Commutative Property of Addition Commutative Property of Multiplication For all real numbers a and b a + b = b + a For all real numbers a and b a b = b a Example:

2

3 Associative Property of Addition Associative Property of Multiplication For all real numbers a, b and c (a + b) + c = a + (b + c) For all real numbers a, b and c (a b) c = a (b c) Examples: Place the parenthesis to illustrate the associative property, then do the math and solve the problem = =

4

5 Distributive Property of Multiplication Over Addition and Subtraction For all real numbers a, b and c: a(b +c) = ab + ac and (b + c)a = ba + ca and a(b - c) = ab - ac and (b - c)a = ba - ca

6 Step 1: Break the term inside the parenthesis into addends that are easier to work with Examples 1. 4(15) 3. 6(125) Step 2: Distribute the term on the outside of the parenthesis to each addend Step 3: Do the math and add the terms together to get the final answer Use the distributive property to find the cost of renting a river tube for 8 hours at $4.75 per hour. Find the cost of renting a river tube for 7 hours at $5.50 per hour.

7 Properties of Equality For all real numbers a, b and c: Reflexive Property: a = a (A number is equal to itself) Symmetric Property If a = b, then b = a Transitive Property If a = b and b= c then a = c Substitution Property If a = b, then a can replace b, and b can be replaced by a