# Properties and Numbers 1.4. Deductive Reasoning Using facts, properties or rules to reach a valid conclusion Conjecture: statement that could be true.

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Properties and Numbers 1.4

Deductive Reasoning Using facts, properties or rules to reach a valid conclusion Conjecture: statement that could be true of false Counter Example: an example that shows a statement is not true.

Ex: State whether each conjecture is true. If not give a counterexample. The sum of an even and an odd number is always even. False: 4+1 =5 which is odd

Commutative Properties: Change Order Addition Rule: Ex: Multiplication Rule: Ex:

Associative Properties: Change Grouping Addition (a+b)+c =a+(b+c) Ex: Multiplication Ex:

Identity Properties Addition (0) Rule: a + 0 = a Ex: 7 + 0 = 7 Multiplication(1) Rule: Ex:

Name the Property Example: 4+(a+3)=(a+3) +4 Answer: Commutative because the numbers changed order Example: 1(3c)=3c Answer: Identity Property because you multiplied by 1 and the number did not change

Name the Property Ex: 14+(9+10)=(14+9)+10 Answer: Associative because the grouping symbols changed Ex: d+0 =d Answer: Identity of addition because you added by 0 and the result stayed the same

Simplify the phrase using the properties Ex: 9 +(5+y)

Answer the following 2 questions: 1.) Is division of whole numbers associative? If not give a counterexample 2.) Is subtraction of whole numbers commutative? If not give a counterexample

Homework Page 22 (14-39 all, 42-48 even)

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