multiplicand in such a way that it is easier to perform mathematical operations with it. For example, we need to multiply 137 by 5.

We represent 137 as 140 − 3. That is, it turns out that we now have to multiply by 5 not 137, but 140 − 3. Or (140 − 3) x 5.

Knowing the multiplication table within 19 x 9, you can count even faster. We decompose the number 137 into 130 and 7. Next, we multiply by 5, first 130, and then 7, and add the results. That is, 137 × 5 = 130 × 5 + 7 × 5 = 650 + 35 = 685.

You can expand not only the multiplicand, but also the multiplier. For example, we need to multiply 235 by 6. We get six by multiplying 2 by 3. Thus, we first multiply 235 by 2 and get 470, and then multiply 470 by 3. Total 1410.

The same action can be done differently by representing 235 as 200 and 35. It turns out 235 × 6 = (200 + 35) × 6 = 200 × 6 + 35 × 6 = 1200 + 210 = 1410.

In the same way, by breaking down numbers into their components, you can perform addition, subtraction and division.

3. Multiplying by 10

Everyone knows how to multiply by 10: simply add zero to the multiplicand. For example, 15 × 10 = 150. Based on this, it is no less simple to multiply by 9. First, we add 0 to the multiplicand, that is, multiply it by 10, and then subtract the multiplicand from the resulting number: 150 × 9 = 150 × 10 = 1500 − 150 = 1,350.

4. Multiplication by 5

It is easy to multiply by 5. You just need to multiply the number by 10, and divide the resulting result by 2.

5. Multiplying by 11

It’s interesting to multiply two-digit numbers by 11. Let’s take 18, for example. Let’s mentally expand 1 and 8, and between them write the sum of these numbers: 1 + 8. We get 1 (1 + 8) 8. Or 198.

6. Multiply by 1.5

If you need to multiply a number by 1.5, divide it by two and add the resulting half to the whole: 24 × 1.5 = 24 / 2 + 24 = 36.

These are just the most simple ways mental calculations, with the help of which we can train our brain in everyday life. For example, counting the cost of purchases while standing in line at the checkout. Or perform mathematical operations with numbers on the license plates of passing cars. Those who like to “play” with numbers and want to develop their thinking abilities can turn to the books of the above-mentioned authors.

Number sense, minimal counting skills are the same element of human culture as speech and writing. And if you easily count in your mind, then you feel a different level of control over reality. In addition, this skill develops thinking abilities: concentration on objects and things, memory, attention to detail and switching between streams of knowledge. And if you are interested in how to learn to count quickly in your head, the secret is simple: you need to constantly practice.

Memory training: myth or reality?

In mathematics, everything is simple for those smart individuals who click equations like seeds. It is more difficult for other people to learn. But nothing is impossible, everything is possible if you practice a lot. There are the following mathematical operations: subtraction, addition, multiplication, division. Each of them has its own characteristics. To understand all the complexities, you need to understand them once, and then everything will be much simpler. If you practice for 10 minutes every day, in a few months you will reach a decent level and learn the truth of counting mathematical numbers.

Many people do not understand how they can vary numbers in their minds. How to become the master of numbers so that it does not look stupid and imperceptible from the outside? When you don’t have a calculator at hand, your brain begins to intensively process information, trying to calculate the necessary numbers in your head. But not all people succeed in achieving the desired results, since each of us is individual personality with your limits. If you want to understand in your mind, then you should study the whole necessary information, armed with a pen, notepad and patience.

The multiplication table will save the situation

We will not talk about those people who have an IQ level above 100; there are special requirements for such individuals. Let's talk about the average person who can learn many manipulations using the multiplication table. So, how to quickly count in your head without losing your health, energy and time? The answer is simple: memorize the multiplication table! In fact, there is nothing difficult here, the main thing is to have pressure and patience, and the numbers themselves will give in to your goal.

For such an amusing undertaking, you will need a smart partner who can test you and keep you company in this process that requires patience. The man who knows is in the mind of even the laziest student. Once you can multiply quickly, counting mentally will become routine. Unfortunately, there are no magic methods. How quickly you can learn a new skill is up to you. You can exercise your brain not only with the help of multiplication tables; there is a more exciting activity - reading books.

Books and no calculator train your brain

In order to learn how to perform computational activities verbally as quickly as possible, you need to constantly harden your brain new information. But how can you learn to count quickly in Uza? a short time? You can train your memory only with useful books, thanks to which not only the work of your brain will be universal, but also, as a bonus, improving your memory and gaining useful knowledge. But reading books is not the end of training. Only when you can forget about the calculator will your brain begin to process information faster. Try to count in your head in any case, think through complex mathematical examples. But if it’s hard for you to do all this on your own, then enlist the help of a professional who will quickly teach you everything.

It may be difficult for you to understand how to learn to count quickly in your head when you are not familiar with mathematics and are not good teacher, which could make the task easier. But you shouldn’t give in to difficulties. Having studied all the necessary recommendations, you can easily quickly learn to count in your head and surprise your peers with new abilities.

  • The ability to work with large numbers goes beyond general development.
  • Knowing the “tricks” of counting will help you quickly overcome all obstacles.
  • Regularity is more important than intensity.
  • Don't rush, try to catch your rhythm.
  • Focus on correct answers, not on memorization speed.
  • Say your actions out loud.
  • Don't be discouraged if you don't succeed, because the main thing is to start.

Never give up in the face of difficulties

During your training, you may have many questions to which you do not know the answers. This shouldn't scare you. After all, you cannot know at first how to quickly count without preliminary preparation. The road can only be mastered by those who always move forward. Difficulties should only strengthen you, and not slow down your desire to join people with non-standard capabilities. Even if you are already at the finish line, return to the easiest thing, train your brain, do not give it the opportunity to relax. And remember, the more you speak information out loud, the faster you will remember it.