1. Properties of Equality Algebra

2. 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

3. 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.

4. 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
Algebra
Equation
Example

5. 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
Algebra
Equation
Example

6. 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 = /1
Algebra
Equation
Example

7. 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
Algebra
Equation
Example

8. 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

9. 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

10. 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

11. 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 = 6 and 6 = then = 5 + 1
Example