| A | B |
|---|
| Commutative Property of addition | a+b=b+a |
| Commutative Property of multiplication | ab=ba |
| Associative Property of addition | (a+b)+c=a+(b+c) |
| Associative Property of multiplication | (ab)c=a(bc) |
| Reflexive Property of equality | a=a |
| Symmetric Property of equality | If a=b then b=a |
| Transitive Property of equality | If a=b and b=c, then a=c |
| Identity Property of Addition | a+0=a and 0+a=a |
| Property of Opposites | a+(-a)=0 and (-a)+a=0 |
| Property of the Opposite of a Sum | -(a+b)=(-a)+(-b) |
| Definition of Subtraction | a-b=a+(-b) |
| Distributive Property (of multiplication with respect to addition) | a(b+c)=ab+ac and (b+c)a=ba+ca |
| Distributive Property (of multiplication with respect to subtraction) | a(b-c)=ab-ac and (b-c)a=ba-ca |
| Identity Property of Multiplication | a*1=a and 1*a=a |
| Multiplicative Property of Zero | a*0=0 and 0*a=0 |
| Multiplicative Property of -1 | a(-1)=-a and (-1)a=-a |
| Property of Reciprocals | a*1/a=1 and 1/a*a=1 |
| Property of the Reciprocal of the Oppostite of a Number | 1/-a=-1/a |
| Property of a Reciprocal of a Product | 1/ab=1/a*1/b |
| Definition od Division | a/b=a*1/b |
