1. Objective - To simplify expressions using commutative and associative properties. Commutative - Order doesn’t matter! You can flip-flop numbers around an operation. Commutative Property of Addition a + b = b + a 5 + 7 = 7 + 5 10 + 3 = 3 + 10 Commutative Property of Multiplication

2. Write an equivalent expression. 2) 3) 4) 9 + 7 1) (6 + 4) 5) = (4 + 6) = 7 + 9

3. Addition and multiplication are commutative. Is subtraction commutative? Difficult to prove true! Easy to prove false! Counterexample -An example that proves a statement false. Counterexample: Therefore, subtraction is not commutative.

4. Give a counterexample that shows division is not commutative. Counterexample: Therefore, division is not commutative.

5. State whether each situation below is commutative or not commutative. 1) Waking up in the morning and going to school. 2) Brushing your teeth and combing your hair. 3) Putting on your socks and putting on your shoes. 4) Eating cereal and drinking orange juice. not commutative commutative

6. Give the property that justifies each step. StatementReasons 16 + 27 + 84Given 16 + 84 + 27 100 + 27 127Simplify Comm. Prop. of Add. Simplify

7. Identities Identity Property of Addition x + 0 = x Identity Property of Multiplication Zero is sometimes called the Additive Identity. One is sometimes called the Multiplicative Identity.

8. Identify the property shown below. 3) (2 + 10) + 3 = (10 + 2) + 3 4) 1) 6 + 8 = 8 + 6 2) 5) 6) 7 + 0 = 7 7) Comm. Prop. of Add. Mult. Prop. of Zero Comm. Prop. of Add. Comm. Prop. of Mult. Identity Prop. of Add. Identity Prop. of Mult. Comm. Prop. of Mult.

9. Identity Property of Multiplication Many Forms of 1 Consequently, there are an infinite number of ways to write any fraction.

10. Models of Equivalent Fractions

11. Find 6 equivalent fractions for the fraction below. Most simplified

12. Write at least 4 equivalent fractions for the given one below. Circle the most simplified form of each value.

13. Simplifying Fractions (Reducing)

14. Identify each fraction below. Reduce!

15. Identify each fraction below. Reduce!

16. Simplify the following fractions.

18. Simplify the variable expressions.