Properties+of+Mathematics

**Communitive Property of Addition** **No matter what order the smae numbers are combined in the sum remains constant:** **a + b = b + a** **3 + 4 = 4 + 3**  **Communitive Property of Multiplication** **Regardless of the order of the numbers being multiplied the product remains constant:** **a x b = b x a** **9 x 6 = 6 x 9**  **Associative Property of Addition and Multiplication** **Regardless of grouping arrangements the sum or product is unchanged:**  **Addition:** **(a + b) + c = a + (b + c)** **(4 + 3) + 2 = 4 + (3 + 2)** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**Multiplication** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**(a x b) x c = a x (b x c)** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**(5 x 4) x 3 = 5 x (4 x 3)** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**Distributive Property of Multiplication over Addition** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**This rule relates the two operations:** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**a(b+c) = (a x b) + (a x c)** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**5(4 + 3) = (5 x 4) + ( 5 x 3)** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**Inverse Operations** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**These axioms relate operations that are oppostie in their effects. The following equations demonstrate inverse operations.** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**Addition and Subtration** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**a + b = c 5 + 4 = 9** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**c - a = b 9 - 5 = 4** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**c - b = a 9 - 4 = 5** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**Multiplication and Division** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;"> <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**a x b = c 9 x 3 = 27** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**c / a = b 27 / 9 = 3** <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">**c / b = a 27/ 3 = 9**