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Simple math tricks for anyone looking to multiply, divide and add like Sheldon Cooper. Math Tricks for Life Calculate Percentages Quickly

", I got a huge amount of information. The book covers dozens of tricks that simplify common mathematical operations. It turned out that multiplication and division in a column is the last century, and it is not clear why this is still taught in schools.

Mental multiplication "3 by 1"

Multiplying three-digit numbers by single-digit numbers is a very simple operation. All you have to do is break down a large task into several smaller ones.

Example: 320 × 7

1. We split the number 320 into two more prime numbers: 300 and 20.
2. Multiply 300 by 7 and 20 by 7 separately (2 100 and 140).
3. Add the resulting numbers (2,240).

Square two-digit numbers

Squaring two-digit numbers isn't much more difficult. You need to split the number by two and get an approximate answer.

Example: 41^2

1. Subtract 1 from 41 to get 40, and add 1 to 41 to get 42.
2. Multiply the two resulting numbers using the previous tip (40 × 42 = 1,680).
3. We add the square of the number by the value of which we have decreased and increased 41 (1,680 + 1 ^ 2 = 1,681).

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

Instantly square a number ending in 5

With squares of numbers ending in 5, you don't have to strain at all. All you need to do is multiply the first digit by one more number and add 25 to the end of the number.

Example: 75^2

1. Multiply 7 by 8 to get 56.
2. Add 25 to the number and get 5 625.

Division by one digit

Mental division is a fairly useful skill. Think about how often we divide numbers every day. For example, a restaurant bill.

Example: 675: 8

1. Find approximate answers by multiplying 8 by convenient numbers that give extreme results (8 × 80 = 640, 8 × 90 = 720). Our answer is 80-plus.
2. Subtract 640 from 675. Having received the number 35, you need to divide it by 8 to get 4 with a remainder of 3.
3. Our final answer is 84.3.

We get not the most accurate answer (the correct answer is 84.375), but you must agree that even such an answer will be more than enough.

Easy getting 15%

To quickly find out 15% of any number, you first need to count 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. Find 10% - 65.
2. We find half of 65 - that's 32.5.
3. Add 32.5 to 65 to get 97.5.

Banal trick

Perhaps we all came across this trick:

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

You got 6, right? Whatever you guess, you still get 6. And here's why:

1. 2x (double the 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 based on the elementary rules of algebra. Therefore, if you ever hear that someone is thinking it, put on your most arrogant grin, make a contemptuous look and tell everyone the answer. :)

The magic of number 1 089

This trick has existed for centuries.

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

Whichever number you choose, the result is 1,089.

Fast cube roots

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 cube root of any number will be trivial.

Example: cubic root of 19,683

1. 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 in the range 20+.
2. Each digit from 0 to 9 appears once in the table as the last digit of the cube.
3. Since the last digit in the problem is 3 (19 68 3 ), this corresponds to 343 = 7 ^ 3. Therefore, the last digit of the answer is 7.
4. The answer is 27.

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

Rule 70

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

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

70:20 = 3.5 years

Rule 110

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

Example: the number of years it takes to triple money at an annual interest rate of 12%.

110: 12 = 9 years old

Mathematics is a magical science. I'm even a little embarrassed that such simple tricks could surprise me, and I can't even imagine how many more mathematical tricks you can learn.

Maths not as difficult science as it might seem at first glance. There are many secrets that allow you to do very complex calculations in your mind.

10 math tricks

1. How to get 15% of any number
   You need to first calculate 10% of it, and then divide the resulting number by 2 and add these numbers.

   Example: 15% of 358

   1. Find 10% - 35.8.
   2. Find half of 35.8 - that's 17.9.
   3. Add 17.9 to 35.8 and you get 53.7.

2. Mental multiplication "3 by 1"
   You have no idea how easy it is. You just need to divide a large task into several smaller ones.

   Example: 450 × 6

   1. Break the number 450 into two simpler ones: 400 and 50.
   2. Multiply 400 by 6 and 50 by 6 separately (2,400 and 300).
   3. Add the resulting numbers (2,700).

3. Square two-digit numbers
   With this trick, you will be able to 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 which you increased and decreased 53 (2800 + 3 ^ 2 = 2809).

   The secret is that when squaring two-digit numbers, you need to turn them into numbers, which are much easier to multiply, as we did with the number 53.

4. Square a number ending in 5
   With this mathematical operation, everything is even simpler. Take the first digit of the number you are squaring. Multiply it by the same number plus 1. Then add 25 to the end.

   Example: 85^2

   1. Multiply 8 by 9 and you get 72.
   2. Add 25 to the number and you get 7225.

5. Division by one digit
   Mental division is a skill you need almost every day.

   Example: 589: 7

   1. It is necessary to find approximate answers by multiplying 8 by such numbers that give extreme results (7 × 80 = 560, 7 × 90 = 630). The answer is over 80.
   2. Subtract 560 from 589. Having received the number 29, divide it by 7 and you get 4 with a remainder of 1.
   3. Answer - 84.1

   The answer, of course, is not as accurate as possible, but even such an answer will be enough for you to, for example, pay in a restaurant.

6. How to quickly find the cube roots of numbers
   To easily find the cube root of any number, you need to learn the cubes of numbers from 1 to 10:

   1 — 1
   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: cube root of 39 304

   1. Take the value of thousands (39) and find between 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 cube roots of numbers from 1 to 10 only times.
   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.

7. Rule 70
   To find out how many years you will be able to double your money, divide the number 70 by the annual interest rate.

   Example: how many dearly years to double money with an annual interest rate of 17%.
   70:17 = 4.1 years

8. Rule 110
   To find out in how many years you will be able to triple your money, you need to divide 110 by the annual interest rate.

   Example: how many years it takes to triple money with an annual interest rate of 20%.
   110: 20 = 5.5 years

9. Magic number 1089
   And such a trick will surprise anyone! Think of any three-digit number, the digits of which are in decreasing order, for example 642 or 864. Then write it down in reverse order and subtract it from the original number. Add the same number to the resulting number, only written in reverse order. What did you do? 1089?
10. A simple trick
    You've probably seen this trick often: Think Any Number. Multiply it by 2. Add 12. Divide the sum by 2. Subtract the original number from it.

    You got 6, right? No matter what you think, you still get 6. And here's why:
    1.2x
    2.2x + 12
    3. (2x + 12): 2 = x + 6
    4.x + 6 - x

"Pure mathematics is a kind of poetry of a logical idea".
Albert Einstein

1. Fast calculation of interest

Perhaps, in the era of loans and installments, the most relevant mathematical skill is the masterly calculation of interest in the mind. The fastest way to calculate a certain percentage of a number is to multiply the given percentage by this number and then discard the last two digits in the resulting result, because the percentage is nothing more than one hundredth.

How much is 20% of 70? 70 × 20 = 1400. We discard two digits and get 14. When you rearrange the factors, the product does not change, and if you try to calculate 70% of 20, then the answer will also be 14.

This method is very simple in the case of round numbers, but what if you need to calculate, for example, the percentage of 72 or 29? In such a situation, you will have to sacrifice accuracy for the sake of speed and round off the number (in our example, 72 is rounded to 70, and 29 to 30), and then use the same technique with multiplying and discarding the last two digits.

2. Fast test of divisibility

Can 408 sweets be divided equally among 12 children? The answer to this question is easy and without the help of a calculator, if we recall the simple divisibility criteria that we were taught at school.

A number is divisible by 2 if its last digit is divisible by 2.

A number is divisible by 3, if the sum of the digits that make up the number is divisible by 3. For example, take the number 501, represent it as 5 + 0 + 1 = 6. 6 is divisible by 3, which means that the number 501 itself is divisible by 3 ...

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, take 2340. The last two digits form the number 40, which is divisible by 4.

A number is divisible by 5 if its last digit is 0 or 5.

A number is divisible by 6 if it is divisible by 2 and 3.

A number is divisible by 9, if the sum of the digits that make up the number is divisible by 9. For example, take the number 6 390, represent it as 6 + 3 + 9 + 0 = 18.18 is divisible by 9, which means that the number 6 itself 390 is divisible by 9.

A number is divisible by 12 if it is divisible by 3 and 4.

3. Fast square root calculation

The square root of 4 is 2. Anyone can count that. What about the square root of 85?

For a quick approximate solution, find the square number closest to the given number, in this case it is 81 = 9 ^ 2.

Now we find the next nearest square. In this case, it is 100 = 10 ^ 2.

The square root of 85 is somewhere between 9 and 10, and since 85 is closer to 81 than 100, the square root of that number would be 9-something.

4. Fast calculation of the time after which the money deposit at a certain percentage will double

Do you want to quickly find out the time it will take for your money deposit with a certain interest rate to double? There is also no need for a calculator, it is enough to know the "rule of 72".

We divide the number 72 by our interest rate, after which we get the approximate period after which the deposit will double.

If the contribution is made at 5% per annum, it will take a little over 14 years for it to double.

Why exactly 72 (sometimes they take 70 or 69)? How it works? These questions will be answered in detail by Wikipedia.

5. Fast calculation of the time after which the money deposit at a certain percentage will triple

In this case, the interest rate on the deposit should become a divisor of 115.

If the contribution is made at 5% per annum, it will take 23 years for it to triple.

6. Fast calculation of hourly rate

Imagine that you are interviewing two employers who do not call the salary in the usual format of “rubles per month”, but talk about annual salaries and hourly wages. How to quickly calculate where they pay more? Where the annual salary is 360,000 rubles, or where they pay 200 rubles per hour?

To calculate the payment for one hour of work when announcing the annual salary, it is necessary to discard the last three digits from the named amount, and then divide the resulting number by 2.

360,000 turns into 360 ÷ 2 = 180 rubles per hour. All other things being equal, it turns out that the second sentence is better.

7. Advanced math on the fingers

Your fingers are capable of much more than simple addition and subtraction.

Using your fingers, you can easily multiply by 9 if you suddenly forgot the multiplication table.

Let's number the fingers from left to right from 1 to 10.

If we want to multiply 9 by 5, then we bend the fifth finger from the left.

Now we look at the hands. It turns out four unbent fingers to bent. They stand for tens. And five unbent fingers after bent. They stand for units. Answer: 45.

If we want to multiply 9 by 6, then bend the sixth finger from the left. We get five unbent fingers before the bent finger and four after. Answer: 54.

Thus, you can reproduce the entire column of multiplication by 9.

8. Fast multiplication by 4

There is an extremely easy way to multiply even large numbers at lightning speed by 4. To do this, it is enough to decompose the operation into two steps, multiplying the required number by 2, and then again by 2.

See for yourself. Not everyone can multiply 1 223 by 4 at once. And now we do 1223 × 2 = 2446 and then 2446 × 2 = 4892. This is much easier.

9. Quick determination of the required minimum

Imagine that you are taking a series of five tests, for which you need a minimum score of 92 to pass successfully. The last test remains, and the results for the previous ones are as follows: 81, 98, 90, 93. How do you calculate the required minimum that you need to get in the last test?

To do this, we count how many points we missed / went over in the tests already passed, denoting the shortfall with negative numbers, and the results with a margin - positive.

So, 81 - 92 = −11; 98 - 92 = 6; 90 - 92 = −2; 93 - 92 = 1.

Adding these numbers together, we get the correction for the required minimum: −11 + 6 - 2 + 1 = −6.

It turns out a deficit of 6 points, which means that the required minimum increases: 92 + 6 = 98. Things are bad. :(

10. Quick view of the value of a common fraction

The approximate value of an ordinary fraction can be very quickly represented as a decimal fraction, if you first reduce it to simple and understandable ratios: 1 / 4.1 / 3, 1/2 and 3/4.

For example, we have a fraction 28/77, which is very close to 28/84 = 1/3, but since we increased the denominator, the initial number will be slightly larger, that is, slightly more than 0.33.

11. Number guessing trick

You can play a little David Blaine and surprise your friends with an interesting but very simple math trick.

1. Ask a friend to guess any whole number.
2. Let him multiply it by 2.
3. Then he adds 9 to the resulting number.
4. Now let's subtract 3 from the resulting number.
5. Now let's divide the resulting number in half (in any case, it will be divided without a remainder).
6. Finally, ask him to subtract from the resulting number the number that he thought at the beginning.

The answer will always be 3.

Yes, very stupid, but often the effect exceeds all expectations.

Bonus

And, of course, we could not help but insert that very picture with a very cool multiplication method into this post.

For many people, math can be terrifying. If you are one of them, and your math is not important, this is not your fault. We were simply not taught at school math tricks, with which any calculations become elementary.

This list may improve your general knowledge of math techniques and speed up your mental math calculations.

1. Multiplication by 11

We all know that when you multiply by 10, you add 0 to a number, but did you know that there is an equally simple way to multiply a two-digit number by 11? Here it is:
Take the original number and imagine the gap between the two digits (in this example we use the number 52):
5_2
Now add the two numbers and write them down in the middle:
5_(5+2)_2
So your answer is 572.
If, when adding the numbers in parentheses, you get a two-digit number, just remember the second number, and add one to the first number:
9_(9+9)_9
(9+1)_8_9
10_8_9
1089 - this always works.

2. Fast squaring

This technique will help you quickly square a two-digit number that ends in 5. Multiply the first digit by itself +1, and add 25 at the end. That's it!
252 = (2 × (2 + 1)) & 25
2 × 3 = 6
625

3. Multiplication by 5

Most people remember the multiplication table by 5 very easily, but when they have to deal with large numbers, it becomes more difficult to do it. Or not? This trick is incredibly simple.
Take any number, divide by 2 (in other words, halve). If the result is an integer, add 0 at the end. If not, ignore the comma and add 5. This always works:
2682 × 5 = (2682/2) & 5 or 0
2682/2 = 1341 (integer, so add 0)
13410
Let's try another example:
5887 × 5
2943.5 (fractional number, omit comma, add 5)
29435

4. Multiplication by 9

It's simple. To multiply any number from 1 to 9 by 9, look at your hands. Bend the finger that corresponds to the number to be multiplied (for example, 9x3 - fold the third finger), count the fingers to the bent finger (in the case of 9x3, this is 2), then count after the bent finger (in our case, 7). The answer is 27.

5. Multiplication by 4

This is a very simple technique, although it is obvious only to a few. The trick is to just multiply by 2 and then multiply by 2 again:
58 × 4 = (58 × 2) + (58 × 2) = (116) + (116) = 232

6. Counting tips

If you need a 15% tip, there is an easy way to do it. Calculate 10% (divide the number by 10), and then add the resulting number to half of it and get the answer:
15% of $ 25 = (10% of 25) + ((10% of 25) / 2)
$2.50 + $1.25 = $3.75

7. Complex multiplication

If you need to multiply large numbers, and one of them is even, you can simply rearrange them to get the answer:
32 × 125 is the same as:
16 × 250 is the same as:
8 × 500 is the same as:
4 × 1000 = 4,000

8. Division by 5

In fact, dividing large numbers by 5 is very easy. All you need to do is just multiply by 2 and move the comma: 195/5
Step1: 195 * 2 = 390
Step2: Move the comma: 39.0 or just 39.
2978 / 5
Step1: 2978 * 2 = 5956
Step2: 595.6

9. Subtract from 1000

To subtract from 1000, you can use this simple rule: Subtract all digits from 9 except the last one. And subtract the last digit from 10: 1000
-648
Step1: subtract 6 = 3 from 9
Step2: subtract 4 = 5 from 9
Step3: subtract 8 from 10 = 2
Answer: 352

10. Systematized rules of multiplication

Multiplication by 5: Multiply by 10 and divide by 2.
Multiplication by 6: Sometimes it is easier to multiply by 3 and then by 2.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add the original number twice.
Multiply by 13: Multiply by 3 and add 10 times the original number.
Multiply by 14: Multiply by 7 and then by 2.
Multiply by 15: Multiply by 10 and add 5 times the original number as in the previous example.
Multiply by 16: If you want, multiply 4 times by 2. Or multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times the original number.
Multiply by 18: Multiply by 20 and subtract the original number twice.
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number.
Multiply by 45: Multiply by 50 and subtract 5 times the original number.
Multiply by 90: Multiply by 9 and add 0.
Multiply by 98: Multiply by 100 and subtract the original number twice.
Multiply by 99: Multiply by 100 and subtract the original number.

Bonus: Interest

Calculate 7% of 300. Sounds complicated?

Percentage: First you need to understand the meaning of the word "Percent". The first part of the word is PRO (PER), like 10 items per page of the listverse site. PER = FOR EVERYONE. The second part is CENT, as 100. For example, STO anniversary = 100 years. 100 CENTS in 1 dollar and so on. So, PERCENTAGE = FOR EACH HUNDRED.

So, it turns out that 7% of 100 will be 7. (7 for every hundred, only one hundred).
8% of 100 = 8.
35.73% of 100 = 35.73

But how can this be useful?

Let's go back to the 7% of 300 problem.7% of
the first hundred is equal to 7. 7%, from the second hundred - the same 7, and 7% of the third hundred - the same 7. So, 7 + 7 + 7 = 21. If 8% of 100 = 8, then 8% of 50 = 4 (half of 8).

Split each number if you need to calculate the percentage of 100, but if the number is less than 100, just move the comma to the left.

EXAMPLES:
8%200 = ? 8 + 8 = 16.
8%250 = ? 8 + 8 + 4 = 20,
8% 25 = 2.0 (Move the comma to the left).
15%300 = 15+15+15 =45,
15%350 = 15+15+15+7,5 = 52,5

It's also helpful to know that you can always swap numbers: 3% of 100 is the same as 100% of 3.35% of 8 is the same as 8% of 35.

The Magic of Numbers book contains dozens of tricks that simplify common mathematical operations. It turned out that multiplication and long division is the last century, but there are much more effective ways of division in the mind.

Here are 10 of the most interesting and useful tricks.

Mental multiplication "3 by 1"

Multiplying three-digit numbers by single-digit numbers is a very simple operation. All you have to do is break down a large task into several smaller ones.

Example: 320 × 7

1. We split the number 320 into two more prime numbers: 300 and 20.
2. Multiply 300 by 7 and 20 by 7 separately (2 100 and 140).
3. Add the resulting numbers (2,240).

Square two-digit numbers

Squaring two-digit numbers isn't much more difficult. You need to split the number by two and get an approximate answer.

Example: 41^2

1. Subtract 1 from 41 to get 40, and add 1 to 41 to get 42.
2. Multiply the two resulting numbers using the previous tip (40 × 42 = 1,680).
3. We add the square of the number by the value of which we have decreased and increased 41 (1,680 + 1 ^ 2 = 1,681).

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

Instantly square a number ending in 5

With squares of numbers ending in 5, you don't have to strain at all. All you need to do is multiply the first digit by one more number and add 25 to the end of the number.

Example: 75^2

Multiply 7 by 8 to get 56.

Add 25 to the number and get 5 625.

Division by one digit

Mental division is a fairly useful skill. Think about how often we divide numbers every day. For example, a restaurant bill.

Example: 675: 8

1. Find approximate answers by multiplying 8 by convenient numbers that give extreme results (8 × 80 = 640, 8 × 90 = 720). Our answer is 80-plus.
2. Subtract 640 from 675. Having received the number 35, you need to divide it by 8 to get 4 with a remainder of 3.
3. Our final answer is 84.3.

We get not the most accurate answer (the correct answer is 84.375), but you must agree that even such an answer will be more than enough.

Easy getting 15%

To quickly find out 15% of any number, you first need to count 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. Find 10% - 65.
2. We find half of 65 - that's 32.5.
3. Add 32.5 to 65 to get 97.5.

Banal trick

Perhaps we all came across this trick:

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

You got 6, right? Whatever you guess, you still get 6. And here's why:

1. 2x (double the 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 based on the elementary rules of algebra. Therefore, if you ever hear that someone is thinking it, put on your most arrogant grin, make a contemptuous look and tell everyone the answer. 🙂

The magic of number 1 089

This trick has existed for centuries.

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

Whichever number you choose, the result is 1,089.

Fast cube roots

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 cube root of any number will be trivial.

Example: cube root of 19,683

1. 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 in the range 20+.
2. Each digit from 0 to 9 appears once in the table as the last digit of the cube.
3. Since the last digit in the problem is 3 (19,683), this corresponds to 343 = 7 ^ 3. Therefore, the last digit of the answer is 7.
4. The answer is 27.

Note: the trick only works when the original number is an integer cube.

Rule 70

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

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

70:20 = 3.5 years

Rule 110

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

Example: the number of years it takes to triple money with an annual interest rate of 12%.

110: 12 = 9 years old

Mathematics is a magical science. If even such simple tricks are surprising, what other tricks can you think of?