Untitled Quiz

Number Sets

• Natural Numbers: Used for counting; includes positive integers (1, 2, 3, …).
• Whole Numbers: Comprise all natural numbers plus zero (0, 1, 2, 3, …).
• Integers: Include whole numbers and their negative counterparts (…, -2, -1, 0, 1, 2, …).
• Rational Numbers: Can be expressed as fractions or quotients of integers with a non-zero denominator; represented as either terminating or repeating decimals.
• Irrational Numbers: Cannot be expressed as fractions; their decimal forms neither terminate nor repeat.

Inverses and Properties

• Additive Inverse: For any number 'a', its inverse is '-a' such that a + (-a) = 0.
• Multiplicative Inverse: For any non-zero number 'a', its inverse is 1/a; multiplying a number by its reciprocal yields 1.

Commutative and Associative Properties

• Commutative Property of Addition: Order of addition does not affect the sum (a + b = b + a).
• Commutative Property of Multiplication: Order of multiplication does not affect the product (ab = ba).
• Associative Property of Addition: Grouping in addition does not change the sum ((a + b) + c = a + (b + c)).
• Associative Property of Multiplication: Grouping in multiplication does not change the product ((ab)c = a(bc)).

Identity and Inverse Properties

• Identity Property of Addition: Adding zero does not change a number (a + 0 = a).
• Identity Property of Multiplication: Multiplying by one does not change a number (a × 1 = a).
• Inverse Property of Multiplication: A number multiplied by its reciprocal equals one (a × (1/a) = 1, where a ≠ 0).

Other Important Properties

• Distributive Property: Multiplying a number by a sum equals the sum of the products (a(b + c) = ab + ac).
• Absolute Value: Represented as |x|, it denotes the distance from zero on the number line, always non-negative.

Algebraic Concepts

• Variable: A symbol representing an unknown value, typically a letter (e.g., x, y).
• Algebraic Expression: Consists of numbers, variables, and operations; does not have an equals sign.
• Term: A single mathematical expression such as a number, variable, or the product of numbers and variables.
• Coefficient: The numerical factor in a term (e.g., in 3x, 3 is the coefficient).
• Evaluate: The process of substituting values for variables in an expression and following order of operations.

Equation and Properties of Equality

• Solution of the Equation: A number that satisfies the equation, making it true.
• Reflexive Property: Any quantity is equal to itself (a = a).
• Symmetric Property: If one quantity equals another, then vice versa (if a = b, then b = a).
• Transitive Property: If two quantities are equal to the same quantity, they are equal to each other (if a = b and b = c, then a = c).

Additional Properties

• Addition Property: If two quantities are equal, adding the same value to both maintains equality (if a = b, then a + c = b + c).
• Subtraction Property: If a = b, then subtracting the same value from both maintains equality (if a = b, then a - c = b - c).
• Multiplication Property: If a = b, then multiplying both by the same value maintains equality (if a = b, then ac = bc).
• Division Property: If a = b and c ≠ 0, dividing both by c maintains equality (if a = b, then a/c = b/c).
• Substitution Property: If a = b, b can replace a in any expression to yield an equivalent expression.

Complex Concepts

• Compound Inequality: Two inequalities connected by "and" or "or".
• Extraneous Solution: A solution obtained from an original equation that does not satisfy the original equation.