Definition

Division means sharing a number equally into groups, or finding out how many times one number fits into another, written with the division sign (/ or the division symbol). Division of $a$ by $b$ ($b \neq 0$) gives a quotient $q$ (and remainder $r$ for integers) such that $a = b \times q + r$ with $0 \le r < b$; for real numbers, $a / b = a \times (1/b)$, and division by zero is undefined. In a field $F$, division is defined as multiplication by the multiplicative inverse, $a / b = a \cdot b^{-1}$ for $b \neq 0$: fields are precisely the rings where every non-zero element has a multiplicative inverse, which is why $\mathbb{Z}$ is a ring but not a field (since $1/2$ is not an integer), while $\mathbb{Q}$, $\mathbb{R}$, and $\mathbb{C}$ are fields.