Understanding Algebra Flashcards

Algebra Fundamentals

• Algebra utilizes symbols (usually letters like x, y, z) to denote unknown numbers, forming a foundational aspect of mathematics.

Expressions and Equations

• An expression is a mathematical phrase comprising numbers, operations (e.g., +, -), and/or variables.
• An equation is a statement equating two expressions, identifiable by the presence of an equals sign; the solution is the value that satisfies the equation.

Variables and Terms

• A variable represents an unknown quantity, denoted by letters or symbols.
• A term can be a standalone number or the product of a number and a variable; terms are separated by addition symbols within expressions.

Operators and Mathematical Functions

• Operators (e.g., +, -, x, /) dictate the type of calculations to perform in mathematical expressions.
• In word problems, specific terms indicate operations: "sum" for addition, "difference" for subtraction, "product" for multiplication, and "quotient" for division.

Mathematical Properties

• Properties are inherent mathematical rules that facilitate equation solving.
• Key properties include:
  • Identity properties (addition and multiplication)
  • Commutative properties (addition and multiplication)
  • Associative properties (addition and multiplication)
  • Distributive property (over addition and subtraction)

Constants and Coefficients

• A constant is a fixed numerical value within an expression (e.g., the constant in 6x + 4 is 4).
• A coefficient is the number that multiplies a variable (e.g., in 6x + 4, the coefficient of x is 6).

Simplifying Expressions

• Like terms are terms with the same variables raised to identical powers and can be combined to simplify expressions.
• If terms do not share the same variable structure, they cannot be combined (e.g., 4y is not combinable with 3y²).

Order and Evaluation

• Descending order arranges values from high to low, such as from 9 to 1 or Z to A.
• Evaluation involves substituting variables with numbers and simplifying expressions per the order of operations (e.g., evaluate 3y - 6 for y = 8).

Variables in Relationships

• The independent variable is the one substituted into an equation, while the dependent variable is solved for in relation to the independent variable (commonly denoted by y).

Isolating Variables and Operations

• Isolating a variable involves manipulating the equation to have the variable alone on one side to find its value.
• Inverse operations are pairs of operations that reverse the effect of each other, crucial for solving equations.

This quiz provides flashcards that cover essential algebraic terms and concepts. Learn definitions for key terms such as 'algebra', 'expression', and 'equation' to enhance your understanding of algebra. Perfect for students looking to solidify their foundational math knowledge.