Section 1.1 Properties of Real Numbers. Living Things Animals Plants Mammals Dogs Border Collies Real Numbers Rational Integers Whole Natural Irrational.

Slides:

Advertisements

Similar presentations

Properties of Real Numbers. TYPES OF NUMBERS NATURAL  5, 3, 1, 700, 26 … positives, no fractions WHOLE  0, 1, 1052, 711, … naturals and 0 INTEGERS 

Advertisements

Applying Properties of Real Numbers Sec. 1.2 Sol: A.11, A.12, A.1.

Objectives: To graph and order real numbers To identify properties of real numbers Vocabulary: OppositeAdditive Inverse ReciprocalMultiplicative Inverse.

Properties of Real Numbers

The Real Number System. The natural numbers are the counting numbers, without _______. Whole numbers include the natural numbers and ____________. Integers.

1.2 Properties of Real Numbers Here we will classify real numbers Use the properties to evaluate expressions.

7.1 - Introduction To Signed Numbers

Real Numbers 1 Definition 2 Properties 3 Examples

Chapter 1 Foundations for Algebra

Warm Up Write each number as a percent. -15, -7, -4, 0, 4, 7{…, -2, -1, 0, 1, 2, 3, …} Add the negative natural numbers to the whole numbers Integers.

Chapter 1 Learning Target: 10

PROPERTIES OF REAL NUMBERS 1 ¾ PI.

1–2: Properties of Real Numbers. Counting (Natural) Numbers {1, 2, 3, 4, 5, …}

Evaluate Each Expression Lesson 2.1 Operations with Numbers.

1 -2 Properties of Real Numbers. Types of Numbers  Often, numbers are grouped or classified as specific types of numbers. We will explore the following.

Section P-1 What are the properties of real numbers?

Drill #2 Evaluate each expression if a = 6, b = ½, and c =

Do Now LT: I can identify the real set of numbers that has special subsets related in particular ways.

Properties of Real Numbers List of Properties of Real Numbers Commutative Associative Distributive Identity Inverse.

1)12 (–28) 2) –23 + (–15) 3) 28 ÷ ( –12) 4) 0.314, , 0.309, Warm-Up Simplify. Order the numbers from least to greatest ,0.309,0.3131,0.314.

Thinking Mathematically Number Theory and the Real Number System 5.5 Real Numbers and Their Properties.

REAL NUMBERS. Real IntegersWhole #’sCounting#’s Rational.

1-1 Properties of Real Numbers

Properties of Real Numbers Algebra A Unit 1, Lesson 4.

Properties of Real Numbers The properties of real numbers allow us to manipulate expressions and equations and find the values of a variable.

Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties.

-(-7.2) 1-(-3) -9+(-4.5) (-3.4)(-2) -15/3 -2/5 + 3/-5

Exploring Real Numbers Lesson 1-3. Real Numbers Rational Numbers Integers Whole Numbers.

Classifying Numbers Properties. Number Sets Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Integers: …-3, -2, -1, 0, 1, 2, 3, … Rational Numbers:

Section P-1 What are the properties of real numbers?

Properties of Real Numbers

1–1: Number Sets. Counting (Natural) Numbers: {1, 2, 3, 4, 5, …}

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.5 Real Numbers and Their Properties.

REAL NUMBERS (as opposed to fake numbers?) Two Kinds of Real Numbers Rational Numbers Irrational Numbers.

1-3 Exploring Real Numbers. Let’s start on the inside…what are natural numbers? Natural numbers are the counting numbers… 1, 2, 3, 4 …

Warm-Up Convert the following to fractions: 1) ) ) ) 0.12.

Section 1-2 Classifying Numbers and the Number Line.

Chapter 1 Section 1 Properties of Real Numbers. 1-1 ALGEBRA 2 LESSON 1-1 Simplify. 1.–(–7.2)2.1 – (–3) 3.–9 + (–4.5) 4.(–3.4)(–2) Properties of Real Numbers.

1.2 Properties of Real Numbers Activity

(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition.

Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×

(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition.

5-3(D) Real Numbers.

Axioms for Rational Numbers 9/14-9/15. Natural Numbers – Numbers used for counting: 1, 2, 3, and so on. Whole Numbers – Natural numbers and zero: 0, 1,

1-1 Properties of Real Numbers Big Idea: -Graph, order, identify, and use properties of real numbers.

REAL NUMBER SYSTEM Number Systems Real Rational (fraction) Irrational Integer Whole Natural.

Algebra 2 Topic 1 Real Numbers Properties Sets of Numbers Naturals - Natural counting numbers. { 1, 2, 3… } Wholes - Natural counting numbers and zero.

Section 1-1 Day 1 – Real number Sets. Whole Numbers Integers Rational Numbers Real Numbers Irrational Numbers 0, 1, 2, 3,......, -3, -2, -1, 0, 1, 2,

INTEGERS Absolute Value Numbers and the Number Line Addition Subtraction Multiplication and Division Add/Subtract Matrices.

Chapter 1 Section 1 Properties of Real Numbers. Real Numbers The largest classification we will deal with Include any number that you can tell me  Ex:

Front of Room Door Josh Edson. Warm Up 1) -(-7.2) = 3) 1 – (-3) = 2) (-3.4)(-2)= 4) Day 1: August 22 nd Objective: To graph and order real numbers To.

Properties of Real Numbers

Appendix A Basic Algebra Review

1.2 Properties of Real Numbers

What are integers? Whole numbers Untouched

Section 2 Properties of Real Numbers

The Real-Number System

Properties of Real Numbers

Drill #3 Evaluate each expression if a = 6, b = ½, and c =

Properties of Real Numbers

Properties of Real Numbers

1.1 Real Numbers & Number Operations

Section 5.5 Real Numbers and Their Properties

Properties of Real Numbers

1.1 & 1.2: Properties of Real Numbers & Algebraic Expressions

Section 5.5 Real Numbers and Their Properties

Apply Properties of Real Numbers

Set – collection of objects

Properties of Real Numbers

Lesson 1 – 2 Properties of Real Numbers

Presentation transcript:

Section 1.1 Properties of Real Numbers

Living Things Animals Plants Mammals Dogs Border Collies Real Numbers Rational Integers Whole Natural Irrational Rat I W N = IRR R

Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers Real Numbers Ex: 1, 2, 3 … Ex: 0, 1, 2, 3 … Ex: …, -2, -1, 0, 1, 2, … Ex: ½, 0.3, 1, 2, 2,,, Ex: -, ,

Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Integers: …, -2, -1, 0, 1, 2, … Rational Numbers: Irrational Numbers: cannot be written as a ratio of integers; non-repeating or non-terminating decimals Textbook: Page 5 Numbers used for counting Natural Numbers and 0 Natural Numbers, 0, and their opposites Repeating or terminating decimal

Graphing on a Number Line: Rational, Real Irrational, Real Natural, Whole, Integer, Rational, Real Integer, Rational, Real Irrational, Real White Boards

The opposite (additive inverse) of any number a is –a The reciprocal (multiplicative inverse) of any nonzero number a is When you add together, = 0 When you multiply together, = 1 The Identity Element!

Opp.Rec.Opp.Rec.Opp.Rec. Mixed Number:Improper Fraction: White Boards

Properties of Real Numbers PropertyAdditionMultiplication Closure Commutative Associative Identity Inverse Distributive a(b + c) = ab + ac Identifying Properties of Real Numbers: 1. (-7)(2  5) = (-7)(5  2) 2. 3  ( 8 + 0) = 3  [2 + (-3)] = (-5 + 2) + (-3) Commutative Property of Multiplication Identity Property of Addition Associative Property of Addition a + b is a real number. ab is a real number. a + b = b + aab = ba (a + b) + c = a + (b + c)(ab)c = a(bc) a + 0 = a, 0 + a = a a  1 = a, 1  a = a a + (-a) = 0 a  = 1, a ≠ 0 White Boards Order Group Mirror Undo 1 st x 1 st + 1 st x 2 nd

Absolute Value Absolute value of a real number is the distance from zero on the number line = 4 = – 18 = 1.5

page White Boards