10 tricks to simplify mathematical operations

Not so long ago on Layfhakere out a review of the book "The Magic Numbers", which contains a huge number of mathematical tricks. The book does not leave us indifferent, and we chose it from 10 of the most interesting tips to simplify mathematical operations.

Recently, after reading the book "magic numbers"I learned a tremendous amount of information. The book describes dozens of tricks that simplify the usual mathematical operations. It turned out that the multiplication and long division - is the last century, and it is unclear why it is still taught in schools.

I chose 10 of the most interesting and useful tricks and want to share them with you.

Multiplication "3 to 1" in mind

Multiplication of three-digit numbers on the clear - this is a very simple operation. All you need to do - is to break a big task into several small ones.

Example: 320 × 7

1. Splitting the number 320 for a two primes: 300 and 20.
2. Multiply 300 7 7 and 20 individually (2100 and 140).
3. Fold the resulting number (2240).

Squaring two-digit numbers

Squaring the two-digit numbers are not much more difficult. We need to break the number by two and get an approximate answer.

Example: 41^2

1. Subtract 1 from 41 to 40 receive and add 1 to 41 to get 42.
2. Multiply the two numbers, using the previous board (40 × 42 = 1680).
3. Add the square of the number, the amount of which we reduced and increased 41 (1 680 + 1 ^ 2 = 1 681).

The key rule here - to turn the desired number in a couple of other numbers that multiply together much easier. For example, for the number 41 is number 42 and 40, for the number of 77 - 84 and 70. That is, we subtract and add the same number.

Instant erection of a square, ending in 5

On the squares of numbers ending in 5, do not need to strain. All you need to do - is to multiply the first digit of the number that is one more, and add to the end of the number 25.

Example: 75^2

1. Multiply 7 by 8 and get 56.
2. Adding to the number 25 and get 5625.

Division by one-digit number

The division in the mind - it is a useful skill. Think about how often we divide the number every day. For example, in a restaurant bill.

Example: 675: 8

1. We find approximate answers by multiplying 8 into convenient numbers that give extreme results (8 × 80 = 640 × 90 8 = 720). Our answer - 80-something.
2. Subtract 640 from 675. Get the number 35, you need to divide it by 8 and 4 to get to the remainder of 3.
3. Our final answer - 84.3.

We get not the most accurate answer (the correct answer - 84.375), but you must admit that even such a response is more than enough.

Simple obtain 15%

To quickly learn 15% of any number, you must first calculate the 10% of it (moving the comma one character to the left), then divide the resulting number by 2 and add it to 10%.

Example: 15% of 650

1. We are 10% - 65.
2. Find half of the 65 - is 32.5.
3. We add 32.5 to 65 and get 97.5.

banal trick

Perhaps all of us stumbled on this trick:

Think of any number. Multiply it by 2. Add 12. Divide the sum by 2. Subtract it from the original number.

You got 6, right? Whatever you make come true, you will still get 6. And that's why:

1. 2x (double number).
2. 2x + 12 (add 12).
3. (2x + 12) 2 = x + 6 (divide by 2).
4. x + 6 - x (subtract the original number).

This trick is built on the basic rules of algebra. So if you ever hear that someone thinks of him, pull his most arrogant grin, make a disdainful look and tell everyone a clue. :)

The magic number 1089

This trick does not exist a century.

Write down any three-digit number, the numbers of which are in descending order (for example, 765 or 974). Now, write it in the reverse order, and subtract it from the original number. To this add the same answer, only in reverse order.

Whichever number you choose, the result will be 1089.

Quick cube roots

In order to quickly take the cube root of any number, you will need to remember the cubes of numbers from 1 to 10:

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Once you remember these values, to find the cube root of any number is simply elementary.

Example: cube root of 19683

1. Take the magnitude of thousands of (19), and look, between which it is numbers (8 and 27). Accordingly, the first digit of the reply will be 2, and the answer lies in the range of 20+.
2. Each digit from 0 to 9 will appear in the table one at a time as the last digit of the cube.
3. Since the last figure in the problem - 3 (19 683), This corresponds to 343 = 7 ^ 3. Consequently, the latter figure is the answer - 7.
4. Answer - 27.

Note: trick works only when the original number is a cube the whole number.

rule 70

To find the number of years required to double your money, you need to divide the number 70 on the annual interest rate.

Example: the number of years required to double the money with an annual interest rate of 20%.

70: 20 = 3.5 years

rule 110

To find the number of years required for a tripling of money, you need to divide the number 110 to the annual interest rate.

Example: the number of years required for a tripling of money with an annual interest rate of 12%.

110: 12 = 9 years

Mathematics - a magic science. I'm even a little embarrassed by the fact that such simple tricks could surprise me, and can not even imagine how much you can learn more mathematical tricks.

Based on the book "magic numbers»

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E-book in English