Properties of Equality Quiz

Questions and Answers

What does the Addition Property of Equality state?

If a = b, then a + c = b + c (correct)

If a = b, then a - c = b - c

If a = b, then a / c = b / c

If a = b, then a * c = b * c

What is the definition of the Multiplication Property of Equality?

If a = b, then a * c = b * c

What is the Reflexive Property of Equality?

a = a

What does the Transitive Property of Equality indicate?

If a = b and b = c, then a = c Signup and view all the answers

What does the Subtraction Property of Equality state?

If a = b, then a - c = b - c Signup and view all the answers

Define the Division Property of Equality.

If a = b and c ≠ 0, then a / c = b / c Signup and view all the answers

What does the Symmetric Property of Equality say?

If a = b, then b = a Signup and view all the answers

State the Distributive Property.

a(b + c) = ab + ac Signup and view all the answers

What is the Substitution Property of Equality?

If a = b, then a can be substituted for b in any equation or expression. Signup and view all the answers

Study Notes

Properties of Equality

Addition Property of Equality: If a equals b (a = b), then adding a constant c to both sides maintains equality (a + c = b + c).
Multiplication Property of Equality: If a equals b (a = b), then multiplying both sides by a constant c preserves the equality (a * c = b * c).
Reflexive Property of Equality: Each value is equal to itself (a = a), emphasizing self-identity in equations.
Transitive Property of Equality: If a equals b (a = b) and b equals c (b = c), then a must equal c (a = c), allowing the transfer of equality across equalities.
Subtraction Property of Equality: Subtracting a constant c from both sides of an equation does not change the equality (a = b leads to a - c = b - c).
Division Property of Equality: If a equals b (a = b) and c is not equal to 0, then dividing both sides by c preserves equality (a / c = b / c).
Symmetric Property of Equality: If a equals b (a = b), then this can be expressed in reverse order as well (b = a), demonstrating bidirectional equality.

Additional Mathematical Properties

Distributive Property: This property states that multiplying a number by a sum is equivalent to multiplying each addend separately and then adding the results (a(b + c) = ab + ac).
Substitution Property of Equality: When a equals b (a = b), a can replace b in any equation or expression, allowing for simplification and manipulation of expressions.

Description

Test your knowledge on the fundamental properties of equality used in mathematics. This quiz covers the addition, multiplication, reflexive, transitive, subtraction, division, and symmetric properties. Perfect for reinforcing your understanding of these essential concepts!