Advanced Pre-Algebra Unit 2 Vocabulary

Flashcards covering the foundational vocabulary terms from Advanced Pre-Algebra Unit 2, including algebraic properties, expressions, and equation concepts.

Commutative Property (of addition and multiplication)

A property stating that changing the order of the numbers being added or multiplied does not change the result ($a + b = b + a$ and $a \cdot b = b \cdot a$).

Associative Property (of addition and multiplication)

A property stating that changing the grouping of the numbers being added or multiplied does not change the result ($(a + b) + c = a + (b + c)$ and $(a \cdot b) \cdot c = a \cdot (b \cdot c)$).

Additive Identity Property

The property stating that the sum of any number and zero equals that number ($a + 0 = a$).

Additive identity

The number $0$, which leaves any number unchanged when added to it.

Multiplicative Identity Property

The property stating that the product of any number and one equals that number ($a \cdot 1 = a$).

Multiplicative identity

The number $1$, which leaves any number unchanged when multiplied by it.

Equivalent Numerical Expression

Numerical expressions that simplify to the same value.

Equivalent Variable Expression

Variable expressions that have the same value regardless of which value is substituted for the variable(s).

Term

A number, a variable, or the product of numbers and variables that are separated by addition or subtraction signs in an algebraic expression.

Coefficient

The numerical factor placed before and multiplying the variable in an algebraic term.

Constant Term

A term in an expression that has a fixed numerical value and contains no variables.

Like Terms

Terms that have identical variable parts raised to the same exponents.

Unlike Terms

Terms that have different variables or the same variables raised to different powers.

Equation

A mathematical sentence that uses an equals sign ($=$) to show that two expressions are equal.

Solution of an Equation

A value for the variable that makes the equation a true statement when substituted.

Inverse Operations

Operations that reverse or undo the effect of each other, such as addition and subtraction, or multiplication and division.

Additive Inverse

The opposite of a number that, when added to the original number, results in zero ($a + (-a) = 0$).

Multiplicative Inverse

The reciprocal of a nonzero number that, when multiplied by the original number, results in one ($a \cdot \frac{1}{a} = 1$ for $a \neq 0$).