Real Numbers and Properties Objective: The students will be able to classify real numbers and recognize different properties that exist with real numbers. M11.A – Locate/identify irrational numbers at the approximate location on a number line. M11.A – Compare and/or order any real numbers (rational and irrational may be mixed).

Key Question What is the difference between rational and irrational numbers and how else can numbers be classified?

Classifying Numbers Real Numbers – all numbers are in this set (rational OR irrational) Rational Numbers – can be written as a fraction or a decimal that stops or repeats Examples: ½ Irrational Numbers – decimals that never stop and never repeat Examples: Set – a collection of objects SUBSETS

Are All Radicals Irrational? Radicand – number under the radical No…If the radicand is a perfect square, the radical is rational.

Perfect Squares Whenever you take the square root (radical) of a perfect square, you get a number that is rational. The square root undoes squaring a number. Common Perfect Squares

Classifying Numbers Natural Numbers – “counting numbers” 1, 2, 3, 4, 5, … Whole Numbers – includes 0 0, 1, 2, 3, 4, 5, … Integers – positive or negative whole number or zero “dashes on the number line” {…-3, -2, -1, 0, 1, 2, 3, …}

Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers

Real Numbers Natural Whole Integers Irrational Rational

Identify the sets into which each number belongs /

Commutative Property of Addition: Commutative Property of Multiplication: Associative Property of Addition: Associative Property of Multiplication: Additive Identity Property: Multiplicative Identity Property: Additive Inverse Property: Multiplicative Inverse Property: Zero Property of Multiplication: 5 + (4 + 2) = (5 + 4)  (3  5) = (2  3)  =  2 = 2  = 5 8  1 = (-12) = 0 3  0 = 0

Tips to Help you Remember Commutative Property: When you commute, you move from one place to another. In math, can move numbers for addition and multiplication. Associative Property: When you associate with your peers, you are often in groups. In math, can group numbers in any order for addition and multiplication. Identity Property: Your identity is who you are. In math, identity properties allow a number to get back to itself. Inverse Property: The inverse properties look at opposites.

Name that Property! = = (-0.8) = 0 4.(4 + 2) + 1 = 4 + (2 + 1)

Name that Property! (x + y) = 13x + 13y 7. 8.(ab)c = a(bc) 9.9(2) = 2(9)

Fill in the Blank ___ = (8 – 3) = (___  8) – (___  3) 3.3  (4  2) = (3  4)  ___ 4.4  ___ = ___ = 0