Division undoes multiplication. If 4 × 3 = 12, then 12 ÷ 4 = 3. The operation splits a quantity into equal groups or finds how many times one number fits into another. The result is the quotient; the number being divided is the dividend; the number dividing is the divisor.

Division is not always exact. 7 ÷ 2 leaves a remainder of 1, or gives 3.5 in decimal. Division by zero is undefined in standard arithmetic because no number times zero gives a nonzero result. That restriction appears throughout algebra and calculus.

Long division, synthetic division, and polynomial division are methods for handling more complex cases. In everyday life, division splits bills, calculates unit prices, and converts units. In mathematics, it extends to fractions, rational numbers, and algebraic expressions. The operation is simple to state but rich in consequences.

• Inverse of multiplication
• Result is the quotient
• Division by zero is undefined
• Extends to fractions and polynomials