associative

(adjective)

Referring to a mathematical operation that yields the same result regardless of the grouping of the elements.

Related Terms

  • Dijfe
  • identity element
  • Distributive
  • difference
  • sum
  • quotient
  • product
  • commutative
  • rational number

Examples of associative in the following topics:

  • Basic Operations

    • The associative property describes equations in which the grouping of the numbers involved does not affect the result.
    • As with the commutative property, addition and multiplication are associative operations:
  • Parts of a Hyperbola

    • We will use the x-axis hyperbola to demonstrate how to determine the features of a hyperbola, so that $a$ is associated with x-coordinates and $b$ is associated with y-coordinates.
    • For a y-axis hyperbola, the associations are reversed.
  • Eccentricity

    • The eccentricity, denoted $e$, is a parameter associated with every conic section.
    • Recall that hyperbolas and noncircular ellipses have two foci and two associated directrices, while parabolas have one focus and one directrix.
  • Parts of an Ellipse

    • We will use the horizontal case to demonstrate how to determine the properties of an ellipse from its equation, so that $a$ is associated with x-coordinates, and $b$ with y-coordinates.
    • For a vertical ellipse, the association is reversed.
  • Multiplying Polynomials

    • Multiplying a polynomial by a monomial is a direct application of the distributive and associative properties.
    • for all real numbers $a,b$ and $c.$ The associative property says that
  • Addition and Subtraction; Scalar Multiplication

    • Matrix addition is commutative and is also associative, so the following is true:
  • Functions and Their Notation

    • In other words, each number you put in is associated with each number you get out.
    • In a function every input number is associated with exactly one output number In a relation an input number may be associated with multiple or no output numbers.
  • Determinants of 2-by-2 Square Matrices

    • In linear algebra, the determinant is a value associated with a square matrix.
  • Secant and the Trigonometric Cofunctions

    • Recall that for any point on the circle, the $x$-value gives $\cos t$ for the associated angle $t$.
    • Applying the $x$- and $y$-coordinates associated with angle $t$, we have
  • Introduction to Complex Numbers

    • Thus, for example, complex number $-2+3i$ would be associated with the point $(-2,3)$ and would be plotted in the complex plane as shown below.
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