One, zero as dividend.

In the division formula, the dividend is the first number we should consider. If the dividend is 0, the whole division process will be impossible. Because any number divided by 0 is undefined, which means we can't get an exact answer. Therefore, 0 cannot be used as a dividend.

Two, 0 as divisor

Divider plays the role of denominator in the division formula, which determines how many parts we divide the dividend into. If the divisor is 0, it means that we can't divide the dividend into any parts, so the whole division formula is meaningless. So you can't divide by 0.

3.0 As a quotient

Quotient is the result of division, indicating the size of each part. If the quotient is zero, it means that our result is zero, which means that every share we get is zero. However, if the divisor is also 0, then the quotient cannot be defined, because it is meaningless to divide any number by 0. Therefore, 0 cannot be used as a quotient.

Fourth, the remainder is 0

The remainder is the remainder of the dividend that is not completely divided in the divisor process. If the remainder is 0, it means that the dividend is completely divided into several parts, each with the same size. However, if the divisor is 0, then the remainder cannot be defined, because it is meaningless to divide any number by 0. Therefore, 0 cannot be used as a remainder.

Similarities and differences between the nature of 0 in division formula and other mathematical operations

1. In division, 0 cannot be used as a divisor.

In other words, any number divided by 0 is undefined. This is because it is impossible to get 0 in any number of equal parts. This property is not common in other mathematical operations. For example, in addition, subtraction and multiplication, 0 can be used as an operand, and the results are all defined.

Second, the position of the same 0 in all mathematical operations is special.

Although you can't divide by 0 in division, in other mathematical operations, 0 is a "neutral element", that is, any number added, subtracted, multiplied or divided with 0 will get the original number. For example, 5+0 = 5, 0 × 5 = 0. This property makes 0 an important part of mathematical system.

Third, the difference

In division, the result of dividing two numbers is a number, while in other mathematical operations, such as addition, subtraction and multiplication, the result is one or more numbers (such as multiplication). This property makes division have a unique position in mathematics.

Fourth, the same.

In all mathematical operations, 0 has the function of "returning to zero". For example, in addition, if several numbers are added, there will be several zeros in the single digits of the result that are the same as these numbers; In subtraction, if one number is subtracted from another number several times, there will be several zeros in the single digit of the result.

In multiplication, if the single digit of two factors has several zeros, then the single digit of the result will also have several zeros; In division, if the dividend is the product of several numbers (excluding 0) and the divisor is the sum of these numbers (which can be 0), then there will be several zeros in the single digit of the quotient.