Math Properties: Chapter 3 Flashcards

Questions and Answers

What does the Addition Property of Equality state?

Subtracting the same number from each side produces an equivalent equation.

Dividing each side by the same number produces an equivalent equation.

Adding different numbers to each side produces an equivalent equation.

Adding the same number to each side produces an equivalent equation. (correct)

What is the Distributive Property?

states that to multiply a sum or difference by a number, multiply each number in the sum or difference by the number outside the parenthesis.

The Division Property of Equality states that dividing each side of an equation by different numbers produces an equivalent equation.

False

What are equivalent equations?

equations with the same solution. Signup and view all the answers

What are like terms?

terms of an algebraic expression that have the same variables raised to the same exponents. Signup and view all the answers

What is a linear expression?

an algebraic expression in which the exponent of the variable is one. Signup and view all the answers

What are inverse operations?

operations that 'undo' each other, such as addition and subtraction or multiplication and division. Signup and view all the answers

What does the Multiplication Property of Equality state?

states that multiplying each side of an equation by the same number produces an equivalent equation. Signup and view all the answers

What is the Order of Operations?

the order in which to perform operations when evaluating expressions with more than one operation. Signup and view all the answers

What is the simplest form of an algebraic equation?

has no like terms and no parentheses. Signup and view all the answers

What does the Subtraction Property of Equality state?

states that subtracting the same number from each side of an equation produces an equivalent equation. Signup and view all the answers

Study Notes

Key Properties and Definitions

Addition Property of Equality: Adding the same number to both sides of an equation maintains equality, resulting in an equivalent equation.
Distributive Property: When multiplying a sum or difference by a number, distribute the multiplier to each term inside the parentheses before evaluating the expression.
Division Property of Equality: Dividing both sides of an equation by the same non-zero number preserves the equality, leading to an equivalent equation.
Equivalent Equations: Two or more equations that have the same solution set; they are true for the same value(s) of the variable(s).
Like Terms: Terms in an algebraic expression that contain the same variables raised to identical exponents, allowing them to be combined or simplified.
Linear Expression: An expression characterized by variables raised only to the first power (exponent of one), reflecting a straight-line relationship when graphed.
Inverse Operations: Operations that reverse the effect of each other, such as addition and subtraction or multiplication and division, crucial for solving equations.
Multiplication Property of Equality: Multiplying both sides of an equation by the same non-zero number preserves equality and results in an equivalent equation.
Order of Operations: A standard sequence to follow when evaluating expressions with multiple operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Simplest Form: An algebraic expression is in its simplest form when it contains no like terms and no parentheses, making it easy to interpret or solve.
Subtraction Property of Equality: Subtracting the same number from both sides of an equation keeps the equation balanced, resulting in an equivalent equation.

Description

Test your understanding of essential math properties in Chapter 3. This quiz features key concepts like the Addition Property of Equality, Distributive Property, and Division Property of Equality. Challenge yourself and reinforce your learning with these flashcards.