| A | B |
|---|
| Identity Property for Addition | For all real numbers a, a + 0 = a and 0 + a = a |
| Additive Inverse Property | For every real number a, there is exactly one real number -a such that a + (-a) = 0 and -a + a + 0 |
| Definition of Absolute Value | The absolute value of a real number x is the distance from x to 0 on the number line. |
| Definition of Subtraction | For all real numbers a and b: a - b = a + (-b) |
| Identity Property for Multiplication | For all real numbers a, a x 1 = a and 1 x a = a |
| Multiplicative Inverse Property | For every nonzero real number a, there is exactly one number 1/a such that a x 1/a = 1 and 1/a x a = 1 |
| Reciprocal or Multiplicative Inverse of a | The number 1/a is called the reciprocal or multiplicative inverse of a |
| Properties of Zero | the product of any real number and zero is zero; Zero divided by any nonzero real numver is zero; Division by zero is undefined. |
| Special properties of Zero | Zero is neither positive nor negative. Zero does not have a reciprocal because any number multiplied by zero is zero. |
| Properties of Zero in Symbols | Zero product a x 0 = 0 and 0 x a =0; 0/a = 0 where a does not equal zero. |
| Associative Property of Addition | For all real numbers a, b and c: (a + b) + c = a + (b + c) |
| Associative Property of Multiplication | For all real numbers a, b, and c: (a x b) x c = a x (b x c) |
| Commutative Property of Addition | For all real numbers a and b: a + b = b + a |
| Commutative Property of Multiplication | For all real numbers a and b: a x b = b x a |
| Distribitive Property of Multiplication Over Addition | For all real numbers a, b and c: a(b + c) = ab + ac and (b - c)a = ba - ca |
| Distributive Property of Multiplication Over Subtraction | For all real numbers a, b, and c: a(b - c) = ab - ac and (b - c)a = ba - ca |
| Reflexive Property of Equality | a = a (a number is equal to itself) |
| Symmetric Property of Equality | For all real numbers a, b, and c: If a = b, then b = a |
| Transitive Property of Equality | For all real numbers a, b, anc c: If a = b and b = c, then a = c |
| Substitution Property of Equality | For all real numbers a, b, and c: If a = b, then a can be replaced by b and b can be replaced by a |
