# Expressions that always have the same value. The Identity Property of Addition states that For any value a; a + 0 = a so = 3

Size: px
Start display at page:

Download "Expressions that always have the same value. The Identity Property of Addition states that For any value a; a + 0 = a so = 3"

Transcription

1 Name Key Words/Topic 2.1 Identity and Zero Properties Topic 2 Guided Notes Equivalent Expressions Identity Property of Addition Identity Property of Multiplication Zero Property of Multiplication The sum of 0 and any number is that number = 4 The product of 1 and any number is that number. 4 x 1 = 4 The product of any number and zero is zero; 4 x 0 = 0 Equivalent Expressions Expressions that always have the same value. Mathematical properties are always true. Today you will learn 3 properties. The Identity Property of Addition states that For any value a; a + 0 = a so = 3 The Identity Property of Multiplication states that For any value a; a 1 = a so 6 1 = 6 The Zero Property of Multiplication For any value a; a 0 = 0 so 5 0 = 0

2 Key Words/Topic 2.2 The Commutative Properties Commutative Property of Addition Commutative Property of Multiplication Addends Factors You can add numbers in any order. For any numbers a + b = b + a (ex = 4 + 3) You can multiply numbers in any order. For any numbers a b = b a (ex 3 4 = 4 3) Numbers that are added together to find a sum. (ex. In = 7, 3 and 4 are addends.) Numbers that are multiplied to give a product. (ex. In 3 4 = 12, 3 and 4 are factors.) The Commutative Property of Addition states that the order in which we add addends doesn t matter. a + b = b + a so = The Commutative Property of Multiplication states that the order in which we multiply factors doesn t matter. a b = b a so 2 6 = 6 2 You can use the commutative properties of addition and multiplication to add, or multiply, more than two numbers together. For example = and = 6 4 5

3 Key Words/Topic 2.3 The Associative Properties Associative Property of Addition Associative Property of Multiplication The way in which addends are grouped doesn't change the sum. {ex. 3 + (4 + 5) = (3 + 4) + 5} The way in which factors are grouped doesn't change the product. {ex. 3(4 5) = (3 4)5} The Associative Property of Addition states that the way in which addends are grouped doesn t matter. a + (b + c) = (a + b) + c so 2 + (3 + 4) = (2 + 3) + 4 The Associative Property of Multiplication states that the way in which factors are grouped doesn t matter. a(b c) = (a b) c so 2(6 3) = (2 6)3

4 Key Words/Topic 2.4 Greatest Common Factor Common Factor Greatest Common Factor Prime Number Composite Number Prime Factorization Factors A number which is a factor of two or more given numbers. (ex. 3 is a common factor of 6 and 9.) The GCF of two or more whole numbers is the greatest number that is a factor of all of the numbers. (ex. The GCF of 12 and 10 is 2.) A whole number greater than 1 with exactly two factors, 1 and the number itself. A whole number greater than 1 with more than 2 factors. The prime factorization of a composite number is the expression of the number as a product of its prime factors. (ex. 30 = 2 3 5) Numbers that are multiplied to give a product. (ex. In 3 4 = 12, 3 and 4 are factors.) When two, or more, numbers have the same factor, the factors are called common factors. Common factors are very helpful in math. The greatest (largest) common factor between the numbers is called the greatest common factor (GCF). There are different methods to find the GCF. We will look at three methods. Method 1: List all of the factors of a number using factor pairs. Compare the factors of the numbers and find the greatest common factor. What is the GCF of 18 & 24? 1. List the factors of 12 and 24. Factor pairs can help us. Factor pairs for 18: 1,18; 2,9; 3;6 Factors for 18: 1, 2, 3, 6, 9, 18 Factor pairs for 24: 1,24; 2;12; 3;8; 4;6 Factors for 24: 1, 2, 3, 4, 6, 8, 12, 24

5 2.4 Greatest Common Factor Continued Pick out the largest common factor between the two numbers: 6 is the GCF. Method 2: For the 2 nd method, you need to know how to prime factor numbers. In math we often have to break numbers down into their simplest parts (factors). The simplest factors of all are prime factors. There are a number of prime factorization methods. One of the most common methods is the tree method. How can we use the tree method to find out the prime factorization of 72? 1. Put 72 at the top of the tree. 2. Use your divisibility rules to break 72 into factor pairs. 3. If one of the factors is a prime number, then continue to bring the branch down to the ground. 4. Any numbers that are still composite numbers and not prime, need to be broken down into factor pairs. 5. Once all of your numbers are prime, you are done! 6. Then rewrite the prime factors into one row (factor string). The factor tree on the last page is not the only way to break 72 down into its primes. How you break a number down may vary, but the result should be the same.

6 2.4 Greatest Common Factor Continued 1. Factor the numbers into prime factorization. 2. Rewrite both factor strings on top of each other. 2*3*3 2*2*2*3 3. Circle any common factors in both strings, picking one number from each string per pair. 2*3*3 2*2*2*3 4. Pick JUST ONE number from each circle and rewrite them as a multiplication problem. Multiply the numbers together and that is the GCF. 2*3=6 GCF Method 3: Upside Down Birthday Cake or Cake Method 1. Write the factors inside the 1 st layer of your upside down cake. 2. Ask yourself what common factor does 24 & 18 have? 2; write the factor on the side of your cake layer. Divide both numbers inside of your cake by the factor outside of your cake. Write the quotients in your next layer. 3. Repeat the process until the numbers at the bottom don t have any common factors. Multiply the numbers on the outside of the cake and you get 6!

7 Key Words/Topic 2.5 The Distributive Property Distributive Property Greatest Common Factor Multiplying a number by a sum, or difference, gives the same result as multiplying that number by each term in the sum, or difference, and then adding or subtracting the corresponding products. a(b + c) = a b + a c and a(b - c) = a b a c so 36( ) = (36 14) + (36 85) The GCF of two or more whole numbers is the greatest number that is a factor of all of the numbers. (ex. The GCF of 12 and 10 is 2.) When we distribute something it is like spreading it out, or giving it to other numbers in the problem. a(b + c) = a b + a c we give the a to the b and the c. 3(2 + 4) = = =18 or a(b - c) = a b - a c we give the a to the b and the c. 3(4 2) = = = 6 We can use the distributive property to break up or join numbers and make some problems easier to solve. Break it up; 6 37 = Join; = 6 40 We can also use common factors to make equivalent expressions using the distributive property. Take the expression The GCF for 24 and 16 is 4. We can set = 4(6 4) by factoring out the GCF. The distributive property is essential to mastering algebra and we can use the distributive property with algebraic expressions. Let s

8 2.5 The Distributive Property Continued take the algebraic expression 25x is a common factor for both terms. If we factor out the 5 from both terms, we get 5(5x + 3). If we start with the algebraic expression 12(42x 3), we can distribute (or give) the 12 to each term in the parentheses and end up with 504x 36.

9 Key Words/Topic 2.6 Least Common Multiple Multiple Common Multiple Least Common Multiple The product of the number and a whole number. (ex. Multiples of 3 are 3, 6, 9, 12...) A multiple that two or more numbers share. (ex. 12 and 24 are common multiples of 4 and 6) The LCM of two or more numbers is the least (lowest value) multiple shared by all of the numbers. (ex. The LCM of 4 and 6 is 12.) Like finding the GCF, there are numerous methods for finding the Least Common Multiple. Method 1: List the common multiples of the numbers until you find the smallest match. Although 24 & 48 are both common multiples, we need to pick the smallest value 24 = LCM. Method 2: Use factor trees to find the prime factorization. Once you find the prime factorization, write the factor strings of the numbers. Circle the greatest number of times a factor appears in the different strings. Then multiply the circled factors together. The product is the LCM. Method 3: You can also use the CAKE method as long as you are using it for just two numbers. It is possible to use it for more than

10 2.6 Least Common Multiple Continued two numbers, but you must know the exception. Once you reach the point where there are no common factors between the two numbers, you form an L around the outside numbers and the lowest level of the cake. Then multiply all of the numbers inside the L. This gives you the LCM. 2x3x4=24

### Divisibility, Factors, and Multiples

Divisibility, Factors, and Multiples An Integer is said to have divisibility with another non-zero Integer if it can divide into the number and have a remainder of zero. Remember: Zero divided by any number

### Slide 1 / 69. Slide 2 / 69. Slide 3 / 69. Whole Numbers. Table of Contents. Prime and Composite Numbers

Slide 1 / 69 Whole Numbers Table of Contents Slide 2 / 69 Prime and Composite Numbers Prime Factorization Common Factors Greatest Common Factor Relatively Prime Least Common Multiple Slide 3 / 69 Prime

### Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers

Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

### INTRODUCTION TO FRACTIONS

INTRODUCTION TO FRACTIONS MEANING AND PROPERTIES OF FRACTIONS Fractions are used to represent parts of a whole. Example: What is the fraction of the shaded area? one-half one-quarter three-eighths 4 The

### August 15, M1 1.4 Common Factors_Multiples Compacted.notebook. Warm Up MI 36. Jun 20 10:53 AM

Warm Up MI 36 8 14 18 Jun 20 10:53 AM 1 Assignment Jun 20 12:36 PM 2 Practice 7 13 A = bh 7 x 13 91 7 7 A = ½bh ½(7 x 7) ½(49) 24.5 Jun 20 12:36 PM 3 Practice 6 4 8 A=½bh 4 6x8 24 A=bh 4x8 32 4 5 8 8 A=bh

### Chapter 7 Rational Expressions, Equations, and Functions

Chapter 7 Rational Expressions, Equations, and Functions Section 7.1: Simplifying, Multiplying, and Dividing Rational Expressions and Functions Section 7.2: Adding and Subtracting Rational Expressions

### Section 1.2 Factors and Factor Operators

Section 1. Factors and Factor Operators The most basic component of mathematics is the factor. Factors are parts of multiplication, therefore, in the product or or the factors are and. And, since 1, we

### A quadratic expression is a mathematical expression that can be written in the form 2

118 CHAPTER Algebra.6 FACTORING AND THE QUADRATIC EQUATION Textbook Reference Section 5. CLAST OBJECTIVES Factor a quadratic expression Find the roots of a quadratic equation A quadratic expression is

### Prime Factorization and GCF. In my own words

Warm- up Problem What is a prime number? A PRIME number is an INTEGER greater than 1 with EXACTLY 2 positive factors, 1 and the number ITSELF. Examples of prime numbers: 2, 3, 5, 7 What is a composite

### Algebra III and Trigonometry Summer Assignment

Algebra III and Trigonometry Summer Assignment Welcome to Algebra III and Trigonometry! This summer assignment is a review of the skills you learned in Algebra II. Please bring this assignment with you

### Second Trimester Exam: STUDY GUIDE: KEY

Second Trimester Exam: STUDY GUIDE: KEY 1. Coordinate Plan - Quadrants: a. The coordinate plane below labels the four quadrants, the origin, x-axis, y-axis, and show how to plot points. b. Quadrant I 2.

### Properties of Real Numbers

Properties of Real Numbers Essential Understanding. Relationships that are always true for real numbers are called properties, which are rules used to rewrite and compare expressions. Two algebraic expressions

### Review Notes - Solving Quadratic Equations

Review Notes - Solving Quadratic Equations What does solve mean? Methods for Solving Quadratic Equations: Solving by using Square Roots Solving by Factoring using the Zero Product Property Solving by Quadratic

### Section 3-4: Least Common Multiple and Greatest Common Factor

Section -: Fraction Terminology Identify the following as proper fractions, improper fractions, or mixed numbers:, proper fraction;,, improper fractions;, mixed number. Write the following in decimal notation:,,.

### Geometry 21 Summer Work Packet Review and Study Guide

Geometry Summer Work Packet Review and Study Guide This study guide is designed to accompany the Geometry Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the

### Math 10-C Polynomials Concept Sheets

Math 10-C Polynomials Concept Sheets Concept 1: Polynomial Intro & Review A polynomial is a mathematical expression with one or more terms in which the exponents are whole numbers and the coefficients

### Algebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials

Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial- an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +

### Topic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3

Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring

### Associative property

Addition Associative property Closure property Commutative property Composite number Natural numbers (counting numbers) Distributive property for multiplication over addition Divisibility Divisor Factor

### Updated: January 16, 2016 Calculus II 7.4. Math 230. Calculus II. Brian Veitch Fall 2015 Northern Illinois University

Math 30 Calculus II Brian Veitch Fall 015 Northern Illinois University Integration of Rational Functions by Partial Fractions From algebra, we learned how to find common denominators so we can do something

### STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 2 nd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 2 nd Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

### Unit 2: Polynomials Guided Notes

Unit 2: Polynomials Guided Notes Name Period **If found, please return to Mrs. Brandley s room, M 8.** Self Assessment The following are the concepts you should know by the end of Unit 1. Periodically

### Math 7 Notes Unit Two: Integers

Math 7 Notes Unit Two: Integers Syllabus Objective: 2.1 The student will solve problems using operations on positive and negative numbers, including rationals. Integers the set of whole numbers and their

### Chapter 1. Making algebra orderly with the order of operations and other properties Enlisting rules of exponents Focusing on factoring

In This Chapter Chapter 1 Making Advances in Algebra Making algebra orderly with the order of operations and other properties Enlisting rules of exponents Focusing on factoring Algebra is a branch of mathematics

### POLYNOMIAL EXPRESSIONS PART 1

POLYNOMIAL EXPRESSIONS PART 1 A polynomial is an expression that is a sum of one or more terms. Each term consists of one or more variables multiplied by a coefficient. Coefficients can be negative, so

### { independent variable some property or restriction about independent variable } where the vertical line is read such that.

Page 1 of 5 Introduction to Review Materials One key to Algebra success is identifying the type of work necessary to answer a specific question. First you need to identify whether you are dealing with

### 29. GREATEST COMMON FACTOR

29. GREATEST COMMON FACTOR Don t ever forget what factoring is all about! greatest common factor a motivating example: cutting three boards of different lengths into same-length pieces solving the problem:

### Numerical and Algebraic Fractions

Numerical and Algebraic Fractions Aquinas Maths Department Preparation for AS Maths This unit covers numerical and algebraic fractions. In A level, solutions often involve fractions and one of the Core

### Free Pre-Algebra Lesson 15! page 1

Free Pre-Algebra esson 15! page 1 esson 15 Simplifying Algebraic Expressions You know from experience with the perimeter of a rectangle that there are sometimes many ways to write the same formula. Depends

### Module 3 Study Guide. GCF Method: Notice that a polynomial like 2x 2 8 xy+9 y 2 can't be factored by this method.

Module 3 Study Guide The second module covers the following sections of the textbook: 5.4-5.8 and 6.1-6.5. Most people would consider this the hardest module of the semester. Really, it boils down to your

### 4.5 Integration of Rational Functions by Partial Fractions

4.5 Integration of Rational Functions by Partial Fractions From algebra, we learned how to find common denominators so we can do something like this, 2 x + 1 + 3 x 3 = 2(x 3) (x + 1)(x 3) + 3(x + 1) (x

### UNIT 4 NOTES: PROPERTIES & EXPRESSIONS

UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics

### Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to

Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to Learning Target #1: Factoring Factor the GCF out of a polynomial Factor a polynomial when a = 1 Factor

### Math Lecture 18 Notes

Math 1010 - Lecture 18 Notes Dylan Zwick Fall 2009 In our last lecture we talked about how we can add, subtract, and multiply polynomials, and we figured out that, basically, if you can add, subtract,

### Rational Expressions & Equations

Chapter 9 Rational Epressions & Equations Sec. 1 Simplifying Rational Epressions We simply rational epressions the same way we simplified fractions. When we first began to simplify fractions, we factored

### We will work with two important rules for radicals. We will write them for square roots but they work for any root (cube root, fourth root, etc.).

College algebra We will review simplifying radicals, exponents and their rules, multiplying polynomials, factoring polynomials, greatest common denominators, and solving rational equations. Pre-requisite

### Unit 2: Polynomials Guided Notes

Unit 2: Polynomials Guided Notes Name Period **If found, please return to Mrs. Brandley s room, M 8.** Self Assessment The following are the concepts you should know by the end of Unit 1. Periodically

### Glossary. Boosting: Rewriting a fraction as an equivalent fraction with a higher denominator.

Glossary Boosting: Rewriting a fraction as an equivalent fraction with a higher denominator. Denominator: Bottom number of a fraction indicating how many parts make a whole. Difference: The result when

### LESSON EII.C EQUATIONS AND INEQUALITIES

LESSON EII.C EQUATIONS AND INEQUALITIES LESSON EII.C EQUATIONS AND INEQUALITIES 7 OVERVIEW Here s what you ll learn in this lesson: Linear a. Solving linear equations b. Solving linear inequalities Once

### Name Date Class HOW TO USE YOUR TI-GRAPHING CALCULATOR. TURNING OFF YOUR CALCULATOR Hit the 2ND button and the ON button

HOW TO USE YOUR TI-GRAPHING CALCULATOR 1. What does the blue 2ND button do? 2. What does the ALPHA button do? TURNING OFF YOUR CALCULATOR Hit the 2ND button and the ON button NEGATIVE NUMBERS Use (-) EX:

### Academic-Clinic.com BASIC ARITHMETIC AND ALGEBRA POINTERS. Whole (natural) numbers. Arithmetical operations

BASIC ARITHMETIC AND ALGEBRA POINTERS Whole (natural) numbers Natural numbers numbers, which appear as a result of calculus of single subjects: peoples, animals, birds, trees, different wares and so on.

### Unit 7: Factoring Quadratic Polynomials

Unit 7: Factoring Quadratic Polynomials A polynomial is represented by: where the coefficients are real numbers and the exponents are nonnegative integers. Side Note: Examples of real numbers: Examples

3.3 Dividing Polynomials Copyright Cengage Learning. All rights reserved. Objectives Long Division of Polynomials Synthetic Division The Remainder and Factor Theorems 2 Dividing Polynomials In this section

### Mathematics Tutorials. Arithmetic Tutorials Algebra I Tutorials Algebra II Tutorials Word Problems

Mathematics Tutorials These pages are intended to aide in the preparation for the Mathematics Placement test. They are not intended to be a substitute for any mathematics course. Arithmetic Tutorials Algebra

### Algebra I. Exponents and Polynomials. Name

Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT

### 8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors

8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.

### Math 110 FOUNDATIONS OF THE REAL NUMBER SYSTEM FOR ELEMENTARY AND MIDDLE SCHOOL TEACHERS

4-1Divisibility Divisibility Divisibility Rules Divisibility An integer is if it has a remainder of 0 when divided by 2; it is otherwise. We say that 3 divides 18, written, because the remainder is 0 when

### Polynomials. This booklet belongs to: Period

HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher

### Unit One Algebraic Thinking (Part A Number Relationships) 1.2 Powers *I can write and understand numerical expressions involving

1.2 Powers *I can write and understand numerical expressions involving and Exponents whole number exponents. Discuss with your group how do you THINK you would find the value? Exponential Form: base 4

### Algebra 31 Summer Work Packet Review and Study Guide

Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the

### Sect Properties of Real Numbers and Simplifying Expressions

Sect 1.7 - Properties of Real Numbers and Simplifying Expressions Concept #1 Commutative Properties of Real Numbers Ex. 1a 9.34 + 2.5 Ex. 1b 2.5 + ( 9.34) Ex. 1c 6.3(4.2) Ex. 1d 4.2( 6.3) a) 9.34 + 2.5

### Full file at RNUM: Real Numbers

RNUM: Real Numbers Workbook Pages - Building Blocks.... Factor Pairings..... Match Up on Fractions.... Fractions Using a Calculator... Charting the Real Numbers.... 5 Venn Diagram of the Real Numbers.....

### Algebra Introduction to Polynomials

Introduction to Polynomials What is a Polynomial? A polynomial is an expression that can be written as a term or a sum of terms, each of which is the product of a scalar (the coefficient) and a series

### Are you ready for Algebra 3? Summer Packet *Required for all Algebra 3/Trigonometry Students*

Name: Date: Period: Are you ready for Algebra? Summer Packet *Required for all Students* The course prepares students for Pre Calculus and college math courses. In order to accomplish this, the course

### NAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4

Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as

### A field trips costs \$800 for the charter bus plus \$10 per student for x students. The cost per student is represented by: 10x x

LEARNING STRATEGIES: Activate Prior Knowledge, Shared Reading, Think/Pair/Share, Note Taking, Group Presentation, Interactive Word Wall A field trips costs \$800 for the charter bus plus \$10 per student

### Finite Mathematics : A Business Approach

Finite Mathematics : A Business Approach Dr. Brian Travers and Prof. James Lampes Second Edition Cover Art by Stephanie Oxenford Additional Editing by John Gambino Contents What You Should Already Know

### Chapter 7 Class Notes. Intermediate Algebra, MAT1033C. SI Leader Joe Brownlee. Palm Beach State College

Chapter 7 Class Notes Intermediate Algebra, MAT033C Palm Beach State College Class Notes 7. Professor Burkett 7. Rational Expressions and Functions; Multiplying and Dividing Chapter 7 takes factoring to

### Math 46 Final Exam Review Packet

Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.

### Simplifying Algebraic Fractions Multiplying and Dividing Monomials

Lesson 4-1 Lesson 4-2 Lesson 4-3 Lesson 4-4 Lesson 4-5 Lesson 4-6 Lesson 4-7 Powers and Exponents Prime Factorization Greatest Common Factor Simplifying Algebraic Fractions Multiplying and Dividing Monomials

Summer Packet th into 6 th grade Name Addition Find the sum of the two numbers in each problem. Show all work.. 62 2. 20. 726 + + 2 + 26 + 6 6 Decimal Addition: Remember to line up the decimals before

### N= {1,2,3,4,5,6,7,8,9,10,11,...}

1.1: Integers and Order of Operations 1. Define the integers 2. Graph integers on a number line. 3. Using inequality symbols < and > 4. Find the absolute value of an integer 5. Perform operations with

### Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is

### Math 75 Mini-Mod Due Dates Spring 2016

Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

### My Math Plan Assessment #1 Study Guide

My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.

### 4.1. Factors and Prime Factorization. Writing Factors. Goal: Write the prime factorization of a number. Vocabulary. Prime number: Composite number:

4.1 Factors and Prime Factorization Goal: Write the prime factorization of a number. Vocabulary Prime number: Composite number: Prime factorization: Factor tree: Monomial: Example 1 Writing Factors A rectangle

### Algebra 2 Summer Work Packet Review and Study Guide

Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the nine specific concepts covered in the

### Part 2 - Beginning Algebra Summary

Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian

### MA094 Part 2 - Beginning Algebra Summary

MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page

### Florida Math Curriculum (433 topics)

Florida Math 0028 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

### Maths Book Part 1. By Abhishek Jain

Maths Book Part 1 By Abhishek Jain Topics: 1. Number System 2. HCF and LCM 3. Ratio & proportion 4. Average 5. Percentage 6. Profit & loss 7. Time, Speed & Distance 8. Time & Work Number System Understanding

### Section 4. Quantitative Aptitude

Section 4 Quantitative Aptitude You will get 35 questions from Quantitative Aptitude in the SBI Clerical 2016 Prelims examination and 50 questions in the Mains examination. One new feature of the 2016

### Math-2. Lesson 1-2 Solving Single-Unknown Linear Equations

Math-2 Lesson 1-2 Solving Single-Unknown Linear Equations Linear Equation: an equation where all of the letters (either variables or unknown values) have NO EXPONENTS. 4x 2 = 6 2x + 3y = 6 Previous Vocabulary

### Basic ALGEBRA 2 SUMMER PACKET

Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout

### Finding Prime Factors

Section 3.2 PRE-ACTIVITY PREPARATION Finding Prime Factors Note: While this section on fi nding prime factors does not include fraction notation, it does address an intermediate and necessary concept to

### Answers to the problems will be posted on the school website, go to Academics tab, then select Mathematics and select Summer Packets.

Name Geometry SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Geometry. We will use these concepts on a regular basis throughout

### Pre-Algebra. Guided Notes. Unit thru 3-6, 4-3b. Equations

Pre-Algebra Guided Notes Unit 4 3-1 thru 3-6, 4-3b Equations Name Lesson 3-1 Distributive Property Distributive Property used to multiply a number by a sum or difference a(b + c) = Write an equivalent

### addend angle composite number capacity Vocabulary Flash Cards Review Review Review Review Review Review

addend angle area bar graph capacity composite number cubic units difference A figure formed by two rays with the same endpoint A number to be added to another number. 2 or 3 in the sum 2 + 3. A graph

### Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression

1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

### Define a rational expression: a quotient of two polynomials. ..( 3 10) (3 2) Rational expressions have the same properties as rational numbers:

1 UNIT 7 RATIONAL EXPRESSIONS & EQUATIONS Simplifying Rational Epressions Define a rational epression: a quotient of two polynomials. A rational epression always indicates division EX: 10 means..( 10)

### ( )( b + c) = ab + ac, but it can also be ( )( a) = ba + ca. Let s use the distributive property on a couple of

Factoring Review for Algebra II The saddest thing about not doing well in Algebra II is that almost any math teacher can tell you going into it what s going to trip you up. One of the first things they

### Math 90 Lecture Notes Chapter 1

Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,

### Introduction Assignment

PRE-CALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying

### 5) ) y 20 y 10 =

Name Class Date 7.N.4 Develop the laws of exponents for multiplication and division Directions: Rewrite as a base with an exponent. 1) 3 6 3-4 = 2) x 7 x 17 = 3) 10-8 10 3 = 5) 12-3 = -3 12 6) y 20 y 10

### Foundations 5 Curriculum Guide

1. Review: Natural Numbers...3 2. Reading and Writing Natural Numbers...6 3. Lines, Rays, and Line Segments...8 4. Comparing Natural Numbers... 12 5. Rounding Numbers... 15 6. Adding Natural Numbers...

### NS8-1 Factors and Multiples

NS- Factors and Multiples The multiples of a number are the numbers you say when counting by that number. is a multiple of both and 0 is a multiple of both 0 and = 0 = 0 and are both factors of 0 and are

### Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression

1 Words to Review Give an example of the vocabulary word. Numerical expression 5 1 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

### LESSON 6.1 EXPONENTS LESSON 6.1 EXPONENTS 253

LESSON 6.1 EXPONENTS LESSON 6.1 EXPONENTS 5 OVERVIEW Here's what you'll learn in this lesson: Properties of Exponents Definition of exponent, power, and base b. Multiplication Property c. Division Property

### Did you know that some scientists devote their study to one species of animal?

The Think Tank Prime Factorization and Factor Trees Learning Goals In this lesson, you will: Determine the prime factorization of a number. Understand the usefulness of prime factors. Recognize that each

### CHAPTER 1 REVIEW Section 1 - Algebraic Expressions

CHAPTER 1 REVIEW Section 1 - Algebraic Expressions A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable. The terms of an expression are the parts

### MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017

Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest

### 8 th Grade Intensive Math

8 th Grade Intensive Math Ready Florida MAFS Student Edition August-September 2014 Lesson 1 Part 1: Introduction Properties of Integer Exponents Develop Skills and Strategies MAFS 8.EE.1.1 In the past,

### Review of Rational Expressions and Equations

Page 1 of 14 Review of Rational Epressions and Equations A rational epression is an epression containing fractions where the numerator and/or denominator may contain algebraic terms 1 Simplify 6 14 Identification/Analysis

### Student Activity: Finding Factors and Prime Factors

When you have completed this activity, go to Status Check. Pre-Algebra A Unit 2 Student Activity: Finding Factors and Prime Factors Name Date Objective In this activity, you will find the factors and the

### Exponents. Let s start with a review of the basics. 2 5 =

Exponents Let s start with a review of the basics. 2 5 = 2 2 2 2 2 When writing 2 5, the 2 is the base, and the 5 is the exponent or power. We generally think of multiplication when we see a number with

### OPTIONAL: Watch the Flash version of the video for Section 6.1: Rational Expressions (19:09).

UNIT V STUDY GUIDE Rational Expressions and Equations Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to: 3. Perform mathematical operations on polynomials and

### P.1 Prerequisite skills Basic Algebra Skills

P.1 Prerequisite skills Basic Algebra Skills Topics: Evaluate an algebraic expression for given values of variables Combine like terms/simplify algebraic expressions Solve equations for a specified variable

### Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating

Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating