How to multiply large numbers in your head. How to quickly multiply two-digit numbers in your head? If it is not entirely clear how multiplication occurs according to the scheme, you can watch a video where this process is reflected more clearly

To multiply any numbers up to 100 in your head, it is important to quickly select the desired algorithm. For the convenience of this selection, this lesson highlights the most convenient cases for each multiplication technique. The methods described above can be divided into universal (suitable for any numbers) and specific (convenient for specific cases).

Universal techniques

The applicability of universal techniques for multiplying numbers up to 100 is as follows:

You'll learn faster, your alert level will increase, and you'll get it all by moving your body. Now, if you don't exercise regularly and already feel guilty that it's not helping your brain, try a brain training program like the Bliss exercise. Remember, as we said earlier, training your brain to do something over and over again will change forever.

Spend some time with your loved ones. If you want to have optimal cognitive abilities, then you must have meaningful relationships in your life. Talking to other people and connecting with loved ones helps you think more clearly and also improves your mood.

Using one reference number():

  • all numbers in the ranges up to 30, 40-60, 85-100 - if both multipliers are near the reference number.
    For example: 13*17, 18*23, 29*22, 53*61, 88*97, etc.
  • if one number is very close to a convenient reference number (+/- 3 from 10, 20, 50, 100), the second can be anything.
    For example: 21*67 (21 is close to 20), 48*33 (48 is close to 50), 98*32 (98 is close to 100)

Using two reference numbers ():

Staying hydrated while you don't sweat for 90 minutes may not dehydrate your body enough to cause your brain to literally shrink inside your skull—the equivalent of a year and a half of aging. When they were asked to play video games after exercise, brain scans showed that their brains had to work much harder, and activities that would have been completed quite easily resulted in much more brain work to complete. Eat right - and make sure chocolate is included.

Foods such as fish, fruits and vegetables help your brain function optimally. However, you may not know that chocolate also gives your brain a good boost. When you eat chocolate, your brain produces dopamine. And dopamine helps you learn faster and remember better. Not to mention, chocolate contains flavonoids, antioxidants that also improve your brain function. So next time you have something difficult, make sure you bite or smoke the chocolate!

  • If one reference number is a multiple of another and if one of the reference numbers is convenient (10, 20, 50, 100)
    For example: 98*24, 12*44, 43*103, 23*62

It is convenient to multiply other numbers using traditional methods from the third lesson, when the tens and ones places are not very large (). Moreover, the traditional method is useful when you don't know which other method to use.

Now that you know how to train your brain, it's time to take action. Put this knowledge into action and smarter than ever! Not everyone has the almost uncanny deduction skills of Sherlock Holmes. However, just practice to build a Memory Palace as extensive as the famous detective story. Here's how you can improve your memory and thinking skills in your free time.

It is believed that this method was developed by the poet Simonides de Seos after a building collapsed at a banquet he was attending. Simonides gave a few minutes to find some guests who were late when the ceiling of the place gave way, crushing people and leaving their bodies unrecognizable. However, Simonides was able to remember everyone who was present on this occasion based only on seat arrangements, i.e. positions in the room, which is why this method is called "loci". Holmes accomplishes a similar feat with disparate facts, connecting the tips of each piece of information to the site of his mental construct - the Memory Court.

  • For example: 42*32 = 12 (2*4+3*2) 4 = 1344

Private methods

It is also useful to remember about private techniques that significantly simplify the solution of some examples:

Multiplication by 10, 20, 25, 50 should be done almost automatically ():

  • For example: 88*25 = 2200 (division by 4)

Multiplying by 11 is always according to the method from

  • For example: 57*11= 5 (5+7) 7 = 627

Numbers ending in 5 are conveniently squared using the method from

You can also do this with a little practice. Your brain is constantly flooded with sensory information, 24 hours a day, 7 days a week. Theoretically, he could save all his life experience. However, it is selective when it comes to dividing up what goes into long-term memory - prioritizing unique, important, surprising or exciting memories and discarding common ones. That's why you still remember your first kiss or that monkey you paid for in math class when you were in fourth grade, but you've completely forgotten about what you had for breakfast last Thursday.

  • For example: 65*65 = (6*7)25 = 4 225

It is convenient to square any numbers using abbreviated multiplication formulas

  • For example: 69*69 = (70-1) 2 = 70 2 - 70*2*1 + 1 2 = 4 900-140+1 = 4 761

Now, you have a serious algorithmic apparatus for solving examples of multiplying numbers up to 100. In addition, you can already multiply some examples with factors greater than 100. The main factor influencing your ability to multiply in your head in the future should be experience and training. You can take the workout below.

There are several ways to do this. Make an acrostic poem: Need to decorate a long shopping list? Now you have one main thing to remember when you're in the market instead of six. Use the keyboard: The same method can be used for number sequences such as phone numbers. This is because "popcorn" is a much stronger connection than line 6 and 7. You can do the same thing by inventing words or phrases from the letters of the alphanumeric keypad on your phone.

This sequence does little to help the known song, but dividing the set of numbers into smaller chunks improves memory retention. And it's not just phone number formats that can be used to separate long strings of numbers. If he had done so, the researchers would have added the figure to the next round; if it fails, they will take one.

Training

If you want to improve your skills on the topic of this lesson, you can use the following game. The points you receive are affected by the correctness of your answers and the time spent on completion. Please note that the numbers are different each time.

The ability to instantly count in your head can become an invaluable aid in work and in the fast paced life of a modern person. Accurate calculations without the use of special devices significantly save time, allow you to constantly train your memory and, to hide it, cause admiration among people who are not endowed with such abilities.

At first he could only remember seven digits, but he was able to improve his performance and remember 80-digit codes simply by separating the numbers over 20 months. Make it memorable: Many people find phrases easier to remember than serial numbers or lists of items.

This method can be extrapolated to a more advanced form known as a mnemonic fixation system, which uses an ordered list of rhymes to associate each element with it. You might think it's not an easy technique to master, but once you nail the fixation rhymes, you can create and memorize almost unlimited lists - or at least for much longer than you could otherwise achieve.

How to multiply quickly big numbers How to master such useful skills? Most people find it difficult to verbally multiply two-digit numbers by single-digit numbers. And there is nothing to say about complex arithmetic calculations. But if desired, the abilities inherent in every person can be developed. Regular training, a little effort and the use of effective techniques developed by scientists will allow you to achieve amazing results.

Create a crazy situation: Phone numbers and shopping lists aren't the only things that mnemonics can use to decorate—details like new names and people's physiognomies can be easily remembered as long as you name each one common name to memory with greater visual impact.

Then come step 2, find a place that stands out in the person to stick it to, such as the nose - imagine Nelson Mandela stuck in the person's nose. The more explicit, vivid, grotesque, or strange the visual anchors you create, the easier it will be for you to remember the person's name at other times.

What will help you learn quickly?

Reaching the heights of child prodigies is quite possible. Especially if you use the abilities given by nature wisely.

  • Not bad if you're blessed logical thinking, concentration and ability to identify important factors.
  • A good start is knowledge effective ways addition and subtraction, understanding of algorithms.
  • The quality of learning is influenced by the ability to daily train memory and attention, making tasks more difficult.

What are the most effective ways to learn how to multiply as quickly as possible? double figures in your mind?

Now that you know the basics of improving your memory and cognition, it's time to start practicing these new skills. The following apps will help keep your brain performing at full capacity at all times. This app uses several mini-games to improve your cognitive abilities and measure the current state of your memory, your cognition, and the health of your brain.

Sudoku and newspaper crossword

The games range from repetition of letter and number sequences to things related to spatial memory, in addition to Sudoku. If you want to train your brain without the finesse of the above-mentioned apps, it's a good idea to keep your mind busy with non-technical games like crosswords and Sudoku: research shows they help prevent.

Choosing traditional methods

Methods of multiplying two-digit numbers that have been proven for decades do not lose their relevance. The simplest techniques help millions of ordinary schoolchildren, students of specialized universities and lyceums, as well as people engaged in self-development, improve their computing skills.

Multiplication using number expansion

Nowadays, more than any other person, man suffers from a well-known psychological evil: overclocking. The excitement of cities, the nervous tension created by most modern professions, the overabundance of information and advertising advertising that no one avoids, all lead to a lack of attention, making it increasingly difficult to concentrate.

The book is read, and suddenly it is seen that the eyes continued the course of the lines, but the spirit is elsewhere: the person has lost the thread of the author's thinker, one has returned to find missing or scattering. In a store, the saleswoman tells you one price for another, or who makes a mistake in manual adding or typing in the cash register: distractions due to lack of attention, his mind wandering elsewhere.

The easiest way to quickly learn to multiply large numbers in your head is to multiply tens and units. First, the tens of two numbers are multiplied, then the ones and tens alternately. The four numbers received are summed up.
To use this method, it is important to be able to remember the results of multiplication and add them in your head.

By car, you take the left path every day at this intersection. On the day when you have to go straight to the race, you still turn left because it's your habit and you weren't careful enough when approaching the transition. We could multiply examples of mental overdrive, lack of attention and concentration. It is obvious that this dispersion and lack of concentration detracts from the quality of our daily and professional lives. It also greatly undermines the quality of our personality.

Less effective if the concentration is insufficient. It takes a lot less money from a book, article, file or conference if you're not careful enough. Good attention, which still depends on what interests us at the moment - best way enrich our memory with fact, data and information that we can use. In addition, developing attention and concentration is a great way to improve memory. The more attention is good, the better the memory.

For example, to multiply 38 by 57 you need:

  • factor the number into (30+8)*(50+7) ;
  • 30*50 = 1500 – remember the result;
  • 30*7 + 50*8 = 210 + 400 = 610 – remember;
  • (1500 + 610) + 8*7 = 2110 + 56 = 2166

Naturally, it is necessary to have excellent knowledge of the multiplication table, since it will not be possible to quickly multiply in your head in this way without the appropriate skills.

Have you also noticed how frustrating it is to try to focus on a subject that you want to think about or want to learn about, and realize that in some cases the spirit has run elsewhere, we are thinking about something else? On the contrary, one who knows how to concentrate becomes extremely effective in his meditation or in his study.

Walter spent several years studying the phenomenon of attention and experimenting with practical ways to improve it. He then prepared a method for developing our powers of attention and concentration. This method will be shown here on this page in a few seconds.

Multiplication by column in the mind

Many people use a visual representation of the usual columnar multiplication in calculations. This method is suitable for those who can memorize auxiliary numbers for a long time and perform arithmetic operations with them. But the process becomes much easier if you learn how to quickly multiply two-digit numbers by single-digit numbers. To multiply, for example, 47*81 you need:

Having understood the phenomenon of attention and concentration, you will find a lot in this method, easy and interesting. Very soon you will make progress and in a few months you will arrive to have complete control over your thoughts. Whatever your degree of inattention or distraction, you will learn to focus on a specific subject until you deliberately decide to move on. And when you meditate, when you want to direct your concentration to this or that inner thought, you will be focused on that thought and effortlessly eliminate all mental images that are not related to your concern.

  • 47*1 = 47 – remember;
  • 47*8 = 376 – remember;
  • 376*10 + 47 = 3807.

Speaking them out loud while simultaneously summing them up in your head will help you remember intermediate results. Despite the difficulty of mental calculations, after a short practice this method will become your favorite.

The above multiplication methods are universal. But knowing more efficient algorithms for some numbers will greatly reduce the number of calculations.

This is an amazing asset that allows you to completely control your thoughts. You will also find that finally developing your concentration is an easy way to naturally lead to self-control. All memory training must begin with concentration training.

There are two types of concentration: immediate concentration, which we have to carefully observe a document, person, event, show, monument, painting, and long-term concentration, which we need to study, learn, save, write, calculate, think, think. Here we will focus on the long-term concentration that is required, for example, to pass a written test during an exam.

Multiplying by 11

This is perhaps the simplest method that is used to multiply any two-digit numbers by 11.

It is enough to insert their sum between the digits of the multiplier:
13*11 = 1(1+3)3 = 143

If the number in brackets is greater than 10, then one is added to the first digit, and 10 is subtracted from the amount in brackets.
28*11 = 2 (2+8) 8 = 308

Multiplying large numbers

It is very convenient to multiply numbers close to 100 by decomposing them into their components. For example, you need to multiply 87 by 91.

  • Each number must be represented as the difference between 100 and one more number:
    (100 - 13)*(100 - 9)
    The answer will consist of four digits, the first two of which are the difference between the first factor and the subtracted from the second bracket, or vice versa - the difference between the second factor and the subtracted from the first bracket.
    87 – 9 = 78
    91 – 13 = 78
  • The second two digits of the answer are the result of multiplying those subtracted from two parentheses.

    13*9 = 144

  • The result is the numbers 78 and 144. If, when writing down the final result, a number of 5 digits is obtained, the second and third digits are summed.

    Result: 87*91 = 7944 .

These are the most simple ways multiplication. After using them multiple times, bringing the calculations to automation, you can master more complex techniques. And after a while, the problem of how to quickly multiply two-digit numbers will no longer worry you, and your memory and logic will improve significantly.