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Objective - To simplify expressions using commutative and associative properties.

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

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Objective - To simplify expressions using commutative and associative properties.

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  1. Objective - To simplify expressions using commutative and associative properties. Order doesn’t matter! You can flip-flop numbers around an operation. Commutative - 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. 1) (6 + 4) = (4 + 6) 2) 3) 4) 9 + 7 = 7 + 9 5)

  3. Difficult to prove true! Addition and multiplication are commutative. Easy to prove false! Is subtraction commutative? 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. not commutative 2) Brushing your teeth and combing your hair. commutative 3) Putting on your socks and putting on your shoes. not commutative 4) Eating cereal and drinking orange juice. commutative

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

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

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

  17. Simplify the following fractions.

  18. Simplify the variable expressions.

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