Properties of Equality Quiz

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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?

<p>If a = b and b = c, then a = c</p> Signup and view all the answers

What does the Subtraction Property of Equality state?

<p>If a = b, then a - c = b - c</p> Signup and view all the answers

Define the Division Property of Equality.

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

What does the Symmetric Property of Equality say?

<p>If a = b, then b = a</p> Signup and view all the answers

State the Distributive Property.

<p>a(b + c) = ab + ac</p> Signup and view all the answers

What is the Substitution Property of Equality?

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

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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.

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