Algebra 1 Properties Flashcards

Questions and Answers

What is the definition of Additive Identity?

a * 1 = a

a + (-a) = 0

a / b * b / a = 1

a + 0 = a (correct)

What is the concept of Additive Inverse?

a + (-a) = 0

Which property states that a * 1 = a?

Reflexive Property

Multiplicative Identity (correct)

Additive Inverse

Commutative Property of Addition

Define the Multiplicative Inverse.

a/b * b/a = 1 Signup and view all the answers

What does the Multiplicative Property of Zero state?

a * 0 = 0 Signup and view all the answers

The Reflexive Property states that a quantity can be greater than itself.

False Signup and view all the answers

Describe the Symmetric Property.

if a = b, then b = a Signup and view all the answers

What is the Transitive Property?

if a = b and b = c then a = c Signup and view all the answers

Explain the Substitution Property.

If a = b then a may be replaced by b in any expression. Signup and view all the answers

Which property shows that a + b = b + a?

Commutative Property of Addition Signup and view all the answers

What is the Commutative Property of Multiplication?

a * b = b * a Signup and view all the answers

What does the Associative Property of Addition express?

(a + b) + c = a + (b + c) Signup and view all the answers

Explain the Associative Property of Multiplication.

(a * b) * c = a * (b * c) Signup and view all the answers

What is the Distributive Property?

a * (b + c) = a * b + a * c and a * (b - c) = a * b - a * c Signup and view all the answers

Study Notes

Additive Properties

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 Properties

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).

Properties of Equality

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 Properties

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 Properties

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)).

Distributive Property

Distributive Property: Multiplication distributes over addition and subtraction (a × (b + c) = a × b + a × c and a × (b - c) = a × b - a × c).

Description

Test your understanding of key algebraic properties with these flashcards. Learn the definitions of additive and multiplicative identities and inverses that are fundamental to Algebra. Perfect for students looking to reinforce their knowledge in Algebra 1.