Questions and Answers
What does the Addition Property of Equality state?
What is the Additive Inverse Property?
Opposites add to be zero.
What does the Additive Identity Property state?
The sum of any number and zero is that number.
What does the Multiplication Property of Equality say?
Signup and view all the answers
What is the Multiplicative Inverse Property?
Signup and view all the answers
What does the Multiplicative Identity Property indicate?
Signup and view all the answers
What are solutions in the context of equations?
Signup and view all the answers
What are equivalent equations?
Signup and view all the answers
What does it mean to isolate the variable?
Signup and view all the answers
What are opposites in mathematics?
Signup and view all the answers
What does the Commutative Property for Addition state?
Signup and view all the answers
What is the Commutative Property for Multiplication?
Signup and view all the answers
What does the Associative Property for Addition imply?
Signup and view all the answers
What does the Associative Property for Multiplication indicate?
Signup and view all the answers
What is unit conversion?
Signup and view all the answers
What are equivalent expressions?
Signup and view all the answers
What does the Distributive Property state?
Signup and view all the answers
What are terms in an expression?
Signup and view all the answers
What is a coefficient?
Signup and view all the answers
What is a constant term?
Signup and view all the answers
What are like terms?
Signup and view all the answers
What is an equation?
Signup and view all the answers
What is a solution in mathematical terms?
Signup and view all the answers
Study Notes
Properties of Equality
- Addition Property of Equality: Adding or subtracting the same number from both sides keeps the equation valid.
- Multiplication Property of Equality: Multiplying or dividing both sides by the same number preserves the equation's equality.
Inverse and Identity Properties
- Additive Inverse Property: Adding opposites yields zero, aiding in solving equations.
- Multiplicative Inverse Property: The product of a number and its reciprocal equals one.
- Additive Identity Property: The sum of any number and zero is the number itself.
- Multiplicative Identity Property: Any number multiplied by one remains unchanged.
Solution Concepts
- Solutions: Values that satisfy the equation, making it true.
- Equivalent Equations: Different equations that yield the same solution set.
- Isolate the Variable: Rearranging an equation to have the variable alone on one side.
Terms and Expressions
- Terms: Components of an expression linked by addition.
- Like Terms: Terms sharing the same variables with identical exponents.
- Constant Term: A term that represents a fixed number without any variables.
- Coefficients: Numbers that multiply variables in terms.
Properties of Operations
- Commutative Property: Order of addition or multiplication can be changed without affecting the result.
- Associative Property: Grouping in addition or multiplication does not influence the outcome.
Other Mathematical Concepts
- Distributive Property: Allows multiplication of a number outside parentheses with each term inside.
- Unit Conversion: Process of converting measurements from one unit to another.
- Equivalent Expressions: Different algebraic forms representing the same value or outcome.
Equations
- Equation: A mathematical statement asserting the equality of two expressions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz provides flashcards covering key properties related to solving equations in pre-algebra. Learn about the Addition Property of Equality, Additive Inverse Property, and more. Test your understanding with these essential mathematical concepts!