The remainder is the number left when the dividend is not divisible. In mathematics, division is a basic mathematical operation, including two main concepts, namely dividend and divisor. The dividend is a number to be divided by another number, and the divisor is a number divided by the dividend. In division, the quotient obtained by dividing the dividend by the divisor is not necessarily an integer, that is, the dividend cannot be divisible by the dividend.
The meaning of the remainder can be explained from two aspects. On the one hand, the remainder can represent the number left by dividing the dividend by the divisor in division, which is a part of the division result. On the other hand, the remainder can also represent the remainder obtained by dividing one number by another, that is, an indivisible number.
In real life, residues are widely used. For example, when we encode numbers, we often use the remainder of the module to block encryption; In number theory, remainder is a very important concept, which is closely related to the concepts of divisibility and congruence, and plays a very important role in solving some mathematical problems.
The relationship between divisor, dividend and quotient;
1. Divider = quotient If 24÷8=3, where 24 is the dividend, the formula is Divider = quotient.
Knowing two numbers A and b(b≠0), it is required to divide a number Q so that the product of Q and B is equal to A. This operation is called division, which is recorded as a÷b=q or A: B = Q, which is read as A divided by B equals Q, or A equals Q greater than B, A is called dividend, B is called divisor, and A: B = Q is called A and.
For any number a, there is always a÷ 1=a, a÷a= 1, 0÷a=0, but zero cannot be divided.
Second, the division formula
1. Failed dividend ÷ Divider = quotient dividend ÷ quotient = divisor × quotient+remainder = dividend.
Divider = (dividend-remainder) ÷ quotient = (dividend-remainder) ÷ divisor
2. The dividend is enlarged (reduced) by n times, and the quotient is correspondingly enlarged (reduced) by n times.
3. The divisor is expanded (reduced) by n times, and the quotient is correspondingly reduced (expanded) by n times.