Exploring Algebraic Properties of Rational Expressions

The video tutorial covers various algebraic properties used to justify steps in solving equations. It begins with basic properties like addition, subtraction, multiplication, and division properties of equality. It then introduces advanced properties such as reflexive, symmetric, and transitive properties. The tutorial also explains identity and inverse properties, followed by associative and commutative properties. Finally, it demonstrates how to apply these properties in algebraic proofs, providing step-by-step examples.

What property is used when you add the same value to both sides of an equation?

• Addition Property of Equality

• Division Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

Which property allows you to rewrite subtraction as adding a negative?

• Subtraction Property of Equality

• Addition Property of Equality

• Reflexive Property of Equality

• Distributive Property of Multiplication over Addition

What does the reflexive property of equality state?

• A value can be distributed across terms in parentheses

• If two quantities are equal to a third, they are equal to each other

• Two equal quantities remain equal if their order is changed

• A value is equal to itself

Which property states that if a = b and b = c, then a = c?

• Reflexive Property of Equality

• Transitive Property of Equality

• Symmetric Property of Equality

• Distributive Property of Multiplication over Addition

What is the additive identity?

• Any number

• 0

• Its reciprocal

• 1

What is the multiplicative identity?

• 0

• Its reciprocal

• 1

• Any number

What is the inverse of 7 in addition?

• 0

• -7

• 1/7

• 7

Which property allows you to change the grouping of numbers being added without changing the result?

• Identity Property of Addition

• Commutative Property of Addition

• Associative Property of Addition

• Distributive Property of Multiplication over Addition

What does the commutative property of multiplication state?

• Multiplying by 0 does not change the number

• Changing the order of multiplication does not change the product

• Changing the grouping of multiplication does not change the product

• Multiplying by 1 does not change the number

What is the first step in an algebraic proof?

• Write the original equation

• Add a number to both sides

• Combine like terms

• Distribute a value