In the history of numbers, fractions are almost as old as natural numbers, and records about numbers can be found in the oldest documents of all ethnic groups. However, it took thousands of years for scores to spread and gain their place in mathematics.
In Europe, these "broken numbers" were once frightening and were regarded as the road to fear. In the 7th century, a mathematician did an exercise of adding eight fractions, which was considered a great thing. For a long time, European mathematicians had to describe the arithmetic of fractions separately when compiling arithmetic textbooks, because many students would be disheartened and unwilling to continue studying mathematics after encountering fractions. Until the17th century, many schools in Europe had to send the best teachers to teach the knowledge of fractions. So far, when Germans describe a person in trouble, they often quote an old proverb that he is "in trouble"
Some ancient Greek mathematicians simply refused to recognize fractions, calling them "the ratio of integers".
The ancient Egyptians were more peculiar. When they represent fractions, they usually add a point to natural numbers. Adding a dot to 5 indicates that the number is1/5; Adding a dot to 7 indicates that the number is 1/7. So, what should I do to represent the score of 2/7? The ancient Egyptians put 1/4 and 1/28 together and said it was 2/7.
How do 1/4 and 1/28 represent 2/7? It turns out that the ancient Egyptians only used single molecular fractions. That is to say, they only use those fractions whose molecules are 1, and when they meet other fractions, they have to divide them by the sum of single molecule fractions. 1/4 and 1/28 are both monomolecular fractions, and their sum is exactly 2/7, so 1/4+ 1/28 is used to represent 2/7. There was no plus sign at that time, and the meaning of addition depended on the context. It seems that 1/4 and 1/28 are put together to represent a score of 2/7.
Because of this peculiar regulation, the operation of ancient Egyptian music score is particularly complicated. For example, to calculate the sum of 5/7 and 5/2 1, you must first decompose these two fractions into monomolecular fractions:
5/7+5/2 1=( 1/2+ 1/7+ 1/ 14)+( 1/7+ 1/ 14+ 1/42);
Then add the fractions with the same denominator:
1/2+2/7+2/ 14+ 1/42;
Because there are general fractions in the molecular formula, they must be broken down into monomolecular fractions:
/2+ 1/4+/7+ 1/28+/42。
The simple problem of fractional addition was so troublesome for the ancient Egyptians to calculate, and how difficult it would be for them to calculate if they encountered complicated fractional operation.
In the west, the development of fractional theory is surprisingly slow. It was not until16th century that western mathematicians got a systematic understanding of fractions. Even in the17th century, mathematician Kirk used the product of denominator 8000 as the common denominator when calculating 3/5+7/8+9//kloc-0+12/20!
China mathematicians have known this knowledge for more than 2000 years.
The earliest mathematical works that can be seen in China at present are engraved on a batch of bamboo slips in the early Han Dynasty, and its name is Shu Shu. 1984 Unearthed in jiangling county, Hubei Province. In this book, the fractional operation is deeply studied.
Later, in China's ancient mathematical masterpiece Nine Chapters Arithmetic, the score was systematically studied for the first time in the world. In the book, the addition of fractions is called "combination", the subtraction is called "subtraction", the multiplication is called "multiplication" and the division is called "division". Combined with a large number of examples, their operation rules, as well as the methods and steps of general division, simplification and transformation of fractions into pseudo-fractions are introduced in detail. What is particularly proud of is that these methods and steps invented by ancient mathematicians in China are basically the same as modern methods and steps.
For example, "there are ninety-one and forty-nine. Ask geometry?" The method introduced in the book is: 9 1 subtract 49 to get 42; 49 MINUS 42 gets 7; Subtract 7 from 42 in a row and get 7 for the fifth time. At this time, the minuend is equal to the minuend, and 7 is the greatest common divisor. The simplest fraction of 49/9 1 713 is obtained by subtracting the numerator and denominator from 7. It is not difficult to see that the common repeated division method evolved from this ancient method.
In 263 AD, Liu Hui, a mathematician in China, added another rule when commenting on Nine Chapters of Arithmetic: Fractional division is to multiply numerator and denominator by divisor in turn. In Europe, it was not until 1489 that Videman put forward a similar law, which was later than Liu Hui 1200 years!
Paul Gorsky, an expert in the history of mathematics in the Soviet Union, fairly commented: "From this brief exposition, we can draw a conclusion: in the early stage of the development of human culture, China's mathematics was far ahead of other countries in the world."