# divided by

In mathematics, especially in elementary arithmetic, division (÷) is an arithmetic operation. Specifically, if b times c equals a, written: a = b × c where b is not zero, then a divided by b equals c, written: a ÷ b = c For instance, 6 ÷ 3 = 2 since 3 × 2 = 6 In the expression a ÷ b = c, a is called the dividend or numerator, b the divisor or denominator and the result c is called the quotient. Conceptually, division of integers can be viewed in either of two distinct but related ways quotition and partition: Partitioning involves taking a set of size a and forming b groups that are equal in size. The size of each group formed, c, is the quotient of a and b. Quotition, or quotative division (also sometimes spelled quotitive) involves taking a set of size a and forming groups of size b. The number of groups of this size that can be formed, c, is the quotient of a and b. (Both divisions give the same result because multiplication is commutative.) Teaching division usually leads to the concept of fractions being introduced to school pupils. Unlike addition, subtraction, and multiplication, the set of all integers is not closed under division. Dividing two integers may result in a remainder. To complete the division of the remainder, the number system is extended to include fractions or rational numbers as they are more generally called.