Multiply, divide, add Sheldon Cooper? Math hacks ...
Tips / / December 19, 2019
Pure mathematics is, in its own way the poetry of logical ideas. Albert Einstein
In this article, we offer you a selection of simple mathematical techniques, many of which are quite relevant to the lives and suggest faster.
1. Fast evaluation of percent
Perhaps, in the era of installment loans and most relevant skill mathematical calculation can be called consummate interest in mind. The quickest way to calculate a certain percentage of the number is the multiplication of the interest on this number followed by dropping the last two digits to get a result, because the interest is not other than the one hundredth share.
How much is 20% of the 70? 70 × 20 = 1400. Discard the two numbers and get 14. When moving the product of the factors does not change, and if you try to calculate the 70% of 20, the answer will also be 14.
This method is very simple in the case of a round number, but what if you need to calculate, for example, the percentage of the number 72 or 29? In such a situation will have to sacrifice accuracy for speed and the round number (in this example 72 rounded to 70 and 29 to 30), then use the same reception with multiplication and discarding the two the latest figures.
2. A quick check divisibility
Is it possible to equally divide the 408 sweets among 12 children? To answer this question easily and without a calculator, if you remember the simple signs of divisibility 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 numbers divisible by 3. For example, take the number 501, represent it as a 5 + 0 + 1 = 6. 6 is divisible by 3, and hence the number 501 itself is divided into three.
- 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 numbers divisible by 9. For example, take the number 6390, will present it as a 6 + 3 + 9 + 0 = 18. 18 is divisible by 9, and hence the number itself 6390 is divided into 9.
- A number is divisible by 12, if it is divisible by 3 and 4.
3. Fast calculation of the square root
The square root of 4 is 2. It considers any. And what about the square root of 85?
To quickly find approximate solutions nearest to a given square number, in this case, 81 = 9 ^ 2.
Now we find the next closest square. In this case, 100 = 10 ^ 2.
The square root of 85 is somewhere in the range between 9 and 10, since 85 is closer to 81 than to 100, the square root of this number will be 9 with something.
4. Quick calculation of time after which the cash contribution under a certain percentage will double
Want to quickly find out the time it will take to get your cash contribution at a certain interest rate doubled? There also does not need a calculator, it is sufficient to know the "rule of 72".
Divide the number 72 on our interest rate, and then to get some time, through which contributions will be doubled.
If the contribution is made under the 5% per annum, it would take 14 years or so that it has doubled.
Why 72 (sometimes take 70 or 69)? How it works? These questions are deployed answer "Wikipedia".
5. Quick calculation of time after which the cash contribution under a certain percentage will triple
In this case, the interest rate on the deposit must be a divisor of the number 115.
If the contribution is made under the 5% per annum, it would take 23 years old, so it has tripled.
6. Quick calculation of the hourly rate
Imagine that you are interviewing with two employers, who are not referred to the salary in the usual format of "rubles a month," and talk about the annual salary and hourly pay. How to quickly find where they pay more? Where the annual salary of 360 000 rubles, or where pay 200 rubles per hour?
To calculate the payment of one hour of work during dubbing annual salary must be dropped from the said sum of the last three signs, and then divide the resulting number by 2.
360,000 converted to 360 ÷ 2 = 180 rubles per hour. All things being equal it turns out that the second sentence better.
7. Advanced Mathematics on the fingers
Your fingers are capable of much more than the simple addition and subtraction.
Using your fingers can easily be multiplied by 9, if you suddenly have forgotten the multiplication table.
We number the fingers from left to right from 1 to 10.
If we want to multiply 9 by 5, then bends to the left fifth finger.
Now look at your hands. It turns out four fingers unfolded to folded. They represent dozens. And after five fingers unfolded folded. They indicate the unit. Answer: 45.
If we want to multiply 9 by 6, the sixth finger bends to the left. We received five fingers unfolded to the folded thumb and four after. Answer: 54.
Thus it is possible to reproduce the entire column is 9 multiplication.
8. Fast multiplication by 4
There is a very easy way to lightning multiplication of large numbers even at 4. To do this, it suffices to expand the operation into two steps by multiplying the required number by 2, and then again at 2.
See for yourself. Multiply 1223 by 4 in mind not everyone can. And now do 1223 × 2 = 2446 and then 2446 × 2 = 4892. So much easier.
9. Rapid determination of the necessary minimum
Imagine that you are going through a series of five tests for the successful completion of which you need a minimum score of 92. Was the last test, and on the previous results are as follows: 81, 98, 90, 93. How to calculate the required minimum, you want to get in the last test?
To do this, we consider how many points we gleaning / moved to have passed the tests, indicating a shortage of negative numbers, and the results with a margin - positive.
Thus, 81 - 92 = -11; 98 − 92 = 6; 90 − 92 = −2; 93 − 92 = 1.
Putting these figures, adjustments to obtain minimum necessary: 6 -11 + - 2 + 1 = -6.
It turns out the deficit in 6 points, which means that the necessary minimum of increases: 92 + 6 = 98. Things are bad. :(
10. Quick view of the values common fraction
Estimated value common fraction can be quickly represented in decimal form, if the pre lead to its simple and straightforward relationships: 1 / 4,1 / 3, 1/2 and 3/4.
For example, we have a 28/77 shot, which is very close to 28/84 = 1/3, but as we have increased the denominator, the original number is slightly larger, ie slightly more than 0.33.
11. Trick guessing numbers
You can play some of David Blaine and impress your friends an interesting, but very simple mathematical trick.
- Ask a friend to think of any integer.
- Let it multiply it by 2.
- Then add to the resulting number 9.
- Now let take away 3 from the resulting number.
- And now let divide the resulting number in half (which in any case will be divided without a remainder).
- Finally, ask them to deduct from the resulting number is the number, which he put forth in the beginning.
The answer will always be 3.
Yes, very stupidly, but often the effect exceeds all expectations.
bonus
And, of course, we could not insert into the post that same picture with a very cool way of multiplication.