Division (mathematics)

Division (mathematics)

In mathematics, especially in elementary arithmetic, division (÷) is an arithmetic operation. Specifically, if b times c equals a, written:

where b is not zero, then a divided by b equals c, written:

a ÷ b = c

For instance,

6 ÷ 3 = 2

since

6 = 3 × 2

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 describes two distinct but related settings. 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. Quotative division involves taking a set of size a and forming groups of size c. The number of groups of this size that can be formed, b, is the quotient of a and c.

Teaching division usually leads to the concept of fractions being introduced to students. 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.