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Download Properties of Real Numbers Lessons and Homework
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Unit 1 - Lesson 1 Date: Objective: Students will learn the definitions of rational and irrational numbers and their subsets. Definitions: Word Natural Numbers Definition Examples Non-Examples Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Fill in each black in the Venn Diagram with the type of number and provide two examples of each: Properties of Addition Property Words Algebra Show Commutative Property of Addition 12+3= 3+12= Associative Property of Addition (7+3)+6= 7+(3+6) Identity Property of Addition 12+0= 8+0= Inverse Property of Addition 4+(-4)= 17+(-17)= Properties of Multiplication Property Words Algebra Show Commutative Property of Multiplication 12 x 3= 3 x 12= Associative Property of Multiplication (2 x 3) x 4= 2 x (3 x 4) = Distributive Property 2(3+5) = 3(1 β 4) = Identity Property of Multiplication 12 x 1= 8 x 1= Inverse Property of Multiplication Property of Zero π× π = π 4x0= π× π = π 5x0= Name: ____________________________ Unit 1 β Lesson 1 β Properties of Real Numbers Homework 1. Check (β) for each number system to which the numbers belongs. Number Real Rational Integer Whole Natural Irrational 5.3 0 -2 π β π π βπ βπ βπ. ππ ββπ. π π. ππ β¦ βπ 3.2332332β¦ 2. Match the property name (Commutative, Associative, Distributive, or Identity) with the proper equation. The terms may be used more than once. a) _______________________________ 8 + 12 = 12 + 8 b) _______________________________ 3 β (5 + 2) = (3 β 5) + (3 β 2) c) _______________________________ 9 + 0 = 9 d) _______________________________ 23 β 1 = 23 e) _______________________________ 7 + 4 + 6 = 6 + 4 + 7 f) _______________________________ (4 β 5) β 6 = 4 β (5 β 6) g) _______________________________ 12 + (11 + 50) = (12 + 11) + 50 h) _______________________________ 1 β 84 = 84 Unit 1 β Lesson 2 Date: Objective: Students use the commutative, associative and distributive properties to recognize structure within expressions and to prove equivalency of expressions. Vocabulary Word The Distributive Property Definition If a, b, and c are real numbers, then a(b + c) = ab + ac Representation What do we already know? 5(6x β 8) = 2y(x + 5y) = The Commutative Property The Associative Property Changing the order in which two or more numbers are added or multiplied does not affect the result. 3+7= Changing the grouping of three or more numbers when adding or multiplying does not affect the result. (5 + 8) + 9 = 3x4x2= 2 x (3 x 4) = Exercise #1: Representing the Distributive Property with a Picture: 1. Draw a picture to represent the expression: π(π + π) (π + π)(π + π) (π + π)(π + π + π) Exercise #2: Use these abbreviations for the properties of real numbers and complete the flow diagram. C+ for commutative property of addition A+ for associative property of addition Cx for commutative property of multiplication Ax for associative property of multiplication π + (π + π) (π + π) + π π + (π + π) π × (π × π) (π × π) × π π × (π × π) π × (π × π) (π × π) × π Exercise #3: Draw a flow diagram to prove that (π + π) + π = (π + π) + π Name: ____________________________ Unit 1 β Lesson 2 β Commutative, Associative and Distributive Properties Homework 1. Draw a picture to represent the following expressions a. (π + π) β (π + π) β (π + π) b. (π + π) β (π β π + π) 2. Use these abbreviations to show that the expression ππ + ππ is equivalent to π π + ππ C+ for commutative property of addition A+ for associative property of addition Cx for commutative property of multiplication Ax for associative property of multiplication 3. Fill in the blanks of this proof showing that (π + π)(π + π) is equivalent to ππ + ππ + ππ. Write either βCommutative Propertyβ, βAssociative Propertyβ, or βDistributive Propertyβ in each blank. 4. Create a flow diagram proof showing that (ππ)π is equivalent to (ππ)π
