Real Numbers and Basic Algebra Terms

Real Numbers

• Real numbers encompass all numbers on the number line, including positive and negative integers, rational numbers, and irrational numbers like π.
• Zero signifies no quantity and is the additive identity, meaning it does not alter the value of other numbers when added.

Basic Terminology in Mathematics

• Algebra: The field of mathematics focused on variables and their relationships.
• Base: The bottom part of geometric figures in both plane and solid geometry.
• Brackets: Denoted by [ and ], used to group or enclose elements.
• Circumference: The total distance around a circle, forming a complete circular arc.
• Coordinate Plane: A two-dimensional space defined by a horizontal (x-axis) and vertical axis (y-axis).
• Compute: To evaluate or calculate a numerical expression.
• Constant: A fixed value in mathematics; does not change over time.
• Curly Brackets: Represented by { and }, used to group related items.
• Denominator: The bottom component of a fraction, indicating how many parts the whole is divided into.
• Diameter of a Circle: The straight line segment passing through the center and connecting two points on the circle.
• Diagonal of a Polygon: A line segment that connects non-adjacent vertices within a polygon.
• Equation: A mathematical statement asserting the equality of two expressions, marked by an equals sign (=).
• Evaluate: The process of computing the value of an expression.
• Expression: A combination of numbers, symbols, and operators representing a value.
• Formula: A mathematical relation or rule expressed in symbols.
• Fraction: Represents a ratio of two numbers or variables.
• Height (Altitude): The shortest distance from the base of a geometric figure to its highest point.
• Horizontal: Represents a perfectly flat and level line.
• Improper Fraction: A fraction where the numerator is larger than the denominator, such as 5/3.
• Inequality: A mathematical expression displaying a relationship of less than, greater than, or equal to.
• Mixed Fraction: A whole number combined with a proper fraction.
• Numerator: The top part of a fraction, representing how many parts are being considered.
• Origin: The point of intersection (0, 0) on a coordinate plane.
• Parentheses: Symbols ( and ) used to indicate that operations within them should be performed first.
• Perimeter: The total length around a two-dimensional shape, calculated by summing the lengths of its sides.
• Polygon: A closed plane figure with sides made of line segments, named by the number of sides.
• Proper Fraction: A fraction with a numerator smaller than its denominator.
• Radius: A segment connecting the center of a circle to a point on its circumference, also representing its length.
• Rectangle: A quadrilateral with four right angles (90°) and opposite sides equal.
• Reduce a Fraction: Simplifying a fraction by eliminating common factors in the numerator and denominator.
• Side of a Polygon: Each line segment forming the polygon.
• Square: A specific type of rectangle with all sides equal in length.
• Triple: To multiply a value by three.
• Variable: A symbol representing an unknown or changing quantity.
• Vertex: The point where two or more lines meet; important in polygons and systems of equations.
• Solve: To determine all possible solutions for an equation or system of equations/inequalities.
• System of Equations: Multiple equations that share common variables.
• System of Inequalities: Multiple inequalities that share common variables.

Prime Numbers and Factors

• Greatest Common Factor (GCF): The largest integer that can evenly divide each member of a set of numbers.
• Least Common Multiple (LCM): The smallest positive integer divisible by two or more integers.
• Prime Factorization: Expressing an integer as a product of its prime numbers.
• Relatively Prime: Two numbers with a GCF of 1, meaning they have no common factors other than 1.

Radicals and Roots

• Cube Root: A value that, when multiplied by itself three times, equals a given number, denoted as ∛x.
• Radical Symbol: The symbol √ used to indicate square and nth roots.
• Radicand: The number under the radical sign.
• Root of a Number: Refers to both square roots and nth roots.
• Square Root: A nonnegative number that when multiplied by itself results in a given number, indicated as √x. For example, √9 = 3.

Basic Geometry

• Acute Angle: An angle measuring less than 90°.
• Adjacent Angles: Two angles sharing a vertex and a side, but do not overlap.
• Alternate Interior Angles: Angles located between two parallel lines and on opposite sides of a transversal.