Solving Equations Pre-Algebra Flashcards

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Questions and Answers

What does the Addition Property of Equality state?

You can ignore one side of the equation

You can add/subtract the same number to both sides of the equations and the solution will stay the same (correct)

You can change the variables in the equation

You can multiply/create a fraction from both sides

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?

You can multiply/divide the same number to both sides of the equations and the solution will stay the same. Signup and view all the answers

What is the Multiplicative Inverse Property?

Reciprocals multiply to be one. Signup and view all the answers

What does the Multiplicative Identity Property indicate?

The product of any number and one is that number. Signup and view all the answers

What are solutions in the context of equations?

Any number that makes an equation true. Signup and view all the answers

What are equivalent equations?

Equations that have the same solution set. Signup and view all the answers

What does it mean to isolate the variable?

Means to get the variable by itself on one side of the equation. Signup and view all the answers

What are opposites in mathematics?

Another name for additive inverses. Signup and view all the answers

What does the Commutative Property for Addition state?

In a sum, you can add the numbers in any order. Signup and view all the answers

What is the Commutative Property for Multiplication?

In a product, you can multiply the numbers in any order. Signup and view all the answers

What does the Associative Property for Addition imply?

Changing the grouping of the numbers in a sum does not change the sum. Signup and view all the answers

What does the Associative Property for Multiplication indicate?

Changing the grouping of the numbers in a product does not change the product. Signup and view all the answers

What is unit conversion?

Changes the units of something to another unit of measure. Signup and view all the answers

What are equivalent expressions?

Expressions that have the same value. Signup and view all the answers

What does the Distributive Property state?

Multiply the number on the outside of parentheses to each number inside the parentheses. Signup and view all the answers

What are terms in an expression?

The parts of an expression that are added. Signup and view all the answers

What is a coefficient?

The number part of a variable term. Signup and view all the answers

What is a constant term?

A term that is a number with no variable. Signup and view all the answers

What are like terms?

Terms that have the same variables raised to the same powers. Signup and view all the answers

What is an equation?

A math sentence that states two expressions are equal. Signup and view all the answers

What is a solution in mathematical terms?

A number(s) that makes the equation true. 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.

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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!