In the four calculations, subtraction is the inverse of addition and division is the inverse of multiplication.
Why not use "0" as divisor?
We all know that "0" is meaningless as a divisor. We can explain it in two cases. In one case, when the divisor is "0" and the dividend is not "0", such as 7 ÷ 0, 12 ÷ 0, etc. That is to ask that the product multiplied by "0" is not equal to the "quotient" of "0". Multiply 0= 7，0 ×？= 12。 Because the product of any number multiplied by "0" is "0", in this case, the quotient does not exist and the division calculation has no result.
Another situation is: when the divisor is "0", and the divisor is also "0", such as 0 ÷ 0. That is to ask for the quotient whose product multiplied by "0" is equal to "0", 0 ×？= 0 Because the product of any number multiplied by "0" is "0", in this case, a definite quotient cannot be obtained. The quotient can be any number, that is, there are infinite numbers of quotients.
We know that the result of a specified operation must exist and should be unique. However, when the divisor is "0", the divisor is not "0", and the quotient does not exist; When the divisor is "0", the divisor is also "0", and the quotient cannot get a definite number. Therefore, it must be clearly stipulated that "0" cannot be divisor. Because with the provision that "0" cannot be divisor, in the basic nature of division, the divisor and the divisor are multiplied by or divided by the same number at the same time (except zero), and the quotient remains unchanged. In the basic nature of fraction, the numerator and denominator of a fraction are multiplied by or divided by the same number (except zero), and the size of the fraction remains the same. In the basic nature of ratio, the preceding and subsequent terms of ratio are multiplied by or divided by the same number at the same time (except zero), and the ratio remains unchanged. The three words "except zero" cannot be lost in the complete expression of the basic properties of division, fraction and ratio.
This shows that in division, "0" cannot be divisor; For scores, the denominator cannot be "0"; For the ratio, the latter term of the ratio cannot be "0". Of course, it should be emphasized that the divisor in division, the denominator in fraction and the last term of ratio are not the same thing. Although there are some connections between "ratio", "fraction" and "division", they are three different concepts after all. "Ratio" refers to the multiple relationship between two numbers (or quantities), "fraction" is a number, and "division" is an operation.
In short, the rule that "0" cannot be divisor is well founded and very important. I hope you can correctly apply it on the basis of understanding.