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Algebra Connections Glossary
absolute value   
  The absolute value of a number is the distance of the number from zero.  Since the absolute value represents a distance, without regard to direction, it is always non-negative.  Thus the absolute value of a negative number is its opposite, while the absolute value of a non-negative number is just the number itself.  The absolute value of x is usually written “| x |”.  For example, | −5 | = 5 and
| 22 | = 22.
Additive Identity Property   
  The Additive Identity Property states that adding zero to any expression leaves the expression unchanged.  That is, a + 0 = a.  For example, −2xy² + 0 = −2xy². 
Additive Inverse Property   
  The Additive Inverse Property states that for every number a there is a number −a such that a + (−a) = 0.  For example, the number 5 has an additive inverse of −5; 5 + (−5) = 0.  The additive inverse of a number is often called its opposite.  For example, 5 and −5 are opposites.
Additive Property of Equality   
  The Additive Property of Equality states that equality is maintained if the same amount is added to both sides of an equation.  That is, if a = b, then a + c = b + c.  For example, if y = 3x, then y + 1.5 = 3x + 1.5.  
algebra tiles   
  An algebra tile is a manipulative whose area represents a constant or variable quantity.  The algebra tiles used in this course consist of large squares with dimensions x-by-x and y-by-y; rectangles with dimensions x-by-1, y-by-1, and x-by-y; and small squares with dimensions 1-by-1.  These tiles are named by their areas: x², y², x, y, xy, and 1, respectively.  The smallest squares are called “unit tiles.”  In this text, shaded tiles will represent positive quantities while unshaded tiles will represent negative quantities.

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area   
 

For this course, area is the number of square units needed to fill up a region on a flat surface.  In later courses, the idea will be extended to cones, spheres, and more complex surfaces.

Associative Property of Addition   
  The Associative Property of Addition states that if a sum contains terms that are grouped, the sum can be grouped differently with no effect on the total.  That is, a + (b + c) = (a + b) + c.  For example, 3 + (4 + 5) = (3 + 4) + 5.
Associative Property of Multiplication   
  The Associative Property of Multiplication states that if a product contains terms that are grouped, the product can be grouped differently with no effect on the result.  That is, a(bc) = (ab)c.  For example, 2 · (3 · 4) = (2 · 3) · 4.
asymptote   
  A line that a graph of a curve approaches as closely as you wish.  An asymptote is often represented by a dashed line on a graph.  For example, the graph below has an asymptote at y = −3.

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average   
  See “mean.”
axes   
  In a coordinate plane, two number lines that meet at right angles at the origin (0, 0).  The x-axis runs horizontally and the y-axis runs vertically.  See the example below.

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