Can u calculate faster than the calculator?

Hi! My name is Dennis Wu and I am a sophomore in Saint Andrew's School now. Recently I am fascinated by a youtube video called "faster than a calculator" made by Arthur Benjamin. In the video, he shows that he can calculate the multiples of 2, 3, 4 or even 5 digits numbers faster than a calculator. As I am always interested in mental math, I decided to do some research on how can we use some special method to calculate faster by just using our brain.

Arthur T. Benjamin

According to Moscoso del Prado, a scholar from MIT University,  "A new way to analyze human reaction times shows that the brain processes data no faster than 60 bits per second". However, the most advanced computer in the world, "TaihuLight," invented in China, can do 200 quadrillion calculations per second. It's true that a computer can literally do calculations faster than human beings because of the advancements in technology, however, there are some ways that can help us to calculate faster by just using our brains. By the way, we, as human beings, only develop less than 10% of our brains.

Sunway Taihu Light, the fastest computer in the world

Here is a video I found that tell us about how powerful the human's brain is:

Here are some methods that I found interesting.

(1) India fast calculates method: an amazing method that was invented by ancient Indians that can let us calculate 2-digit-number multiples (only between 10 to 19) mentally under only 3 seconds.

Basically, this method can be concluded as

Here is an example of the India Fast Calculates Method:

(2) Another method that deals with multiplying 2-digit-numbers - I called it "cross out digits."

First, we need to multiply the number in the tens digit with the number that comes after the number in the tens digit in counting. Now, we have the first 2 digits of your answer. (e.g if it is 33 times 37, we multiply 3 with 4 firstly and then we got “12” for the first 2 digits of your answer)

Then, we need to multiply the number in the units digit and get the last 2 digits of your number. (e.g if it is 33 times 37, we multiply 3 with 7 and get 21 for the last 2 digits)

Then we have the answer to this multiplication. (e.g so 33 times 37 would be 1221)

There are two restricting conditions when we apply this method.

1. The number of the tens digit must be the same number
2. The addition of two unit digits must equal to 10

Here is an introduction video of this method:

(3)Tricks of calculation of perfect squares ( I am using 33 as a demonstrate number)

First, we need to find the difference between the number you want to calculate and the nearest tens number. So for 33, it would be 3.

Then we multiply the addition of the difference and the original number with the difference of the original number and difference which we got from the first step. So for 33, we multiply 30 with 36 which can be done fastly in our mind and got 1080.

Lastly, we calculate the square of the number’s unit digit number and add to the number we got from the second step. Then we will get the answer. So for 33, we add the square of 3 which is 9 and 1080 which we got from the second step, then, we got 1089 which is the final answer.

Here is the introduction of this method:

Last but not least, I found out that all of these tricks are basically applying the same thing, which is very simple that we might learn from primary school -- Multiplicative Distribution Law.

So I conclude my personal trick to deal with all the situation of 2-digit-number multiplication:

ab*cd=ab*c0+ab*d

For example, 54*32 = 54*30 + 54*2 = 1620 + 108 = 1728

My personal way seems very simple but it is actually very practical. So...try it in the future and do not rely on your calculator all the times. Your brain needs some practice!

Math is FUN!

After all, I want to say, for me, what is interesting and amazing about math is that we can use simple things to create fantastic and unbelievable stuff in the world of math. The charm of math lies in its unexpectedness. Only an open mind, can discover how interesting it is.

Citations (For the pictures):
https://shop.spreadshirt.com/niftees/math+is+fun+t-shirt-A8593554
https://en.wikipedia.org/wiki/Arthur_T._Benjamin