Math Properties Flashcards

Reflexive Property

• States that a number is equal to itself, expressed as a = a.

Symmetric Property

• If one quantity is equal to another (a = b), then the second quantity is equal to the first (b = a).

Transitive Property

• Establishes a chain of equality: if a = b and b = c, then it follows that a = c.

Substitution Property

• Allows for replacing one quantity with another equivalent quantity in equations or expressions: if a = b, then a can be substituted for b.

Addition Property of Equality

• Adding the same value to both sides of an equation keeps the equation balanced: if a = b, then a + c = b + c.

Subtraction Property of Equality

• Subtracting the same value from both sides of an equation maintains equality: if a = b, then a - c = b - c.

Multiplication Property of Equality

• Multiplying both sides of an equation by the same quantity preserves equality: if a = b, then ac = bc.

Division Property of Equality

• Dividing both sides of an equation by the same non-zero quantity keeps the equation balanced: if a = b, then a/c = b/c.

Additive Identity

• States that adding zero to any number will not change its value: any number + 0 = that number.

Additive Inverse

• The sum of a number and its opposite equals zero: x + (-x) = 0.

Multiplicative Identity

• States that multiplying any number by one does not change its value: x * 1 = x.

Multiplicative Property of Zero

• Any number multiplied by zero results in zero: a * 0 = 0.

Multiplicative Inverse

• Involves multiplying a number by its reciprocal to form one: if 3/4 = x, then (4/3) * (3/4) = x * (4/3).

Commutative Property

• The order of addition or multiplication does not affect the sum or product: a + b = b + a.

Associative Property

• Changing how numbers are grouped does not change the result in addition or multiplication: (7 + 4) + 8 = 7 + (4 + 8).

Closure Property

• The sum or product of any two real numbers will always yield another real number.

Distributive Property

• Indicates how multiplication distributes over addition: a(b + c) = ab + ac.