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  2. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    These are the three main logarithm laws/rules/principles, [3] from which the other properties listed above can be proven. Each of these logarithm properties correspond to their respective exponent law, and their derivations/proofs will hinge on those facts. There are multiple ways to derive/prove each logarithm law – this is just one possible ...

  3. 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 ...

  4. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    In approximate arithmetic, such as floating-point arithmetic, the distributive property of multiplication (and division) over addition may fail because of the limitations of arithmetic precision. For example, the identity 1 / 3 + 1 / 3 + 1 / 3 = ( 1 + 1 + 1 ) / 3 {\displaystyle 1/3+1/3+1/3=(1+1+1)/3} fails in decimal arithmetic , regardless of ...

  5. Division (mathematics) - Wikipedia

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

    In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...

  6. Algebraic structure - Wikipedia

    en.wikipedia.org/wiki/Algebraic_structure

    Addition and multiplication are prototypical examples of operations that combine two elements of a set to produce a third element of the same set. These operations obey several algebraic laws. For example, a + (b + c) = (a + b) + c and a(bc) = (ab)c are associative laws, and a + b = b + a and ab = ba are commutative laws. Many systems studied ...

  7. Elementary arithmetic - Wikipedia

    en.wikipedia.org/wiki/Elementary_arithmetic

    Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction , broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools.

  8. Cancellation property - Wikipedia

    en.wikipedia.org/wiki/Cancellation_property

    Although the cancellation law holds for addition, subtraction, multiplication and division of real and complex numbers (with the single exception of multiplication by zero and division of zero by another number), there are a number of algebraic structures where the cancellation law is not valid.

  9. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Multiplication (often denoted by the cross symbol ×, by the mid-line dot operator ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

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