Use a number line to graph and order real numbers. Identify properties of and use operations with real numbers.

1. Objective - To identify the properties and use operations with real numbers. Sets of Numbers Naturals - Natural counting numbers { 1, 2, 3… } Wholes - Natural counting numbers and zero { 0, 1, 2, 3… } Integers - Positive or negative natural numbers or zero { … -3, -2, -1, 0, 1, 2, 3… } Rationals - Any number which can be written as a fraction. Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal. Reals - Rationals & Irrationals

2. Sets of Numbers Reals Rationals Irrationals - any number which can be written as a fraction. , 7, -0 . 4 Fractions/Decimals Integers , -0 . 32, - 2 . 1 … -3, -2, -1, 0, 1, 2, 3 ... Negative Integers Wholes … -3, -2, -1 0, 1, 2, 3 ... Zero 0 Naturals 1, 2, 3 ... - non-terminating and non-repeating decimals

3. Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Naturals 1, 2, 3 ... Wholes 0 Integers -3 -19 Rationals -2 . 65 Irrationals Reals

4. Naturals 1, 2, 3 ... Wholes 0 Integers -3 -19 Rationals -2 . 65 Irrationals Reals Imaginary Numbers

5. Graphing Real Numbers on a Number Line Graph the following numbers on a number line. -4 -3 -2 -1 0 1 2 3 4

6. Commutative Properties Commutative Property of Addition a + b = b + a Commutative Property of Multiplication Example: 3 + 5 = 5 + 3 Example: Properties of Real Numbers

7. Associative Properties Associative Property of Addition ( a + b ) + c = a + ( b + c ) Associative Property of Multiplication Example: Example: ( 4 + 11 ) + 6 = 4 + ( 11 + 6 )

8. Identities Identity Property of Addition x + 0 = x Identity Property of Multiplication Properties of Zero Multiplication Property of Zero Division Property of Zero

9. Distributive Property a ( b + c ) = ab + ac or a ( b - c ) = ab - ac Inverses Additive Inverse or Opposite Multiplicative Inverse or Reciprocal

10. Closure Property A set of numbers is said to be ‘closed’ if the numbers produced under a given operation are also elements of the set . Addition Multiplication

11. Identify the property shown below. 1) (2 + 10) + 3 = (10 + 2) + 3 2) 3) (6 + 8) + 9 = 6 + (8 + 9) 4) 5) 6) 5 + (-5) = 0 7) Comm. Prop. of Add. Mult. Prop. of Zero Assoc. Prop. of Add. Mult. Inverse Additive Inverse Identity Prop. of Mult. Distributive