| A | B |
|---|
| inequalities | equations with <,> |
| Commutative property of addition | a + b=b+a |
| commutative property of multiplication | a x b=b x a |
| associative property of addition | a+(b+c)=(a+b)+c |
| associative property of multiplication | a(bc)=(ab)c |
| reflexive axiom of equality | for all real #'s, a=a |
| symetric axiom of equality | If a=b, then b=a |
| transitive axiom of equality | If a=b and b=c , then a=c |
| Distributive axiom of multiplicationwith respect to addition | a(b+c)=ab+ac |
| substitution | you may replace an expresssion with an expression with equal values |
| cancellation property of opposites | -(-a)=a |
| definition of subtraction | a-b=a+(-b) |
| identity axiom of addition | a+0=a |
| Axiom of the additive inverse | a+(-a)=0 |
| Property of opposite of sum | -(a+b)=-a +-(b) |
| Identity axiom of multiplication | a x 1= a |
| multiplicative property of 0 | a x0=0 |
| multiplicative property of -1 | a(-1)=-a |
| property of opposites in products | -a(b)=-ab, a(-b)=-ab, -a(-b)=ab |
| axiom of multiiplicative inverse | a x 1/a=a |
| property of reciprical of opposite of # | 1/-a=-1/a |
| property of recipricol of product | 1/ab=1/a x 1/b |
| Definition of division | a/b=a(1/b) |
| Addition property of equality | a+c=b+c when a=b |
| multiplicative property of equality | ab=ac when b=c |
| Subtraction property of equality | a-c=b-c when a=b |
| Division property of equality | a/c=b/c when a=b |
| Transitive property of order | if a<b and b<c then a<c |
| Axiom of comparison | for all real #s a,b one and only one is true a<b a=b a>b |
| addition property of order | a+c<b+c when a<b |
| multiplication property of order | ac<ab when a<b |
