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Briefly describe the main contents and historical significance of Nine Chapters Arithmetic.
Nine Chapters Arithmetic is the earliest book in the world that systematically describes fractional operation. Among them, the residual algorithm is an amazing creation; The chapter "Equation" also expounds the negative number and its addition and subtraction algorithm for the first time in the history of world mathematics. In algebra, Nine Chapters Arithmetic put forward the concept of negative number and the law of addition and subtraction of positive and negative numbers for the first time in the history of world mathematics. The solution of linear equations taught in middle school is basically the same as that introduced in Chapter 9 Arithmetic. Paying attention to practical application is a remarkable feature of nine chapters arithmetic. Some knowledge of the book has also spread to India and Arabia, and even to Europe through these areas.

Nine Chapters Arithmetic is the crystallization of several generations, and its appearance marks the formation of the ancient mathematical system in China. Most mathematicians in later generations began to learn and study mathematical knowledge from Nine Chapters of Arithmetic. Both Tang and Song Dynasties were clearly defined as textbooks by the state. 1084 was published by the Northern Song Dynasty, and it was the earliest printed mathematics book in the world. It can be said that Nine Chapters Arithmetic is another outstanding contribution made by China to the development of mathematics.

There are many mathematical problems in Nine Chapters of Arithmetic, which is the earliest record in the world. For example, the algorithm of proportion is the same as that of16th century in western Europe. The double method problem was once called the Khitan algorithm in Arabia, and it was also called in European mathematical works after13rd century, which is also an evidence that China's ancient mathematical knowledge spread to the west.

Nine Chapters Arithmetic had a great influence on the development of ancient mathematics in China until the middle of Qing Dynasty. The narrative mode of Nine Chapters Arithmetic is mainly inductive. Give a few examples first, and then give the solution. Different from the narrative mode of western deduction, China's later mathematical works also adopted narrative mode. Many mathematicians in the past dynasties have annotated the book, among which Liu Hui and Li's annotations are the most famous.

"Nine Chapters Arithmetic" also spread to Japan and Korea, which also had a great influence on the development of its ancient mathematics.