| A | B |
|---|
| Closure Property | a + b and ab are unique real numbers |
| 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 | a = a |
| Symmetric Property | If a = b, then b = a |
| Transitive Property | If a = b and b = c, then a = c |
| Identity Property of Addition | a + 0 = a |
| Property of Opposites | a + (-a) = 0 |
| Property of the Opposite of a Sum | -(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 Opposites in Products | (-a)(b) = -ab; a(-b) = -ab; (-a)(-b) = ab |
| Property of Reciprocals | a(1/a) = 1 and (1/a)a = 1 |
| Property of Reciprocal of the Opposite of a Number | 1/-a = -(1/a) |
| Definition of Subtraction | a - b = a + (-b) |
| Property of the Reciprocal of a Product | 1/ab = (1/a)(1/b) |
| Definition of Division | a/b = a(1/b) |
| Addition Property of Equality | If a = b, a+c = b+c and c+a = c+b |
| Subtraction Property of Equality | If a = b, a-c = b-c |
| Multiplicative Property of Equality | If a = b, ca = cb and ac = bc |
| Division Property of Equality | If a = b, a/c = b/c |
