[[Multiply|Multiplication]] is a mathematical operator that combines two numbers, called multiplicands, to produce a third number, called the product. It is denoted by the symbol "×" or "*", and can be thought of as repeated addition. The relationship between multiplication and addition is that multiplication can be seen as a shortcut for adding a number multiple times. For example, 3 × 4 can be understood as adding 3 four times: 3 + 3 + 3 + 3 = 12. Multiplication also has a relationship with the [[Division|quotient]] operator, which is used to find the result of division. The quotient is the number obtained when one number (the dividend) is divided by another (the divisor). Multiplication and division are inverse operations of each other. If we have a × b = c, then c ÷ b = a and c ÷ a = b. In relation to addition, multiplication exhibits symmetric properties when using the same set of numbers. This means that changing the order of the multiplicands does not affect the product. For example, 2 × 5 = 5 × 2 = 10. This property holds true for all real numbers. On the other hand, subtraction and division are considered antisymmetric operators because changing the order of operands does affect the result. For example, 7 - 2 ≠ 2 - 7 and 14 ÷ 2 ≠ 2 ÷ 14. Subtraction and division do not possess this symmetry property like addition and multiplication do. So in summary, multiplication is an operator that combines two numbers to produce their product. It relates to addition as a shortcut for repeated addition and has an inverse relationship with division. Multiplication exhibits symmetric properties in relation to adders but differs from antisymmetric operators like subtraction and division where changing operand order affects results.