Properties of Equality Algebra

Table of Contents Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Symmetric Property of Equality Reflexive Property of Equality Substitution Property of Equality Transitive Property of Equality

Properties of Equality in Algebra This presentation will cover the eight properties of Equality in Algebra. After you have finished viewing these slides, you should be able to successfully answer questions on the worksheets.

The Addition Property a + c = b + c 2x - 4 = 10 + 4 + 4 The addition property of equality allows us to add the same number to both sides of an equation. a + c = b + c 2x - 4 = 10 + 4 + 4 Algebra Equation Example

The Subtraction Property The subtraction property of equality allows us to subtract the same number from both sides of the equation. a - c = b - c 3x + 5 = - 10 - 5 - 5 Algebra Equation Example

The Multiplication Property The multiplication property of equality allows us to multiply both sides of an equation by the same number. ac = bc 1/3 x = 15 3/1 . 1/3 x = 15 . 3/1 Algebra Equation Example

3 3 c c The Division Property a = b ; c ≠ 0 3x = 45 The division property of equality allows us to divide both sides of an equation by the same number. a = b ; c ≠ 0 c c 3x = 45 3 3 Algebra Equation Example

The Symmetric Property The symmetric property of equality states that if one quantity equals a second quantity, then the second quantity equals the first. If a = b, then b = a 2x + 6 = 18; 18 = 2x + 6 Algebra Equation Example

The Reflexive Property The reflexive property of equality states that any quantity is equal to itself. For any number a, a = a 8 = 8 or 6 + 2 = 6 + 2 Example

The Substitution Property The substitution property of equality states that a quantity may be substituted for its equal. If a = b, then a may be replaced by b If 9x = 405 then x = 45 Algebra Equation Example

The Transitive Property The transitive property of equality is like a syllogism. It goes like this: If a = b and b = c then a = c If 4 + 2 = 6 and 6 = 5 + 1 then 4 + 2 = 5 + 1 Example