Exploring the Properties of Equality

This lesson covers the properties of equality used in solving equations, including reflexive, symmetric, and transitive properties, which are more relevant for proofs and higher-level algebra. The focus is on the addition, subtraction, multiplication, and division properties of equality, which allow for maintaining balance in equations by performing operations on both sides. The lesson emphasizes using inverse operations to solve equations effectively.

What is the main purpose of the properties of equality?

• To create new equations

• To compare different equations

• To solve equations

• To simplify expressions

Which property states that a equals a?

• Addition

• Reflexive

• Transitive

• Symmetric

If a equals b, which property allows you to state that b equals a?

• Reflexive

• Symmetric

• Transitive

• Multiplication

Which property is used to rearrange the sides of an equation?

• Transitive

• Symmetric

• Division

• Addition

What does the addition property of equality allow you to do?

• Multiply both sides of an equation by zero

• Subtract the same quantity from both sides of an equation

• Add the same quantity to both sides of an equation

• Add different quantities to both sides of an equation

What should you avoid when using the multiplication property of equality?

• Multiplying by fractions

• Multiplying by zero

• Multiplying by one

• Multiplying by negative numbers

What does the subtraction property of equality state?

• If a equals b, then a divided by c equals b divided by c

• If a equals b, then a times c equals b times c

• If a equals b, then a minus c equals b minus c

• If a equals b, then a plus c equals b plus c

How should you divide both sides of an equation according to the division property of equality?

• Divide each term separately

• Divide the entire side by the same number

• Divide by zero

• Divide by different numbers

Which property is represented by the acronym 'depo'?

• Subtraction

• Addition

• Division

• Multiplication

What is the goal when solving an equation?

• To create a new equation

• To simplify the equation

• To maintain the balance of the equation

• To compare two equations