(1), the main achievements in arithmetic are fractional operation, proportional problem and "remainder" algorithm. "Nine Chapters Arithmetic" is the earliest book that systematically describes fractional operation in the world. There are many proportional problems in the second, third and sixth chapters, which are also relatively early in the world. The "residual" algorithm needs to be given twice, and it is a creation, which was called in medieval Europe.

(2) In geometry, it is mainly the calculation of area and volume.

(3) In algebra, there are mainly solutions, square roots, square roots and general quadratic equations of linear equations. The chapter "Equation" also introduces negative numbers and their addition and subtraction algorithms for the first time in the history of world mathematics. As a world-famous scientific work, Nine Chapters Arithmetic was introduced to Korea and Japan during the Sui and Tang Dynasties. Now it has been translated into Japan, Russia, Germany, Britain, France and other countries.

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, the concept of negative number and the law of addition and subtraction of positive and negative numbers were first put forward in the history of mathematics in the world. 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 this book has also spread to India and Arabia, and even to Europe through these areas.

Nine-chapter arithmetic is the crystallization of several generations' joint efforts, and its appearance marks the formation of China's ancient mathematical system. 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. Published by the Northern Song Dynasty court at that time, 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.