Multiply, divide, add like Sheldon Cooper? Math hacks

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2024-01-13 00:26

Don't you learn matan? Go to methane!

Pure mathematics is, in a way, the poetry of a logical idea. Albert Einstein

In this article, we offer you a selection of simple mathematical tricks, many of which are quite relevant in life and allow you to count faster.

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 one, 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 will 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? Wikipedia will answer these questions in detail.

5. Fast calculation of the time after which a cash 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, then 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 we 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 going through 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, 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 presentation 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 original 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.