2. Commutative Properties The Commutative Property is when a change in the order of the numbers does not change the answer. For example, addition would be: a + b = b + a And multiplication would be: a x b = b x a

3. Associative Properties The Associative Property is if you put the parentheses in a different position, the answer stays the same. For example, addition would be: a + (b + c) = (a + b) + c And multiplication would be: a x (b x c) = (a x b) x c

4. Identity Properties The Identity Property for addition is when you add 0 to a number, the sum is that number. For example: a + 0 = a The Identity Property for multiplication is when you multiply 1 to a number, the product is that number. For example: a x 1 = a

5. Distributive Property The Distributive Property for addition is when you remove parentheses from an equation and multiply the number outside the parentheses with each of the numbers in the brackets. For example: A(a + b) = Aa + Ab The Distributive Property for multiplication is when you do the same thing as addition, but with one number at a time. For example: (a x b) + (A x a) = ab + Aa

6. Equality Property The Equality Property for addition is when you can add the same number to both sides of an equation, and the statement will still be true. For example: if a = b, then a + c = b + c The Equality Property for subtraction is when you can subtract the same number from both sides of an equation, and the statement will still be true. For example: if a = b, then a – c = b – c The Equality Property for multiplication is when you can multiply both sides of an equation by the same number, and the statement will still be true. For example: if a = b, then c x a = c x b The Equality Property of division is when you can divide both sides of an equation by the same nonzero number, and the statement will still be true. For example: if a = b, then a / c = b / c

7. Inverse Properties The Inverse Property for addition is that a number plus its inverse equals 0. For example: For every number a, a + (-a) = 0 The Inverse Property for multiplication is when you multiply a number by its inverse and the positive numbers cancel out. For example: For every nonzero number a, a x (1 / a) = 1