Algebra Foundations Vocabulary

Algebra Foundations Vocabulary

• Absolute Value: Represents the distance of a number from zero on the number line, regardless of direction.

• Additive Identity: The number zero; adding it to any real number does not change the value of that number.

• Additive Inverse: The inverse of a number that results in zero when added; for example, the additive inverse of 5 is -5.

• Algebraic Expression: A combination of numbers, variables, and arithmetic operations, but does not have an equality sign.

• Associative Property: States that the way numbers are grouped in addition or multiplication does not affect the outcome, e.g., (a + b) + c = a + (b + c).

• Base: In an exponential expression, the base is the number that gets multiplied by itself.

• Coefficient: A constant factor that multiplies a variable in a term; for instance, in 3x, 3 is the coefficient.

• Commutative Property: Indicates that the order of addition or multiplication does not alter the result, e.g., a + b = b + a.

• Constant: A specific numeric value that does not change; can be a standalone term without variables.

• Distributive Property: Shows how to multiply a single term by terms in parentheses, expressed as a(b + c) = ab + ac.

• Evaluate: The process of calculating the numerical value of an expression.

• Exponent: The superscript indicating how many times the base is multiplied by itself; for example, in x^3, 3 is the exponent.

• Expression: A mathematical phrase composed of numbers, variables, and operators, but lacking an equality statement.

• Integer: Any whole number, including negatives, zero, and positive numbers, forming a complete set: {..., -3, -2, -1, 0, 1, 2, 3, ...}.

• Irrational Number: A number that cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal (e.g., π or √2).

• Like Terms: Terms that share the same variables raised to identical powers; they can be combined in algebraic expressions.

• Multiplicative Inverse: The reciprocal of a number; for any number x, the multiplicative inverse is 1/x, and their product equals one (1).

• Natural Number: Positive integers beginning from one onward, used primarily for counting: 1, 2, 3, ...

• Rational Number: Any number that can be expressed as a fraction, where both numerator and denominator are integers, and the denominator is not zero.

• Substitution: The process of replacing a variable with its equivalent value in an equation or expression.

• Term: The individual components of an expression that can be a number, a variable, or a product of both.

• Whole Number: A number in the set that includes zero and all natural numbers, defined as non-negative integers.