Quotient - Definition and Overview

In mathematics, a quotient is the end result of a division problem. For example, in the problem 6 ÷ 3, the quotient would be 2, while 6 would be called the dividend, and 3 the divisor.

A quotient can also mean just the integral part of the result of dividing two integers. For example, the quotient of 13 ÷ 5 would be 2 while the remainder would be 3. For more, see the division algorithm.

In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structures whose elements are the equivalence classes of some equivalence relation on another set, space, or algebraic structure. See:

• quotient set
• quotient group
• quotient ring
• quotient space (linear algebra)
• quotient space
• quotient object
• right quotient and left quotient (operations on formal languages)

Quotients also come up in certain tests, like the IQ test, which stands for Intelligence Quotient. In this case, your quotient is basically your score.