Algebra 2 Properties Flashcards

Study Notes

Properties of Algebra

Commutative Property
- For addition: ( a + b = b + a )
- For multiplication: ( a(b) = b(a) )
Associative Property
- For addition: ( a + (b + c) = (a + b) + c )
- For multiplication: ( (ab)c = a(bc) )
Distributive Property
- Multiplies a number by a sum: ( a(b + c) = ab + ac )
Identity Property
- For addition: Adding zero does not change the value: ( a + 0 = a )
- For multiplication: Multiplying by one does not change the value: ( a = 1(a) )
Inverse Property
- Additive inverse: A number plus its negative equals zero: ( a + (-a) = 0 )
- Multiplicative inverse: A number times its reciprocal equals one, ( a(1/a) = 1 ) (where ( a \neq 0 ))
Closure Property
- For addition: The sum of two real numbers is a real number.
- For multiplication: The product of two real numbers is a real number.
Equality Properties
- Reflexive: ( a + b = a + b )
- Symmetric: If ( a = b + c ), then ( b + c = a )
- Transitive: If ( a = b + c ) and ( b + c = d ), then ( a = d )
Equality with Operations
- Addition Property: If ( a = b ), then ( a + c = b + c )
- Multiplication Property: If ( a = b ), then ( ac = bc )
Cancellation Properties
- Addition: If ( a + c = b + c ), then ( a = b )
- Multiplication: If ( ab = ac ), then ( b = c )
- Additive Inverse: ( -(-a) = a )
Special Multiplication Properties
- Multiplying by -1 reverses the sign: ( -1b = -b )
- Multiplying by 0 results in 0: ( 0(a) = 0 )
Properties of Sums and Products
- Opposite of a Sum: ( -(a + b) = -a + (-b) )
- Reciprocals of a Product: ( \frac{1}{ab} = \frac{1}{a} \cdot \frac{1}{b} )
Subtraction and Division Definitions
- Subtraction: ( a - b = a + (-b) )
- Division: ( \frac{a}{b} = a \times \frac{1}{b} )
Substitution Principle
- If ( x = 8 - 5 ), then ( x = 3 )
Product with Opposites
- ( x(-y) = -xy ) demonstrates the product of a number and a negative is negative.

Description

Explore the essential properties of Algebra 2 through flashcards, including the Commutative, Associative, and Distributive properties. Each card provides a definition and an example to enhance your understanding of these fundamental concepts in mathematics.