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2. Commutative property - Wikipedia

   en.wikipedia.org/wiki/Commutative_property

   The Egyptians used the commutative property of multiplication to simplify computing products. [7] [8] Euclid is known to have assumed the commutative property of multiplication in his book Elements. [9] Formal uses of the commutative property arose in the late 18th and early 19th centuries, when mathematicians began to work on a theory of ...

3. Distributive property - Wikipedia

   en.wikipedia.org/wiki/Distributive_property

   Therefore, one would say that multiplication distributes over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields.

4. Field (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Field_(mathematics)

   In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra , number theory , and many other areas of mathematics.

5. Order of operations - Wikipedia

   en.wikipedia.org/wiki/Order_of_operations

   Sometimes multiplication and division are given equal precedence, or sometimes multiplication is given higher precedence than division; see § Mixed division and multiplication below. If each subtraction is replaced with addition of the opposite (additive inverse), then the associative and commutative laws of addition allow terms to be added in ...

6. Addition - Wikipedia

   en.wikipedia.org/wiki/Addition

   The fact that addition is commutative is known as the "commutative law of addition" or "commutative property of addition". Some other binary operations are commutative, such as multiplication, but many others, such as subtraction and division, are not.

7. Ring (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Ring_(mathematics)

   In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. Informally, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers.