1. B Y A S H L I S P R U I L L
Algebraic Properties

2. What are they?
 We use these properties when working with an
algebraic equation

3. Associative
 Addition:
(a+b)+c = a+(b+c)
(x+2)-3y = x+ (2-3y)
 Multiplication:
(ab)c = a(bc)
(x x 2)3y = x(2 x 3y)

4. Communitive
 Addition:
a+b = b+a
x+2 = 2+x
 Multiplication:
ab = ba
y x 2= y2

5. Identity
 Addition:
a+0= a =0+a
 Multiplication:
a x 1/a = 1 = 1/a x a

6. Inverse
 Addition:
a +(-a) = 0 = (-a) +a
 Multiplication:
a x 1/a = 1 = 1/a

7. Distributive
 Addition AND multiplication
a(b+c) = ab + ac and ab+ac = a(b+c)

8. PROPERTIES OF EQUALITIY AND
INEQUALITY

9. Multiplicative Property of Zero
 Equality:
a x 0 = 0 = 0 x a

10. Zero Product
 Equality:
If ab = 0, then a = 0 or b = 0

11. Reflexive
 Equality:
a=a

12. Symmetric
 Equality:
If a = b and b = a

13. Transitive
 Equality:
If a = b and b = c, then a = c
 Inequality:
If a > b and b > c, then a > c
If a < b and b < c, then a < c

14. Addition
 Equality:
If a = b, then a + c = b + c
 Inequality:
If a < b, then a + c < b + c
If a > b, then a + c > b + c

15. Subtraction
 Equality:
If a = b, then a – c = b – c
 Inequality:
If a < b, then a – c < b – c
If a > b, then a –c > b – c

16. Multiplication
 Equality:
If a = b, then ac = bc
 Inequality:
If a < b and c > 0, then ac < bc
If a < b and c < 0, then ac > bc
If a > b and c > 0, then ac > bc
If a > b and c < 0, then ac < bc

17. Division
 Equality:
If a = b and c does not equal to 0, then a/c = b/c
 Inequality:
If a < b and c > 0, then a/c < b/c
If a < b and c < 0, then a/c > b/c
If a > b and c > 0, then a/c > b/c
If a > b and c < 0, then a/c < b/c

18. Substitution
 Equality AND Inequality
If a = b, then b can be substituted for any equation or
inequality