1. 1-4 Properties How are real-life situations commutative?

2. Vocabulary properties – statements that are true for any numbers counterexample – an example that shows a conjecture is not true simplify – to simplify an algebraic expression means to write it in a simpler form deductive reasoning – using facts, properties, or rules to justify reasoning or reach valid conclusions

3. Properties Commutative Property of Addition – the order in which numbers are added does not change the sum Ex. 4 + 6 = 6 + 4 10 = 10 Commutative Property of Multiplication – the order in which numbers are multiplied does not change the product Ex. 4 * 6 = 6 * 4 24 = 24

4. Associative Property of Addition – the way in which the numbers are grouped when added does not change the sum Ex. (4 + 2) + 3 = 4 + (2 + 3) 6 + 3 = 4 + 5 9 = 9 Associative Property of Multiplication – the way in which the numbers are grouped when multiplied does not change the product Ex. (4 * 2) * 3 = 4 * (2 * 3) 8 * 3 = 4 * 6 24 = 24

5. Additive Identity – when 0 is added to any number, the sum is the number Ex. 4 + 0 = 4 Multiplicative Identity – when any number is multiplied by 1, the product is the number Ex. 4 * 1 = 4 Multiplicative Property of Zero – when any number is multiplied by 0, the product is 0. Ex. 4 * 0 = 0

6. Please name the property shown. 3 + 7 + 9 = 7 + 3 + 9 – Commutative Property of Addition 17 * 1 = 17 – Multiplicative Identity (a * 6) * 5 = a * (6 * 5) – Associative Property of Multiplication 0 * 12 = 0 – Multiplicative Property of Zero 3 * 10 * 2 = 3 * 2 * 10 – Commutative Property of Multiplication (2 + 5) + m = 2 + (5 + m) – Associative Property of Addition

7. Please find 4 * (25 * 11) mentally. 1100 Please find (18 * 5) * 20 mentally. 1800

8. Please state whether the following conjecture is true or false. If false, provide a counterexample: Division of whole numbers is commutative. false Please state whether the following conjecture is true or false. If false, provide a counterexample: Subtraction of whole numbers is associative. true

9. Please simplify each expression.