Addition is one of the most basic operations in mathematics, which means the process of combining two numbers into one number. Addition has a long history. As early as ancient times, people began to use addition to calculate quantity and measurement. In addition, we need two numbers as input and get one number as output. These two inputs are called addends and the outputs are called sums. The mathematical expression of addition is: a+b=c, where A and B are addends and C is sum.

The basic properties of addition include commutative law, associative law and reflexivity. Commutative law means that addition is commutative, that is, a+b = b+a, and associative law means that addition is combinable, that is, (a+b)+c=a+(b+c). Reflexivity means that any number added to 0 is equal to itself, that is, a+0 = a.

In practical application, addition is widely used in various scenarios. For example, when shopping, we use addition to calculate the total price of goods in the shopping cart. When making tables, we use addition to calculate the sum of a column of data. When calculating wages and bonuses, we also need to use addition.

In addition to basic addition operations, there are some special addition operations, such as carry and borrow of addition. These operations are very useful in calculating large numbers. For example, when we need to add two large numbers, we need to use carry to avoid digital overflow. Similarly, when we need to subtract a larger number from a number less than another addend, we need to use borrowing to avoid the shortage of numbers.

Some special addition formulas and techniques

Such as multiplication and distribution law and rounding method. The law of multiplication and distribution means (a+b) × c = a× c+b× C. Rounding is a common addition technique, which simplifies the calculation by adding some smaller numbers to larger numbers.

In a word, addition is one of the most important operations in mathematics, which is not only widely used in daily life, but also the basis of other mathematical operations. By learning and mastering the basic concepts, properties, operation methods and skills of addition, we can better understand and apply mathematics and solve various problems.