Algorithm is a very important concept in mathematics, which refers to some laws and properties in mathematical operations, such as additive commutative law, additive associative law, multiplicative commutative law and multiplicative associative law. These algorithms sometimes seem simple, but it is very basic and important for beginners to understand and master them, because they are the foundation of mathematics and involve many profound concepts and formulas in mathematics. Next, I will show you the concepts and laws of arithmetic in mathematics by drawing.

1. additive commutative law, that is, a+b = b+a shows that when two numbers are added, the exchange position will not change their sum.

We can represent additive commutative law graphically, as shown in the following figure:

! [additive commutative law icon] (/2021102155829399.png? x-oss-process=image/watermark，type_ZmFuZ3poZW5naGVpdGk=，size_ 15，text_NjAweDEzMg==，color_FFFFFF，t_70，g_se，x_ 16)

Second, the law of addition and association, that is, a+(b+c) = (a+b)+c, shows that when three numbers are added, two of them are added first, which does not affect the final result.

We can use a graphic way to represent the law of addition and association, as shown in the following figure:

! [Illustration of Additive Binding Law] (/2021102155844577.png? x-oss-process=image/watermark，type_ZmFuZ3poZW5naGVpdGk=，size_ 15，text_NjAweDEzMg==，color_FFFFFF，t_70，g_se，x_ 16)

Third, the law of multiplication and exchange, that is, a × b = b × a, shows that when two numbers are multiplied, the exchange position will not change the product.

We can graphically represent the multiplicative commutative law, as shown in the following figure:

! [method of substitution diagram of multiplication] (/2021102155903714.png? x-oss-process=image/watermark，type_ZmFuZ3poZW5naGVpdGk=，size_ 15，text_NjAweDEzMg==，color_FFFFFF，t_70，g_se，x_ 16)

Fourth, the law of multiplication and association, that is, a × (b × c) = (a × b) × c, means that when three numbers are multiplied, two of them are multiplied first, and the final result is not affected.

We can graphically represent the law of multiplicative association, as shown in the following figure:

! [Diagram of the Law of Multiplication and Association] (/2021102155920240.png? x-oss-process=image/watermark，type_ZmFuZ3poZW5naGVpdGk=，size_ 15，text_NjAweDEzMg==，color_FFFFFF，t_70，g_se，x_ 16)

5. The law of distribution, that is, a × (b+c) = a × b+a × c, shows that when a number is multiplied by the addition in a bracket, you can multiply this number by each number in the bracket and then add the results.

We can use the graphic way to represent the distribution law, as shown in the figure below:

! [Distribution Pattern] (/2021102155937385.png? x-oss-process=image/watermark，type_ZmFuZ3poZW5naGVpdGk=，size_ 15，text_NjAweDEzMg==，color_FFFFFF，t_70，g_se，x_ 16)

6. Associative law, commutative law and distributive law are the most basic algorithms in mathematics, which are widely used in various branches of mathematics, such as algebra, calculus, probability theory and so on.

The above are the concepts and laws of arithmetic in mathematics, as well as the methods expressed by charts. I hope this article will help beginners to understand and master the related concepts and applications of algorithm faster.