Algebraic Proofs

Front

What is the Subtraction Property of Equality?

Back

If two expressions are equal, subtracting the same value from both sides maintains the equality. For example, if a = b, then a - c = b - c.

Front

What is the Addition Property of Equality?

Back

If two expressions are equal, adding the same value to both sides maintains the equality. For example, if a = b, then a + c = b + c.

Front

What is the Multiplication Property of Equality?

Back

If two expressions are equal, multiplying both sides by the same non-zero value maintains the equality. For example, if a = b, then ac = bc.

Front

What is the Division Property of Equality?

Back

If two expressions are equal, dividing both sides by the same non-zero value maintains the equality. For example, if a = b, then a/c = b/c.

Front

What is the Symmetric Property of Equality?

Back

If a = b, then b = a. This property states that equality can be reversed.

Front

What is the Transitive Property of Equality?

Back

If a = b and b = c, then a = c. This property allows us to link equalities.

Front

What does 'Given' mean in algebraic proofs?

Back

'Given' refers to the information or statements that are accepted as true without proof in a problem.

Front

What is the purpose of a proof in algebra?

Back

A proof is a logical argument that demonstrates the truth of a statement or theorem based on previously established statements.

Front

What is an algebraic expression?

Back

An algebraic expression is a combination of numbers, variables, and operations (like addition, subtraction, multiplication, and division) without an equality sign.

Front

What is a variable in algebra?

Back

A variable is a symbol (often a letter) that represents an unknown value in mathematical expressions or equations.