Algebra Vocabulary Flashcards

Algebra Fundamentals

• Opposites: Two numbers with different signs, possessing equal absolute values.
• Whole Numbers: Include 0 and all positive integers (0, 1, 2, 3...).
• Natural Numbers: Positive integers also referred to as counting numbers (1, 2, 3...).

Algebraic Expressions

• Expression: A combination of numbers and variables involving addition, subtraction, multiplication, and division.
• Term: A single mathematical component, like a number, variable, or a product of both.
• Coefficient: The numerical factor associated with a term in an expression.

Equations and Solutions

• Solution: A specific value assigned to a variable that satisfies an equation.
• Equation: A mathematical statement asserting that two expressions are equal.

Values and Operations

• Constant: A symbol representing a fixed number, unchanging within the context of an equation.
• Variable: A letter symbolizing one or more numerical values.

Properties and Processes

• Order of Operations: A mnemonic ("Please Excuse My Dear Aunt Sally") indicating the sequence to solve mathematical expressions.
• Distributive Property: The rule stating a(b + c) = ab + ac, which facilitates multiplication over addition.
• Simplifying: The process of eliminating grouping symbols and combining like terms to simplify an expression.

Numbers and Their Types

• Integers: All positive and negative whole numbers, including zero (..., -3, -2, -1, 0, 1, 2, 3, ...).
• Rational Numbers: Numbers expressible as a fraction of integers.
• Irrational Numbers: Cannot be represented as fractions; non-repeating, non-terminating decimals.
• Real Numbers: The complete set encompassing both rational and irrational numbers.

Functionality

• Absolute Value: Represents the distance of a number from zero on a number line, regardless of direction.
• Radicand: The value located inside a radical sign in square roots and higher roots.
• Square Root: The value that, when multiplied by itself, yields the original number.

Operations and Their Results

• Difference: The result from the operation of subtraction.
• Product: The result obtained from multiplication.
• Quotient: The outcome of division.
• Multiplicative Inverse: Two numbers whose multiplication yields one; also known as reciprocals.

Exponents

• Base: The repeated factor in exponential expressions.
• Exponent: Indicates how many times a base is multiplied by itself.

Term Relationships

• Like Terms: Terms that share the same variable raised to the same exponent, making them combinable in expressions.