In Latin, the word fraction comes from frangre, which means to break or break, so fractions were also called "fragmented numbers".
In the history of numbers, fractions are almost as old as natural numbers. Records about numbers can be found in the oldest documents of various nations. However, fractions spread and gained their own status in mathematics. But it took thousands of years.
In Europe, these "broken numbers" once made people laugh and regarded them as a daunting prospect. In the 7th century, a mathematician calculated a problem of adding eight fractions, and was considered to have done a great thing. For a long time, when European mathematicians wrote arithmetic textbooks, they had to describe the operation rules of fractions separately, because many students would become discouraged and unwilling to continue learning mathematics after encountering fractions. Until the 17th century, many schools in Europe had to send their best teachers to teach fractions. To this day, when Germans describe someone who is in trouble, they often quote an old proverb, saying that he "fell into the score."
Some ancient Greek mathematicians simply did not recognize fractions and called them "ratios of whole numbers."
The ancient Egyptians were even more peculiar. When they express fractions, they usually add a small dot to the natural number. Add a small dot above 5 to indicate that the number is 1/5; add a small dot to 7 to indicate that the number is 1/7. So, what should we do to express the fraction 2/7? The ancient Egyptians put 1/4 and 1/28 together and said this was 2/7.
How can 1/4 and 1/28 represent 2/7? It turns out that the ancient Egyptians only used single-molecule fractions. In other words, they only use those fractions whose numerator is 1. When encountering other fractions, they have to be divided into the sum of single-molecule fractions. 1/4 and 1/28 are both single-molecule fractions, and their sum is exactly 2/7, so 14+128 is used to represent 2/7. There was no plus sign at that time, and the meaning of addition had to be shown by the context. It looked like putting 1/4 and 1/28 together to express the fraction 2/7.
Due to this peculiar regulation, the fractional operations in ancient Egypt were particularly cumbersome. For example, to calculate the sum of 5/7 and 5/21, you must first split these two fractions into single-molecule fractions:
57+521=(12+17+114)+(17+ 114+142);
Then add the fractions with the same denominator:
12+27+214+1 42;
Because of the General fractions, and then they have to be split into single-molecule fractions:
12+14+17+1 28+142.
It was so troublesome for the ancient Egyptians to calculate such a simple fraction addition problem. How difficult it would be for them to calculate if they encountered complex fraction operations.
In the West, the development of fraction theory was surprisingly slow. It was not until the 16th century that Western mathematicians had a more systematic understanding of fractions. Even in the 17th century, the mathematician Coke used the product of the denominator 8000 as the common denominator when calculating 35+78+911220!
Chinese mathematicians have known this knowledge more than 2,000 years ago.
The earliest mathematical work that can still be seen in our country is engraved on a batch of bamboo slips in the early Han Dynasty, and its name is "Shu Shu Shu". It was unearthed in Jiangling County, Hubei Province in early 1984. In this book, fraction operations have been studied in depth.
Later, in the ancient Chinese mathematics masterpiece "Nine Chapters on Arithmetic", fractions were systematically studied for the first time in the world. The book calls the addition of fractions "sum", the subtraction "subtraction", the multiplication "multiplication", and the division "meridian". It combines a large number of examples to introduce in detail their operation rules and the general understanding of fractions. Methods and steps for dividing, reducing, and converting mixed numbers into improper fractions. What is particularly proud is that the methods and steps invented by ancient Chinese mathematicians are roughly the same as modern methods and steps.
For example: "There are 49/91, what is the approximate geometry?" The method introduced in the book is: subtract 49 from 91 to get 42; subtract from 49 42, get 7; subtract 7 from 42 continuously, and get 7 at the fifth time. At this time, the minuend and the subtrahend are equal, and 7 is the greatest common divisor. Use 7 to reduce the numerator and denominator, and you get the simplest fraction 7/13 of 49/91. It is not difficult to see that the commonly used euclidean division method evolved from this ancient method.
In 263 AD, when Chinese mathematician Liu Hui commented on "Nine Chapters of Arithmetic", he added another rule: fractional division is to reverse the numerator and denominator of the divisor and multiply them by the dividend. In Europe, it was not until 1489 that Wittmann proposed a similar law, which was more than 1,200 years later than Liu Hui!
Balgarsky, an expert on the history of Soviet mathematics, fairly commented: “From this brief discussion, we can draw the conclusion that in the early days of the development of human culture, China’s mathematics was far ahead of other countries in the world. .
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