I. Definition:
1, binding law:
The law of multiplicative association refers to the multiplication of three numbers, the first two numbers are multiplied or the last two numbers are multiplied first, and the product is unchanged. Specifically, if a, b and c are three numbers, then (a×b)×c=a×(b×c). This rule is very useful when dealing with the multiplication of multiple numbers, which can ensure that the order of operations will not affect the results.
2, the distribution law:
Multiplication and distribution law refers to the multiplication of a number and the sum of two numbers, which is equal to the multiplication of this number and two numbers, and then the sum. Specifically, if A is a number and B and C are other two numbers, then A× (B+C) = A× B+A× C, which is very useful in solving complex multiplication problems. It can simplify the calculation process and make the problem easier to solve.
Second, the application of associative law and distributive law in mathematics
In higher mathematics, the laws of association and distribution still play an important role. For example, in algebra, the associative law is one of the basic properties of basic algebraic structures such as groups, rings and fields. In these structures, the satisfaction of the associative law ensures the smooth operation and provides convenience for proving various theorems.
Distribution law often appears in higher mathematics. For example, when dealing with mathematical concepts such as polynomial, matrix and linear transformation, the distribution law can often simplify the calculation process and make us solve problems more efficiently.
Scope of application of associative law and distributive law
First, the law of association:
1, mathematics field:
In addition, the law of combination tells us that the addition order of three numbers does not affect the result, which allows us to freely combine numbers without worrying about the accuracy of the result.
2, computer science:
In the design and implementation of programming languages, associative laws can be used to explain and optimize the execution efficiency of programs. For example, in the design of compiler, the calculation order of arithmetic expressions can be optimized by combination law, thus reducing the calculation time and memory occupation.
Second, the distribution law:
1, mathematics field:
Distribution law is widely used in various operations, including addition, multiplication and division. For example, addition and multiplication operations, distribution law can help us simplify complex calculations and improve operational efficiency.
2, the field of physics:
When calculating the kinetic energy of a particle, we can decompose the complex motion into simple parts through the distribution law, which makes it easier to calculate the amount of energy.