| A | B |
|---|
| property | a rule that holds true in mathematics |
| commutative | a word meaning to switch order |
| associative | a word meaning to switch groupings |
| commutative property of addition | the orders of the addends may be changed wihtout changing the sum A+B=B+A |
| associative property of addition | the groupings of the addends may be changed without changing the sum (A+B)+C=A+(B+C) |
| additive identity property | a number, zero, may be added to any other number without changing the sum A+0=A or 0+A=A; alos known as the identity property of addition, of zero, addition property of zero |
| additive inverse property | the opposite of a number may be added to the original number resulting in a sum of 0 A+(-A)=0 or (-A)+A=0 |
| commutative property of multicplication | the order of the factors may be changed without changing the productAB=BA |
| association property of multiplication | the grouping of the factors may be changed without changing the product(AB)C=A(BC) |
| multiplicative identity property | the product of one times any number is that number; 1A=A(1)=A |
| multiplicative inverse property | the product of any nember, except 0, times its multiplicative inverse (the reciprocal) is 1 A(1/A)=1 |
| multiplicative property of 0 | the product of zero times any number is zero; 0A=O or A(0)=0 |
| multiplicative property of -1 | the product of negative one times a number is the opposite of that number -1A=-A |
| distributive property of multiplication over addition | a factor times two or more addends may be taken times each addend and the add the porducts; A(B+C_=AB+AC, (B+C)A=BA+CA, AB+AC=A(B+C), BA+CA=(B+C)A |
