Properties of Real Numbers: Commutative, Associative, Identity, and Zero Properties, Exercises of Reasoning

Download Properties of Real Numbers: Commutative, Associative, Identity, and Zero Properties and more Exercises Reasoning in PDF only on Docsity!

9/4: Warm Up

Simplify:

Name the subsets the number belongs in:

1.4: Properties of Real Numbers Date: 9/ Two algebraic expressions are equivalent expressions if they have the same value for all values of the variable(s). PROPERTIES OF REAL NUMBERS: Let a, b, and c be any real number.

1. Commutative Properties of Addition and Multiplication: The order does not matter. Addition: ____________________________________________________ **Multiplication: _________________________________________________
2. Associative** Properties of Addition and Multiplication. Changing the grouping does not matter. Addition: ____________________________________________________ Multiplication: _________________________________________________

Ex 1). Which property is illustrated by each statement? a) 31 ∙ 0 = 0 : _____________________________________________________ b) (x + 3) + 6 = x + (3 + 6) : _________________________________________ c) 5x + 0 = 5x : ___________________________________________________

Ex 2). Use properties to solve the following using mental math. A movie ticket costs $6.75. A drink costs $1.90. Popcorn costs $2.25. What is the total cost for a ticket, a drink, and popcorn? Use mental math.

Deductive Reasoning is the process of reasoning logically from given facts to a conclusion. To show that a statement is not true (false), find a counterexample , an example for which it is not true. You need only one counterexample to prove that a statement is false. Ex 4). Is the statement true or false? If false, given a counterexample. a). For all real numbers a and b : b). For all real numbers a, b, and c : a – b = b – a a x b x c = a x c x b

Homework:

pg. 26 #1 – 6, 8 – 18(e), 19 21 , 28, 32, 33, 38, 40, 41, 42 Quiz #1 (1.1 1.4) Wednesday