Let’s make remembering these properties a little more memorable. Created by: Mike Walker

a + b = b + a Example:7 + 3 = Two real numbers can be added in either order to achieve the same sum. Does this work with subtraction? Why or why not?

a x b = b x a Example:3 x 7 = 7 x 3 Two real numbers can be multiplied in either order to achieve the same product. Does this work with division? Why or why not?

(a + b) + c = a + (b + c) Example: ( ) + 7 = 29 + (13 + 7) When three real numbers are added, it makes no difference which are added first. Notice how adding the first makes completing the problem easier mentally.

(a x b) x c = a x (b x c) Example: (6 x 4) x 5 = 6 x (4 x 5) When three real numbers are multiplied, it makes no difference which are multiplied first. Notice how multiplying the 4 and 5 first makes completing the problem easier.

a + 0 = a Example: = 9 The sum of zero and a real number equals the number itself. Memory note: When you add zero to a number, that number will always keep its identity.

a x 1 = a Example: 8 x 1 = 8 The product of one and a number equals the number itself. Memory note: When you multiply any number by one, that number will keep its identity.

a(b + c) = ab + ac ora(b – c) = ab – ac Example: 2(3 + 4) = (2 x 3) + (2 x 4) or 2(3 - 4) = (2 x 3) - (2 x 4) Distributive Property is the sum or difference of two expanded products.

a + (-a) = 0 Example:3 + (-3) = 0 The sum of a real number and its opposite is zero.

Go forth and use them wisely.Go forth and use them wisely. Use them confidently.Use them confidently. And use them well, my friends!And use them well, my friends!