1, reflexivity: for any real number or algebraic expression, it is equal to itself. For example, for any real number A, A = A. Symmetry: If the values on both sides of the equation are equal, they can be interchanged. For example, a=b, then B = A. Transitivity: If the values on both sides of the equation are equal and are multiplied or divided by the same non-zero real number or algebra, then the new equation still holds.
2. Law of addition and distribution: The equation still holds when the same number is added to both sides of the equation. For example, a+b=c, then A+(B+D) = C+D. Multiplication and distribution law: When both sides of the equation are multiplied by the same number at the same time, the equation still holds. Zero property: any number added to zero equals itself. For example, for any real number a+0 = a+0 = a.
3. Multiplicative commutative law: Multiply the products of two numbers on both sides of the equation at the same time, and the equation still holds. For example, a×b=c, then (a× d )× (b× d) = c× d 2. Division rule: divide both sides of an equation by a nonzero number or algebra at the same time, and the equation still holds. For example, a/b=c, then (a/d)/(b/d) = c/d.
The benefits of learning mathematics
1. Mathematics is a subject that needs rigorous logical reasoning, and learning mathematics is helpful to cultivate logical thinking ability. This ability can be applied to our daily life and work to help us analyze, reason and solve problems better. Mathematical problems usually need innovative and unique methods to solve.
2. Learning mathematics can help us improve our ability to solve problems and make us more adaptable to complex and changeable problem situations. Geometric and graphic processing in mathematics is helpful to enhance spatial thinking ability. This ability can help us better understand the concepts of shape, size, distance and direction in three-dimensional space, which is very important for architectural design, mechanical design and other fields.
3. The calculation and data analysis skills in mathematics can help us to understand and interpret the data better. This ability is very important in science, engineering, finance and other fields, which can help us make accurate predictions and analysis. Mathematics is the foundation of many other disciplines, including science, engineering, economics, computer science and so on.