Daming: I, Yang Xian, really govern Yang!

Chapter 55 Four Arithmetic Operations
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Do you need tools for such simple arithmetic?

Yang Xian tilted his head and looked at Wang Yuemin.

She could hardly stand the look of fooling him again.

"Of course you need tools. Even if you don't have an abacus, at least you have to give me some calculations!" Wang Yuemin glared at Yang Xian, gritted his silver teeth, and spoke word by word.

After all, not everyone is a math genius like you.

She thought Yang Xian was playing tricks on him on purpose.

Only then did Yang Xian realize that he subconsciously thought that any normal person who had received nine-year compulsory education could do such a simple arithmetic. For a moment, he forgot that this was the Hongwu period of the Ming Dynasty.

The calculation chips mentioned by Wang Yuemin were the most important arithmetic tool in ancient times before the popularity of abacus.

The so-called calculation chips are small sticks of the same length and thickness. They are mostly made of bamboo, but also made of wood, animal bones, ivory and other materials. There are about 270 pieces in a bunch, which are placed in a cloth bag and tied. Carry it around your waist.

When you need to count and calculate, you can take them out at any time and put them on the floor or table to play with.

In the TV series "The Ming Dynasty under the Microscope" adapted from the novel of the same name by Prince Ma, the male protagonist Shuai Jiamo has used arithmetic calculations many times.

After listening to Wang Yuemin's words, Yang Xian found some wooden sticks for her.

"Sun Tzu's Suan Jing" records that the rules of counting are as follows: For any calculation method, first know its position, one vertical and ten horizontal, hundreds standing and thousands standing, thousands and ten facing each other, and thousands and hundreds equal.

After standing aside and watching Wang Yuemin fiddle with it, Yang Xian roughly understood the principle of arithmetic, which was actually equivalent to the principle of modern decimal arithmetic.

However, it is still too complicated compared to modern arithmetic.

The efficiency is far inferior.

Addition and subtraction are fine, but when it comes to multiplication, it takes a long time just to set up the calculation chips.

But you must know that it is impossible to check when calculations first appeared, but the latest time they appeared was in the Spring and Autumn Period and the Warring States Period.

In other words, our ancestors understood such sophisticated calculations more than 2000 years ago, which is really amazing.

You must know that at the same time, the ancient Roman number system did not have a place value system and only had seven basic symbols. It was quite difficult to remember larger numbers.Although the Mayans of ancient America knew the place value system, they used base 20; the ancient Babylonians also knew the place value system, but they used base 60. Carrying 20 requires at least 19 digits, and carrying 60 requires 59 digits, which makes counting and operations very complicated. It is far less simple and convenient than the decimal system, which can represent any natural number with only 9 digits.

This is also an important reason why ancient Chinese mathematics was so developed in the early days.

The reason why ancient Chinese mathematics has achieved many outstanding achievements in calculations should be attributed to this counting method that conforms to the decimal system to a certain extent.

During the Northern Dynasties, Zu Chongzhi used this small wooden stick called "calculation chip" to finally calculate pi.

"1621." Yang Xian suddenly said.

At this time, Wang Yuemin had just started to arrange the chips. She ignored it and continued to arrange the chips at her own pace.

after a little while.

Wang Yuemin raised his head and looked at Yang Xian, his face full of disbelief.

The numbers Yang Xian reported at the beginning were exactly the same as the results she calculated.

"How did you do it?"

In Wang Yuemin's view, even using an abacus to calculate at such a speed would be impossible.

You must know that Yang Xian did not use any tools to assist him throughout the process.

How could this not shock Wang Yuemin. "It's easy, I'll teach you."

Yang Xian took a blank piece of paper and wrote ten Arabic numerals from 0 to 9 on it.

In fact, Wang Yuemin wanted to ask Yang Xian just now what these characters meant.

Arabic numerals, also called Hindu-Arabic numerals.It was first invented in India in the 6th century AD.Later it spread to Arabia, where the font of this number changed and became East Arabic numerals.By the beginning of the 13th century, Eastern Arabic numerals were introduced to Europe via North Africa.In Europe, this numeral changed again, and its printing style gradually changed to Latin font, and finally developed into Western Arabic numerals.

In fact, Arabic numerals were introduced to China by Muslims as early as the Yuan Dynasty, but they did not attract much attention and did not spread.

Furthermore, the Arabic numerals introduced to China at this time were also East Arabic numerals.

It is still very different from modern Arabic numerals (Western Arabic numerals).

Western Arabic numerals were introduced to China by Jesuits who came to China in the early 17th century.But even at that time, Arabic numerals were not widely used until the late 19th century.

Therefore, it is not surprising that Wang Yuemin could not recognize the numbers written by Yang Xian.

Yang Xian then wrote the Chinese characters corresponding to the numbers below the ten numbers.

"You mean the ten numbers you wrote represent zero to ten?" Now Wang Yuemin understood.

But she still didn't understand what these numbers had to do with Yang Xian's ability to calculate the results so quickly.

Then she saw Yang Xian starting to write and draw on the paper again.

"One horizontal and one vertical. This character represents the addition of two numbers. A single horizontal line represents the subtraction of two numbers. The intersection of the two represents the multiplication of the two, which is what you call the product in your calculations."

Yang Xian was very patient. After introducing the characters of addition, subtraction, multiplication and division, Wang Yuemin almost digested it.

Then I started to write down a few examples of operations on paper.

"This arrangement seems to be somewhat similar to calculations." Wang Yuemin asked.

Yang Xian nodded and said, "This is my arithmetic method."

"The numbers are arranged from left to right, and read in order from the highest order. For example, 1186 means one thousand, one hundred and eighty six."

"When adding two numbers, you should pay attention to the following points. First, align the same digits. Second, remember to add from the ones digit. If the ones digit reaches 10, add 1 to the tens digit."

While explaining the principles, Yang Xian wrote a few more examples and performed the calculations in person.

It wasn't until Wang Yuemin basically understood what was going on that he stopped.

"Subtraction is similar to addition. The same digits are also aligned, and the subtraction starts from the ones digit. The only difference is that in subtraction, which digit is not enough to subtract, 1 is returned from the previous digit, and 10 is added to the base digit and then subtracted."

This time Wang Yuemin obviously accepted it faster.

Yang Xian almost wrote two examples, and she was already able to answer the questions.

"Do you know the multiplication table?" Yang Xian suddenly asked.

"Master Yang, is he referring to Fang Tian in Suan Jing?" Wang Yuemin asked a little uncertainly. "Is this what 81 and 72 are?"

"Yes, that's it." Yang Xian smiled.

"If you know this, it will be much easier to teach multiplication and division."

(End of this chapter)