In mathematics, the remainder is the amount “left over” after performing some computation. In algebra, the remainder is the polynomial “left over” after dividing one polynomial by another. The modulo operation is the precalculus ron larson pdf that produces such a remainder when given a dividend and divisor.

Formally it is also true that a remainder is what is left after subtracting one number from another, although this is more precisely called the difference. Give me two dollars back and keep the rest. The number q is called the quotient, while r is called the remainder.

See Euclidean division for a proof of this result and division algorithm for algorithms describing how to calculate the remainder. The remainder, as defined above, is called the least positive remainder or simply the remainder.

In this case, s is called the least absolute remainder. A unique remainder can be obtained in this case by some convention such as always taking the positive value of s.