How to learn to count?
It is no secret that there are some people who can produce medium-complex arithmetic operations in the mind with enviable speed. For them it is not difficult, for example, to multiply two two-digit numbers or divide several three-digit values into each other. They do it quickly and without the help of additional devices and do not even use records, that is, they make calculations in their mind! Understandably, for many it’s not difficult to ask how to learn to count quickly in the mind - this is a daily practice, a forced job or a type of activity. But this does not mean that any of us who want to learn how to learn to count in the mind must finish a mathematical university. So, today we will talk about how to learn to count. Quickly count!
Learning to count quickly, necessary training
Without a doubt, your experience and training abilities will play an important role in the development of such abilities. But this in no way means that the skill of fast counting is available only to people with experience. Mental arithmetic is a rationalization path based on basic arithmetic.By following our tips on how to quickly learn to count, you will be able to surprise those around you with a quick solution of examples that not everyone can solve even with a calculator.
What do you need to quickly master the technique of instant counting "in mind"? The main components of success can be divided into three groups:
- Predisposition and ability. Your analytical mind will be a good help. The ability to keep in memory several quantities at once is necessary.
- Directly algorithms of your thinking. One can learn to learn quickly only by strict algorithmization of one’s actions, their rationalization and the ability to choose the necessary method in a specific situation. We will talk about situations and other things a bit later.
- Training and practice skills. No one has overturned the importance of these actions in any area of activity, and especially in mental activity. The more you train and perform various calculations, the better you will get it.
Attention should be paid to the third factor in the development of rapid counting skills. Even perfectly being guided in all existing algorithms, you will hardly be able to learn how to count quickly,if there is not enough practice.
Tricks and basic algorithms, how to quickly count
Consider a few common simplifications of the account, with their help you will be able to learn how to count quickly. I would also like to draw your attention to the fact that no one forbids you to improvise - mathematics is remarkable for that, with all its accuracy and rigor it does not forbid to act beautifully, like art. And the skill to count quickly is exactly art! So, some tricks, how to learn to count quickly.
Suppose you need to make the addition of multi-valued components. Easily! Add the digits: add a major digit to a larger number of a smaller number, then add up to the lower order bits. Suppose you need to add 361 and 523. Immediately hold in memory will not be easy, agree? Therefore, our course of action will be as follows:
- A smaller number identified - 361.
- What is 361? This is 300 + 60 + 1. It is difficult to challenge if you strive to be rational.
- First add 300 to 523. We get 823.
- Then we add 60 - we get 883.
- And in the end - our unit, added to the amount received earlier, will give us the result of 884.
You see, it was much easier to keep 3 numbers in your head than to add two three-digit at a time! We are beginning to get counted quickly in the mind!
Do the same with subtraction, but only with consistent removal of discharges, we will not achieve the required speed! You can cheat a little by adding one more skill to our arsenal - increase / subtract to a round (convenient number).
For example, you need to subtract 93 from 250. Well, inconvenient!
What is 93? That's right, it's 100-7!
250 – 100 = 150.
We make an amendment to our "correction" of the number. If we added - you need to add to the private, and vice versa. In our case, we “increased” the number 93 to 100, adding 7. So, we add 7 to the particular.
150 + 7 = 157.
Check on the calculator. Noticeably more time spent on a set of numbers than on the calculation? This is a sign that you already have a good skill in how to count quickly in your mind!
Now with multiplication. You can speed up the account in different ways. For example, when multiplying numbers, divide the factors into second-level factors.
12 x 150
A lot of ways to solve! And then your algorithm may differ from the paths of other people - do not worry, we, geniuses, people, and unique =)
It is possible so: 12 = 3x4. Multiply 150 x 4 = 600, then 600 x 3 = 1800.
I did not hesitate, began to read like this: 12 = 10 + 2. And now it's elementary: (150 x 10) + (150 x2). All these are elementary school rules that we, unfortunately, forget.It is easy to notice that in this case it is practically not necessary to count - add zero to 150, receiving one and a half thousand, and multiply 150 by 2, receiving 300. The result is the same, 1800.
Based on the experience of rapid multiplication, it is easy to guess how quickly to divide numbers in the mind. You can again go in different ways, from parallel division by a simplified divisor of a dividend to rounding the dividend up to the elementary division of the amendment.
First, drop the same number of zeros. In this example, it's just 39: 4. Our brain is much more willing to operate with small numbers than with multi-digit values.
You probably noticed that the number 39 is just what you want to round up to 40. So, what's stopping us? (39 + 1): 4 = 10.
But by changing the dividend, we need to correct the answer. So, it is obvious that it will be less than 10, since we added a certain number 1 to the dividend. Now we need to subtract from 10 the result of dividing the offset number by the divisor (4). If we took away, the procedure would be reverse, it goes without saying.
So, 1: 4 = 0.25
10-0.25 = 9.75.
The answer is: 9.75 (93/4)
It is much easier for our brain to perceive natural fractions, that is, we represent 0.25 as 1/4 (one fourth, a quarter), and then it will be quite easy to quickly calculate the result in mind!
Remember, it is not so difficult to understand how to quickly learn to count.It is much more difficult to quickly select a method for a specific situation, but this is solved with the help of colossal practice.
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