People rarely use the knowledge gained in algebra and geometry lessons in life. The most valuable and necessary skill associated with mathematics is the ability to do quick mental math, so it's worth figuring out how to learn it. In everyday life, this allows you to quickly count change, calculate time, etc.
It is best to develop it from childhood, when the brain absorbs information much faster. There are several effective techniques that many people use.
How to learn to count very quickly in your head?
To achieve good results, you need to train regularly. After achieving certain goals, it is worth complicating the task. A person’s abilities are of great importance, that is, the ability to retain several things in memory at once and concentrate attention. People with a mathematical mind can achieve the most. To quickly learn to count, you need to know the multiplication table well.
The most popular calculation methods:
- Let's figure out how to quickly count two-digit numbers in your head if you need to multiply by 11. To understand the technique, consider one example: 13 multiplied by 11. The task is that between numbers 1 and 3 you need to insert their sum, that is, 4. The result is that 13x11=143. When the sum of the digits gives a two-digit number, for example, if you multiply 69 by 11, then 6+9=15, then you only need to insert the second digit, that is, 5, and add 1 to the first digit of the multiplier. The result is 69x11=759. There is another way to multiply a number by 11. First, multiply by 10, and then add the original number to it. For example, 14x11=14x10+14=154.
- Another way to quickly count large numbers in your head works for multiplying by 5. This rule is suitable for any number that first needs to be divided by 2. If the result is an integer, then you need to add a zero at the end. For example, to find out how much 504 will be multiplied by 5. To do this, 504/2 = 252 and add 0 at the end. The result is 504x5 = 2520. If, when dividing a number, the result is not an integer, then you simply need to remove the resulting comma. For example, to find out how much 173 is multiplied by 5, you need 173/2 = 86.5, and then simply remove the comma, and it turns out that 173x5 = 865.
- Let's learn how to quickly count two-digit numbers in your head by adding. First you need to add tens, and then units. To get the final result, you should add the first two results. For example, let’s figure out how much 13+78 is. The first action: 10+70=80, and the second: 3+8=11. The final result will be: 80+11=91. This method can be used when you need to subtract another from one number.
Another hot topic is how to quickly calculate percentages in your head. Again, for a better understanding, let's look at an example of how to find 15% of a number. First, you should determine 10%, that is, divide by 10 and add half of the result -5%. Let's find 15% of 460: 
to find 10%, divide the number by 10, you get 46. The next step is to find half: 46/2=23. As a result, 46+23=69, which is 15% of 460.
There is another method for calculating interest. For example, if you need to determine how much 6% of 400 will be. First, you should find out 6% of 100 and it will be 6. To find out 6% of 400, then you need 6x4 = 24.
If you need to find 6% of 50, then you should use the following algorithm: 6% of 100 is 6, and for 50, it is half, that is, 6/2 = 3. As a result, it turns out that 6% of 50 is 3.
If the number from which you need to find a percentage is less than 100, then you should simply move the comma to the left. For example, to find 6% of 35. First, find 6% of 350 and it will be 21. The value of 6% for 35 is 2.1.
Many parents probably dream that their baby will grow up special and certainly become something that they can be proud of. But if some fathers and mothers only boast about the abilities of their children, others take them to special schools that help develop the inclinations given by nature.
Is it possible to raise a child to be a genius? If in earlier times the answer to such a question was unambiguous and required talent and amazing abilities, today the task has become much simpler. For example, in order for a child to show remarkable knowledge in mathematics and count as quickly and correctly as a calculator, an unusual program is offered that will teach the child mathematics. And it is called “mental arithmetic”. What is this program and what advantages does it have?
Popularity of the technique
Since 1993, mental arithmetic has been used to teach children in 52 countries, from Canada to the UK. Some of them recommend the technique for inclusion in the school curriculum.
Mental arithmetic is most widespread in the countries of the Middle East, as well as in China, Australia, Thailand, Austria, the USA and Canada. Specialized organizations are beginning to appear in Kazakhstan, Kyrgyzstan and Russia.
Mental arithmetic is one of the youngest and fastest growing methods used for children's education. Thanks to this technique, you can easily develop a child’s mental abilities, which are primarily mathematically oriented. Thanks to children mastering the technique of mental calculation, any mathematical problem turns into a simple and fast computational process for them.
History of origin
The method of mental calculation has ancient roots. And this despite the fact that it was developed relatively recently by a scientist from Turkey, Halit Shen. What did he use for his mental counting system? Abacus, which was created in China 5 thousand years ago. This item represents an abacus, which made a huge contribution to the development of all world arithmetic. After its invention, the abacus began its gradual spread throughout the world. In the 16th century, it came from China to Japan. For four hundred years, the inhabitants of the Land of the Rising Sun not only successfully used such abacus, but also carefully worked on them, trying to improve an object so necessary for performing arithmetic operations. And they succeeded. The Japanese created the soroban abacus, which is still used to this day to teach children in elementary school.
Throughout the history of human development, mathematical science has been improved. And today she can offer us a huge number of her achievements. But despite this, scientists believe that using an abacus is more beneficial in teaching children accurate counting.
The benefits of mental arithmetic
It is believed that each of the hemispheres of the human brain is responsible for its own directions. So, the right one allows you to develop creativity, imaginative perception and thinking. The left is responsible for logical thinking.
The activity of the hemispheres is activated at the moment when a person begins to work with his hands. If the right one is active, then the left hemisphere begins to work. And vice versa. A person working with his left hand helps to activate the work of the right hemisphere.
The goal of menara is to force the whole brain to take part in the educational process. How to achieve such results? This is possible by performing mathematical operations on the abacus with both hands. Ultimately, menard contributes to the development of quick counting, as well as the development and improvement of analytical skills.
Scientists compared the calculator with an abacus and came to the clear conclusion that the first one relaxes brain activity. Abacus, on the contrary, sharpens and trains the hemispheres.
When should you start learning mental arithmetic? Reviews from adherents of this technique claim that it is best to master this method between the ages of four and twelve years. And only in some cases the period can be extended for another four years. This is the time when rapid brain development occurs. And this fact is a wonderful message to instill in a child basic skills, study foreign languages, develop thinking, master playing musical instruments and martial arts.
The essence of the mental technique
The entire program for mastering mental arithmetic is built on the sequential passage of two stages. At the first of them, one becomes familiar with and masters the technique of performing arithmetic operations using bones, during which two hands are used simultaneously. Thanks to this, both the left and right hemispheres are involved in the process. This allows you to achieve the fastest possible learning and execution of arithmetic operations. The child uses an abacus in his work. This subject allows him to completely freely subtract and multiply, add and divide, and calculate square and cube roots.
During the second stage, students learn mental counting, which is done in the mind. The child stops constantly becoming attached to the abacus, which also stimulates his imagination. The left hemispheres of children perceive numbers, and the right hemispheres perceive the image of dominoes. This is what the mental counting technique is based on. The brain begins to work with an imaginary abacus, while perceiving numbers in the form of pictures. Performing mathematical calculations is associated with the movement of the bones.
Learning quick mental arithmetic is a very interesting and exciting process. It is appreciated by hundreds of thousands of people and received a huge number of positive reviews.
Abacus
What is this mysterious and ancient adding machine? The abacus, or mental abacus, is very reminiscent of the old Soviet “knuckles.” The principle of operation on these two devices is also very similar. What is the difference between these accounts? It lies in the number of knuckles located on the knitting needles and in ease of use.
It is worth saying that to obtain a result, the abacus will require more movements with your hands. How does this ancient object, which came to us from China, work? It is a frame into which the knitting needles are inserted. Moreover, their number may be different. There are five pieces of strung knuckles on the knitting needles.
The length of each spoke is crossed by a dividing strip. Above it there is one domino, and below it, respectively, four.
The mental counting technique involves a certain movement of a person’s fingers. Of these, only the index and thumb are used. All movements must be brought to automaticity, which is facilitated by their repeated repetition.
Interestingly, this skill can easily be lost. That is why, when mastering the technique, you should not skip classes.
Number arrangement
What are the basics of counting in mental arithmetic? In order to master this technique, you need to know how the number lines are located on the abacus. On its right side there are ones. After that there are tens, then hundreds, then thousands, tens of thousands and so on. Each of these discharges is located on a separate spoke.
The dominoes located below the dividing bar are “1”, and those above it are “5”. For example, in order to dial the number 3 on the abacus, you will need to separate three dominoes located under the dividing bar on the knitting needle located to the right of the others. Let's look at an example with double numbers, for example, 15. To dial it on the abacus, you should raise up one domino on the tens needle and lower the one located above the top bar on the units needle.
Addition Operations
How to learn mental arithmetic? To do this, you will need to study how arithmetic operations are carried out on the abacus. Consider, for example, addition. Let's see what the sum of the numbers 22 and 13 will be equal to. First, you will need to put two dominoes on the tens and units knitting needles located at the bottom of the dividing bar. Next, let's add one more to the two dozen. The result is 30. Now let's start adding ones. Let's add three more to two. The result is the number “five”, which is indicated by the knuckle at the top of the dividing bar. The result is 35. To master more complex operations, you will need to carefully study special literature. After mastering the simplest examples, it is recommended to practice on the abacus. This way, learning becomes as interesting as possible.
Mastering the second stage
After operations on the abacus do not cause any difficulties, you can begin to perform mental arithmetic orally. This is the next level of learning. It involves mental counting, that is, done in the mind. To do this, you will need to make a picture of an abacus for your child. The simplest option is to print out an image of this item, which should then be pasted onto cardboard (you can take it from a shoe box). If possible, the picture should be in color. This will make it easier for the child to imagine it in his imagination.
To avoid mistakes, it is worth remembering that mental counting should be done from left to right. What needs to be done to put a two-digit number on the abacus? To do this, the child should first pick up the knuckles corresponding to the tens with his left hand, and then separate the required units on the knitting needle with his right hand.
So, for the set 6, 7, 8 and 9 you should use the “Pinch”. This process consists of bringing the index finger and thumb together onto the dividing bar and collecting the knuckles representing the number 5 and the required number of them on the knitting needle, which is located at the bottom of the abacus. Subtracting numbers is done in a similar way. The same “Pinch” simultaneously discards the “fives” and the required number of stones below.
Goals and results of the methodology
Learning mental arithmetic allows a child to achieve unprecedented success in the field of mathematics. Children who have completed a special course can easily calculate ten-digit numbers in their heads, multiply and subtract them. But it is worth saying that this is not the main goal of such training. Counting is just a way by which a person's mental abilities develop.
Mastering mental arithmetic contributes to the following:
- activation of visual and auditory memory;
- ability to concentrate;
- improving ingenuity and intuition;
- creative thinking;
- manifestation of self-confidence and independence;
- rapid mastery of foreign languages;
- realization of abilities in the future.
In cases where a professional approach was used to master menara and specialists achieved their goals, the child can easily begin to solve both simple and complex mathematics problems in his head. And it performs arithmetic operations for multiplication and addition even faster than a calculator.
Schools for teaching mental arithmetic
Where can you learn this unique technique? Today, to study mental arithmetic, you need to enroll in a specialized educational center. In them, specialists work with children for two to three years. In addition to the steps described above, with which you can master the technique, there are ten more steps. Moreover, students complete each of them in 2-3 months.
Each of these specialized centers develops its own training programs. However, despite this, there are general rules that absolutely everyone adheres to. They consist in the fact that groups of students are formed depending on their age. So, there are three basic types of such groups.
These are kinder, kids and junior. Classes are conducted by experienced, highly qualified psychologists and teachers who have undergone appropriate training and have the necessary certification.
In addition to centers for teaching mental arithmetic, today there are also specialized schools that train specialists in the relevant profile. As a rule, menara teachers are people who have not only psychological and pedagogical education, but also some experience working with children. And this is very important. After all, learning mental abacus is not only about mastering skills that allow you to work with ancient abacus. In this process, the psychological characteristics in the development of the child used in pedagogical practice are certainly taken into account.
Pure mathematics is, in its own way, the poetry of the logical idea. Albert Einstein
In this article we offer you a selection of simple mathematical techniques, many of which are quite relevant in life and allow you to count faster.
1. Quick interest calculation
Perhaps, in the era of loans and installment plans, the most relevant mathematical skill can be called masterly calculation of interest in the mind. The fastest way to calculate a certain percentage of a number is to multiply the given percentage by that number and then discard the last two digits in the resulting result, because a percentage is nothing more than one hundredth.
How much is 20% of 70? 70 × 20 = 1400. We discard two digits and get 14. When rearranging the factors, the product does not change, and if you try to calculate 70% of 20, the answer will also be 14.
This method is very simple in the case of round numbers, but what if you need to calculate, for example, the percentage of the number 72 or 29? In such a situation, you will have to sacrifice accuracy for the sake of speed and round the number (in our example, 72 is rounded to 70, and 29 to 30), and then use the same technique with multiplication and discarding the last two digits.
2. Quick divisibility check
Is it possible to divide 408 candies equally among 12 children? It’s easy to answer this question without the help of a calculator, if you remember the simple signs of divisibility that we were taught at school.
- A number is divisible by 2 if its last digit is divisible by 2.
- A number is divisible by 3 if the sum of the digits that make up the number is divisible by 3. For example, take the number 501, imagine it as 5 + 0 + 1 = 6. 6 is divisible by 3, which means the number 501 itself is divisible by 3 .
- A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, take 2,340. The last two digits form the number 40, which is divisible by 4.
- A number is divisible by 5 if its last digit is 0 or 5.
- A number is divisible by 6 if it is divisible by 2 and 3.
- A number is divisible by 9 if the sum of the digits that make up the number is divisible by 9. For example, take the number 6 390, imagine it as 6 + 3 + 9 + 0 = 18. 18 is divisible by 9, which means the number itself is 6 390 is divisible by 9.
- A number is divisible by 12 if it is divisible by 3 and 4.
3. Fast square root calculation
The square root of 4 is 2. Anyone can calculate this. What about the square root of 85?
For a quick approximate solution, we find the square number closest to the given one, in this case it is 81 = 9^2.
Now we find the next closest square. In this case it is 100 = 10^2.
The square root of 85 is somewhere between 9 and 10, and since 85 is closer to 81 than 100, the square root of this number would be 9-something.
4. Quick calculation of the time after which a cash deposit at a certain percentage will double
Do you want to quickly find out the time it will take for your cash deposit with a certain interest rate to double? You don’t need a calculator here either, just know the “rule of 72.”
We divide the number 72 by our interest rate, after which we get the approximate period after which the deposit will double.
If the investment is made at 5% per annum, then it will take a little over 14 years for it to double.
Why exactly 72 (sometimes they take 70 or 69)? How it works? Wikipedia will answer these questions in detail.
5. Quick calculation of the time after which a cash deposit at a certain percentage will triple
In this case, the interest rate on the deposit should become a divisor of the number 115.
If the investment is made at 5% per annum, it will take 23 years for it to triple.
6. Quickly calculate your hourly rate
Imagine that you are undergoing interviews with two employers who do not give salaries in the usual format of “rubles per month”, but talk about annual salaries and hourly wages. How to quickly calculate where they pay more? Where the annual salary is 360,000 rubles, or where they pay 200 rubles per hour?
To calculate the payment for one hour of work when announcing the annual salary, you need to discard the last three digits from the stated amount, and then divide the resulting number by 2.
360,000 turns into 360 ÷ 2 = 180 rubles per hour. All other things being equal, it turns out that the second offer is better.
7. Advanced math on your fingers
Your fingers are capable of much more than simple addition and subtraction.
Using your fingers you can easily multiply by 9 if you suddenly forget the multiplication table.
Let's number the fingers from left to right from 1 to 10.
If we want to multiply 9 by 5, then we bend the fifth finger to the left.
Now let's look at the hands. It turns out four unbent fingers before the bent one. They represent tens. And five unbent fingers after the bent one. They represent units. Answer: 45.
If we want to multiply 9 by 6, then we bend the sixth finger to the left. We get five unbent fingers before the bent finger and four after. Answer: 54.
In this way you can reproduce the entire column of multiplication by 9.
8. Multiply by 4 quickly
There is an extremely easy way to multiply even large numbers by 4 at lightning speed. To do this, simply split the operation into two steps, multiplying the desired number by 2, and then again by 2.
See for yourself. Not everyone can multiply 1,223 by 4 in their head. Now we do 1223 × 2 = 2446 and then 2446 × 2 = 4892. This is much simpler.
9. Quickly determine the required minimum
Imagine that you are taking a series of five tests, for which you need a minimum score of 92 to pass. The last test remains, and the previous results are as follows: 81, 98, 90, 93. How to calculate the required minimum that you need to get in the last test?
To do this, we count how many points we have under/overtaken in the tests we have already passed, denoting the shortfall with negative numbers, and the results with a margin as positive.
So, 81 − 92 = −11; 98 − 92 = 6; 90 − 92 = −2; 93 − 92 = 1.
Adding these numbers, we get the adjustment for the required minimum: −11 + 6 − 2 + 1 = −6.
The result is a deficit of 6 points, which means that the required minimum increases: 92 + 6 = 98. Things are bad. :(
10. Quickly represent the value of a fraction
The approximate value of an ordinary fraction can be very quickly represented as a decimal fraction if it is first reduced to simple and understandable ratios: 1/4, 1/3, 1/2 and 3/4.
For example, we have a fraction 28/77, which is very close to 28/84 = 1/3, but since we increased the denominator, the original number will be slightly larger, that is, a little more than 0.33.
11. Number guessing trick
You can play a little David Blaine and surprise your friends with an interesting, but very simple mathematical trick.
- Ask a friend to guess any integer.
- Let him multiply it by 2.
- Then he will add 9 to the resulting number.
- Now let him subtract 3 from the resulting number.
- Now let him divide the resulting number in half (in any case, it will be divided without a remainder).
- Finally, ask him to subtract from the resulting number the number he guessed at the beginning.
The answer will always be 3.
Yes, it’s very stupid, but often the effect exceeds all expectations.
Bonus
And, of course, we couldn’t help but insert into this post that same picture with a very cool method of multiplication.
Why count in your head when you can solve any arithmetic problem on a calculator. Modern medicine and psychology prove that mental arithmetic is an exercise for gray cells. Performing such gymnastics is necessary for the development of memory and mathematical abilities.
There are many techniques for simplifying mental calculations. Everyone who has seen Bogdanov-Belsky’s famous painting “Oral Abacus” is always surprised - how do peasant children solve such a difficult problem as dividing the sum of five numbers that must first be squared?
It turns out that these children are students of the famous mathematics teacher Sergei Aleksandrovich Rachitsky (he is also depicted in the picture). These are not child prodigies - primary school students from a 19th-century village school. But they all already know how to simplify arithmetic calculations and have learned the multiplication table! Therefore, these kids are quite capable of solving such a problem!
Secrets of mental counting
There are mental counting techniques - simple algorithms that it is desirable to bring to automation. After mastering simple techniques, you can move on to mastering more complex ones.
Add numbers 7,8,9
To simplify calculations, the numbers 7,8,9 must first be rounded to 10 and then subtracted. For example, to add 9 to a two-digit number, you must first add 10 and then subtract 1, etc.
Examples :
Add two-digit numbers quickly
If the last digit of a two-digit number is greater than five, round it up. We perform the addition and subtract the “addition” from the resulting amount.
Examples :
54+39=54+40-1=93
26+38=26+40-2=64
If the last digit of a two-digit number is less than five, then add by digits: first add tens, then add ones.
Example :
57+32=57+30+2=89
If you swap the terms, you can first round the number 57 to 60, and then subtract 3 from the total:
32+57=32+60-3=89
Adding three-digit numbers in your head
Fast counting and addition of three-digit numbers - is it possible? Yes. To do this, you need to parse three-digit numbers into hundreds, tens, units and add them one by one.
Example :
249+533=(200+500)+(40+30)+(9+3)=782
Features of subtraction: reduction to round numbers
We round the subtracted ones to 10, to 100. If you need to subtract a two-digit number, you need to round it to 100, subtract it, and then add the correction to the remainder. This is relevant if the amendment is small.
Examples :
576-88=576-100+12=488
Subtract three-digit numbers in your head
If at one time the composition of numbers from 1 to 10 was well mastered, then subtraction can be done in parts and in the indicated order: hundreds, tens, units.
Example :
843-596=843-500-90-6=343-90-6=253-6=247
Multiply and divide
Instantly multiply and divide in your head? This is possible, but you can’t do it without knowing the multiplication tables. - this is the golden key to quick mental arithmetic! It is used in both multiplication and division. Let us remember that in the primary grades of a village school in the pre-revolutionary Smolensk province (the painting “Oral Calculation”), children knew the continuation of the multiplication table - from 11 to 19!
Although, in my opinion, it is enough to know the table from 1 to 10 to be able to multiply larger numbers. For example:
15*16=15*10+(10*6+5*6)=150+60+30=240
Multiply and divide by 4, 6, 8, 9
Having mastered the multiplication table by 2 and 3 to the point of automaticity, making other calculations will be as easy as shelling pears.
To multiply and divide two- and three-digit numbers we use simple techniques:
multiply by 4 is multiplied by 2 twice;
multiply by 6 - this means multiply by 2, and then by 3;
multiply by 8 is multiplied by 2 three times;
Multiplying by 9 is multiplying by 3 twice.
For example :
37*4=(37*2)*2=74*2=148;
412*6=(412*2) 3=824 3=2472
Likewise:
divided by 4 is divided by 2 twice;
to divide by 6 is to first divide by 2 and then by 3;
divided by 8 is divided by 2 three times;
dividing by 9 is dividing by 3 twice.
For example :
412:4=(412:2):2=206:2=103
312:6=(312:2):3=156:3=52
How to multiply and divide by 5
The number 5 is half of 10 (10:2). Therefore, we first multiply by 10, then divide the result in half.
Example :
326*5=(326*10):2=3260:2=1630
The rule for dividing by 5 is even simpler. First, multiply by 2, and then divide the result by 10.
326:5=(326·2):10=652:10=65.2.
Multiply by 9
To multiply a number by 9, it is not necessary to multiply it twice by 3. It is enough to multiply it by 10 and subtract the multiplied number from the resulting number. Let's compare which is faster:
37*9=(37*3)*3=111*3=333
37*9=37*10 - 37=370-37=333
Also, particular patterns have long been noticed that significantly simplify the multiplication of two-digit numbers by 11 or 101. Thus, when multiplied by 11, the two-digit number seems to move apart. The numbers that make it up remain at the edges, and their sum is in the center. For example: 24*11=264. When multiplying by 101, it is enough to add the same to the two-digit number. 24*101= 2424. The simplicity and logic of such examples is admirable. Such tasks occur very rarely - these are entertaining examples, so-called little tricks.
Counting on fingers
Today you can still find many advocates of “finger gymnastics” and the method of mental counting on fingers. We are convinced that learning to add and subtract by bending and unbending our fingers is very visual and convenient. The range of such calculations is very limited. As soon as the calculations go beyond the scope of one operation, difficulties arise: you need to master the next technique. And it’s somehow undignified to bend your fingers in the era of iPhones.
For example, in defense of the “finger” method, the technique of multiplying by 9 is cited. The trick of the technique is as follows:
- To multiply any number within the first ten by 9, you need to turn your palms towards you.
- Counting from left to right, bend the finger corresponding to the number being multiplied. For example, to multiply 5 by 9, you need to bend the little finger on your left hand.
- The remaining number of fingers on the left will correspond to tens, on the right - to ones. In our example - 4 fingers on the left and 5 on the right. Answer: 45.
Yes, indeed, the solution is quick and clear! But this is from the realm of tricks. The rule only applies when multiplying by 9. Isn’t it easier to learn the multiplication table to multiply 5 by 9? This trick will be forgotten, but a well-learned multiplication table will remain forever.
There are also many similar techniques using fingers for some single mathematical operations, but this is relevant while you are using it and is immediately forgotten when you stop using it. Therefore, it is better to learn standard algorithms that will remain for life.
Oral counting on a machine
Firstly, you need to have a good knowledge of the composition of numbers and the multiplication table.
Secondly, you need to remember the techniques for simplifying calculations. As it turned out, there are not so many such mathematical algorithms.
Thirdly, in order for the technique to turn into a convenient skill, you must constantly conduct short “brainstorming” sessions - practice mental calculations using one or another algorithm.
Training should be short: solve 3-4 examples in your head using the same technique, then move on to the next one. We must strive to use every free minute - both usefully and not boringly. Thanks to simple training, all calculations will eventually be performed at lightning speed and without errors. This will be very useful in life and will help out in difficult situations.
Learning to quickly count in your head is not difficult; all you need is experience and training. The ability to operate with complex numbers increases the level of control over many life processes and makes a person more collected and organized. Also, quick mental arithmetic allows you to take your mind off sad thoughts, improves memory, attention and a sense of self-confidence.
Features and benefits of fast mental arithmetic
Currently, almost every educated person can operate in their minds with numbers up to 20. However, it is already difficult to make mental calculations with values that have three or more numbers. This can only be done by those who regularly carry out mathematical operations in their minds; these include mathematicians, scientists, accountants, etc.
How can you acquire the same fast counting skills as these specialists? This is not impossible. Each of us has the ability to do this by nature. Some have them more developed, others need a little practice. Exercises for training can be found freely available on the Internet. You can develop your own methodology that will take into account all personal characteristics and help you quickly master the necessary skills.
In order to succeed in this business, you must follow the following basic rules:
- regular workouts
First you need to develop your own training regimen, and then, if you really want to achieve impressive results, strictly follow it. During the first month, training should be carried out once a day for 10-15 minutes. It is not recommended to do them longer, since you can get very tired and cool down from this activity.
If it becomes difficult, you can take a break for one or two days. Take your time, master the technique at your own pace. Mastering quick counting is like learning poetry. If something doesn’t work out right away, then don’t give up, keep training and success will follow.
- attentiveness and concentration
This is a very important point when learning the fast counting technique. First of all, you need to remember the algorithm for working with complex numbers. Then, during the training process, it will be remembered, and it will not be difficult to perform the action in your mind even with three- and four-digit numbers.
Try not to be distracted by extraneous matters so as not to overload your brain with unnecessary information and quickly master the necessary skills.
- adherence to training regimen
This is one of the foundations of success. Only patience and regular work on yourself will allow you to get what you want. Make a schedule for what time the classes will take place. You can even mark information about the exercise you performed there every day.
- motivation
It is also one of the keys to success, when a person sees a goal in front of him, he will strive to achieve it, even if this requires acquiring certain skills and abilities.
- patience
In any business, to achieve success, you need patience and perseverance, even if everything does not work out right away. All people are different, some need more time to acquire these skills, others less. The main thing is not to give up after the first failures.
Also, before starting training, you need to consider the following basic points:
- natural abilities
Not all people are naturally gifted with a mathematical mind, so they will need a little more time to master quick counting algorithms. Just don’t make this fact your main excuse for not learning the technique.
- knowledge and understanding of mathematical algorithms
This is necessary in order to subsequently make quick calculations in the mind according to a previously learned pattern.
- nutrition
During the period of intense mental training, you should include foods to nourish the brain in your diet, for example, walnuts, honey, and fruits are good options.
Using these skills, it will be very pleasant to carry out mental calculation operations without resorting to the use of a calculator and other means for calculation.
Basic techniques
There are many ways to develop mental arithmetic skills. Everyone can choose the most convenient one for themselves. There are four operations with numbers: addition, multiplication, subtraction, division.
It is enough to understand the algorithm once to then develop the necessary skills. It will be enough to train 10-15 minutes a day, and then periodically maintain the acquired abilities with episodic training. The first results will be noticeable within half a month, and after two to three months you will be able to reach a decent account level.
- technique for quick addition
This is the easiest level to start with when training. It's best to start with two-digit numbers. For example, you need to add the numbers 23 and 51. First, add the tens: 20+50 = 70, then add the remainder 3+1=4 to the resulting sum. As a result, we get the number 74.
Mastering the addition of multi-digit numbers is also not difficult. For example, let's add 342 and 741. To do this, we divide these numbers into digits 300, 40, 2 and 700, 40 and 1, respectively. Then, by analogy with two-digit numbers, we begin to add in our heads: 300 + 700 = 1000, 40+40 = 80, 2+1 = 3, then add 1000+80+3 = 1083.
- technique for quick subtraction
Just like addition, subtracting two values is not difficult. Let's start with two-digit numbers, for example, we need to subtract the number 23 from 35. Let's also start with the digits: 30-20 = 10, 5-3 = 2, then add the resulting values 10 + 2 and get the desired number 12.
Subtracting multi-digit numbers is also not difficult, for example, subtract the number 154 from 377. To do this, we divide the digital values into digits 300, 70, 7 and 100, 50 and 4, respectively.
Let's subtract 300-100 = 200, 70-50 = 20, 7-4 = 3, then add the resulting numbers: 200+20+3 = 223.
In the same way, you can subtract digits l in your head with a higher bit depth.
- technique for fast multiplication
This procedure can be greatly facilitated by learning the multiplication table. It is known that multiplication is a simplification of the addition operation. For example, 3 * 6 = 18, but in fact this is the sum of three sixes. When multiplying, you can also use the bit depth method, for example, you need to find the product 42 * 3. First, 2*3 = 6, 4*3 =12, then we combine these numbers, putting the last before the first, i.e. we get the number 126. This algorithm is suitable for calculating the product of two-digit numbers.
When multiplying three-digit numbers in your head, the technique will be slightly different. For example, we need to multiply 421 and 372. Here we will have to use addition. We multiply 421 in turn by each digit of the second number: 421*2 = 842, 421*7= 2942, 421*3 = 1263, then add these numbers, observing the digit offset: 2000+1000 = 120000, 800+900+200 = 29800 , 40+40+60=6440, 2+7+3 = 372, as a result we get the number 156612.
When multiplying three-digit numbers, you need to be especially careful so as not to make mistakes with adding digits in your head.
- technique for rapid division
Dividing single-digit and two-digit numbers in the mind is carried out according to a simple principle using the multiplication table. For example, we need to divide 35 by 5, remembering the multiplication table, we know in advance that the result will be 7.
Dividing multi-digit numbers is a little more difficult. For example, let’s divide 345 by 5, we also do this taking into account the bit depth: 300/5 = 60, 45/5 = 9, then add 60+9 and get the desired number 69.
As far as one can see, the principle of performing any mental calculations is based on the principle of digit capacity.
Need to know
Acquiring quick mental arithmetic abilities is a significant advantage for an individual, since only a limited number of people possess such skills. However, subsequently, the following points must be taken into account:
- regularly maintain acquired skills;
- recite mathematical operations out loud during training;
- do not overdo it.
The one who walks will master the road. Only with proper patience and motivation is it possible to retain the ability to quickly do mathematical calculations in your head for a long time.
Learning to count quickly in your head is not an impossible task. Anyone can master the technique of fast mathematical calculations; this requires perseverance, concentration and regular training. There are many ways to gain this skill, everyone can choose the one they like best. Carrying out fast computational operations in the mind is based on the principle of bit depth.
