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Algebraic properties pp

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Algebraic properties pp

1. 1. B Y A S H L I S P R U I L L Algebraic Properties
2. 2. What are they?  We use these properties when working with an algebraic equation
3. 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. 4. Communitive  Addition: a+b = b+a x+2 = 2+x  Multiplication: ab = ba y x 2= y2
5. 5. Identity  Addition: a+0= a =0+a  Multiplication: a x 1/a = 1 = 1/a x a
6. 6. Inverse  Addition: a +(-a) = 0 = (-a) +a  Multiplication: a x 1/a = 1 = 1/a
7. 7. Distributive  Addition AND multiplication a(b+c) = ab + ac and ab+ac = a(b+c)
8. 8. PROPERTIES OF EQUALITIY AND INEQUALITY
9. 9. Multiplicative Property of Zero  Equality: a x 0 = 0 = 0 x a
10. 10. Zero Product  Equality: If ab = 0, then a = 0 or b = 0
11. 11. Reflexive  Equality: a=a
12. 12. Symmetric  Equality: If a = b and b = a
13. 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. 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. 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. 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. 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. 18. Substitution  Equality AND Inequality If a = b, then b can be substituted for any equation or inequality