Algebra 1 Properties Flashcards

Study Notes

Additive Identity: Adding zero to any number does not change the value (a + 0 = a).
Additive Inverse: The sum of a number and its negative is zero (a + (-a) = 0).

Multiplicative Identity: Multiplying any number by one leaves the number unchanged (a × 1 = a).
Multiplicative Inverse: The product of a number and its reciprocal equals one (a/b × b/a = 1), given b ≠ 0.
Multiplicative Property of Zero: Any number multiplied by zero equals zero (a × 0 = 0).

Reflexive Property: Any number is equal to itself (a = a).
Symmetric Property: If one number equals another, then the second number equals the first (if a = b, then b = a).
Transitive Property: If one number equals a second, and that second equals a third, then the first equals the third (if a = b and b = c, then a = c).
Substitution Property: If two quantities are equal, one can be replaced with the other in any expression (if a = b, a can be replaced by b).

Commutative Property of Addition: The order of addition does not affect the sum (a + b = b + a).
Commutative Property of Multiplication: The order of multiplication does not affect the product (a × b = b × a).

Associative Property of Addition: Rearranging the grouping of numbers in addition does not affect the sum ((a + b) + c = a + (b + c)).
Associative Property of Multiplication: Rearranging the grouping of numbers in multiplication does not affect the product ((a × b) × c = a × (b × c)).