mathematics Not so difficult science as it may seem at first glance. There are a lot of secrets that allow you to make very complex calculations in the mind.
If it's hard for you to calculate how many tips to leave for the waiter or it's difficult to split an account in a restaurant at all, these 10 tricks are just for you. And, by the way, it's great Warm-up For your brain!
10 mathematical tricks
- How to get 15% of any number
You need to first calculate 10% of it, and then divide the number by 2 and add these numbers.
example: 15% from 358
1. Find 10% - 35.8.
2. Find half of 35.8 - this is 17.9.
3. Add 17.9 to 35.8 and you will get 53.7.
- Multiplication of "3 by 1" in the mind
You can not even imagine how simple it is. You just need to divide the big problem into a few small ones.
example: 450 × 6
1. break the number 450 into two more simple ones: 400 and 50.
2. Multiply 400 by 6 and 50 by 6 individually (2,400 and 300).
3. Put together the resulting numbers (2,700).
- Squaring of two-digit numbers
With this trick, you will square two-digit numbers very quickly. All you need is to divide the number by two and get an approximate answer.
example: 53 ^ 2
1. subtract 3 from 53 to get 50, and add 3 to 53 to get 56.
2. multiply the two resulting numbers, using the previous advice (50 × 56 = 2800).
3. add the square of the number, by the amount of which you decreased and increased 53 (2800 + 3 ^ 2 = 2809).
The secret is that when you square two-digit numbers, you need to turn them into numbers that are much easier to multiply, since we did with the number 53.
- Squaring a number ending in 5
With this mathematical operation everything is even simpler. Take the first digit of the number that you square. Multiply it by the same number plus 1. then add to the end of the number 25.
example: 85 ^ 2
1. multiply 8 by 9 and you get 72.
2. Add to the number 25 and you will get 7225.
- Division by a single digit
Division in the mind is a skill that you need almost every day.
example: 589: 7
1. it is necessary to find approximate answers by multiplying 8 by such numbers that yield extreme results (7 × 80 = 560, 7 × 90 = 630). The answer is more than 80.
2. subtract 560 from 589. get the number 29, divide it by 7 and you will get 4 with the remainder 1.
3. The answer is 84.1
The answer, of course, is not as accurate as possible, but even such an answer will be enough for you, for example, to settle in a restaurant.
- How to quickly find the cube roots of numbers
To easily find the cube root from any number, you need to learn the cubes of numbers from 1 to 10:
2 - 8
3 - 27
4 - 64
5 - 125
6 - 216
7 - 343
8 - 512
9 - 729
10 - 1000
Knowing them by heart, you can easily find the cube root of any number.
example: Cubic root of 39 304
1. Take the value of thousands (39) and find out what numbers it is (27 and 64). This means that the first digit in the answer is 3, and the answer lies in the range of 30.
2. Each digit from 0 to 9 appears in the cubic roots of numbers from 1 to 10 only once.
3. since the last digit in our case is 4, which means that the last digit of the answer will be 4, since in its cube root the last digit is 4.
4. The answer is 34.
- Rule 70
To find out how many years you can double your money, divide the number 70 by the annual interest rate.
example: How many tender years to double the money with an annual interest rate of 17%.
70: 17 = 4.1 years
- Rule 110
To find out how many years you can triple your money, you need to divide the number 110 by the annual interest rate.
example: How many years it takes to triple the money with an annual interest rate of 20%.
110: 20 = 5.5 years
- Magic number 1089
But such a focus will surprise anyone! Think of any three-digit number whose digits are in decreasing order, for example 642 or 864. then write it down in reverse order and subtract it from the original number. To the number obtained add the same number, only written down in the reverse order. What did you do? 1089?
- Simple trick
You probably often saw such a trick: think of any number. Multiply it by 2. add 12. divide the sum by 2. subtract from it the original number.
You got 6, do not you? Whatever you want, you will still get 6. and that's why:
2. 2x + 12
3. (2x + 12): 2 = x + 6
4. x + 6 - x
These are elementary rules of algebra, now such tricks will not surprise you.
Strange why us Do not teach this at school. It turns out that the multiplication in the column is long overdue and these secrets are much more useful than most of what we were taught in math lessons.
Show your friends how you can do complex mathematical calculations in your mind!