Not so long ago, Lifehacker published a review of the book “Magic of Numbers”, which contains a huge number of mathematical tricks. The book did not leave us indifferent, and we chose from it 10 most interesting tips to simplify mathematical operations.

Recently, after reading the book “The Magic of Numbers”, I learned a lot of information. The book tells about dozens of tricks that simplify the usual mathematical operations. It turned out that multiplication and division into a column is the last century, and it is unclear why this is still taught in schools.

I have chosen the 10 most interesting and useful tricks and I want to share them with you.

Multiplication “3 by 1” in your mind.
Multiplication of three-digit numbers by single digits is a very simple operation. All you have to do is break a big task into a few small ones.

An example: 320 × 7

We break down the number 320 into two simpler numbers: 300 и 20.
Multiply 300 by 7 and 20 by 7 individually (2 100 and 140).
Add up the resulting numbers (2 240).
Putting two-digit numbers in a square
It’s not much harder to square two-digit numbers. You need to split the number into two and get an approximate answer.

An example: 41^2

Subtract 1 of 41 to get 40 and add 1 of 41 to get 42.
Multiply the two resulting numbers using the previous advice (40 × 42 = 1,680).
We add the square of the number by which we reduced and increased 41 (1 680 + 1^2 = 1 681).
The key rule here is to turn the desired number into a pair of other numbers, which are easier to multiply. For example, for number 41 it is 42 and 40, for number 77 it is 84 and 70. That is, we subtract and add the same number.

The instant square of a number ending in 5…
With squares of numbers ending in 5, there’s no need to strain at all. All you have to do is multiply the first digit by a number that is one more, and add 25 at the end of the number.

Here’s an example: 75^2

Multiply 7 by 8 and we get 56.
We add to number 25 and get 5 625.
Dividing by an unambiguous number
Division in the mind is a useful enough skill. Think about how often we divide numbers every day. For example, the restaurant bill. How to quickly learn multiplication for 4th grade.

An example: 675 : 8

Find approximate answers by multiplying 8 by convenient numbers that give extreme results (8 × 80 = 640, 8 × 90 = 720). Our answer is 80 with a tail.
We subtract 640 from 675. Having received number 35, it is necessary to divide it by 8 and to receive 4 with the balance 3.
Our final answer is 84.3.
We do not get the most accurate answer (the correct answer is 84.375), but you agree that even such an answer will be more than enough.

Easy to get 15%.
To quickly find out 15% of any number, you must first count 10% of it (moving a comma to the left by one character), then divide the resulting number by 2 and add it to 10%.

Example: 15% of 650

We find 10% to 65.
We find half of 65 is 32.5.
We add 32.5 to 65 and we get 97.5.
It’s a trite trick.
I think we’ve all stumbled upon a trick like that:

Think of any number. Multiply it by two. Add up 12. Divide it by two. Subtract the original number from it.

You got six, right? Whatever you wish for, you still get a six. And that’s why:

2x (double the number).
2x + 12 (add 12).
(2x + 12) : 2 = x + 6 (divide by 2).
x + 6 – x (subtract the original number).
This trick is built on elementary algebra rules. So, if you ever hear someone riddle it, pull up your most arrogant smile, make a contemptuous look and tell everyone the solution. 🙂

Math grade 3, all you need to know

The magic of the number 1 089
This trick has been around for centuries.

Write down any three-digit number that goes in decreasing order (e.g. 765 or 974). Now write it down in reverse order and subtract it from the original number. Add it to the answer you receive, only in reverse order.

Whichever number you choose, you will get 1 089 as a result.

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

1 2 3 4 5 6 7 8 9 10
1 8 27 64 125 216 343 512 729 1 000
»
Once you memorize these values, finding the cubic root of any number is easy.

Example: a cubic root of 19,683

We take the value of thousands (19) and look between what numbers it is (8 and 27). Accordingly, the first digit in the answer will be 2, and the answer lies within the range of 20 +.
Each digit from 0 to 9 appears in the table once as the last cube digit.
Since the last digit in the problem is 3 (19 683), this corresponds to 343 = 7^3. Consequently, the last digit of the answer is 7.
The answer is 27.
Note: the trick works only when the initial number is the cube of the whole number. Interesting math grade 3 quests

Rule 70
To find the number of years needed to double your money, divide the number 70 by the annual interest rate.

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

70 : 20 = 3.5 years

Rule 110
To find the number of years needed to triple the money, divide the number 110 by the annual interest rate.

Example: The number of years needed to triple money with an annual interest rate of 12%.

110 : 12 = 9 years

Mathematics is a magic science. I’m even a little embarrassed that such simple tricks could surprise me, and I have no idea how many more mathematical tricks you can learn.

From the book Magic of Numbers.