Remember to read the textbook before attempting to do your homework. Answer: 1. Why? x is the same as 1 x, and 1 x = 1x

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Remember to read the textbook before attempting to do your homework. Answer: 1. Why? x is the same as 1 x, and 1 x = 1x"

Transcription

1 Remember to read the textbook before attempting to do your homework. Section.6/.7: Simplifying Expressions Definitions: A variable is a letter used to represent an unknown number, e.g. x, y, z, m, n A number by itself is called a constant, e.g. 5,, 0,, 0.3, 3 5 7,.9, 9 4 A term is a constant or a variable, or a product of constants and variables, e.g., x, x 3, xy, 3 x An algebraic expression is a collection of numbers, variables, grouping symbols and operation symbols such as +,,,. e.g. 3x 6, 3 + [5(m ) + 6], 5xy 3z + 9 To evaluate an expression is to give the expression a numerical value by substituting a value for a variable and simplifying. The numerical coefficient (or coefficient) is the number in front of the variable, e.g. Looking at 7bc, 7 is called the coefficient, and bc is called the variable part. What is the coefficient of the term x 3? Answer: What is the coefficient of the term x? Answer: Why? x is the same as x, and x = x Moral of the story: If there is not a number written next to a variable, then the coefficient is understood to be. What is the coefficient of the term x 3? Answer: What is the coefficient of the term x? Answer: Why? x is the same as x, and x = x Moral of the story: If there is only a negative sign,, next to a variable, then the coefficient is understood to be. Example : Evaluate the expression for the given value of the variable. No calculators allowed. p 3pq + 5; p = 4, q = Please note: The answer is not 45. Example : Panchito needs your help. He has been assigned a set of homework problems. Write down every single problem that he will have to do for that assignment. Note: eoo means every other odd a. 7 odd, 6 0 ALL, 9 53 eoo b eoo No, Ms. Torres has not made a type-o CH LECTURE Notes by M. Torres Pg Math 60 Beginning Algebra

2 Definition: Like terms are terms that are constants, or terms that contain the same variable(s) raised to the same powers. e.g., 5, ¾, 0.5 all constants (numbers) x, 5x, 0.5x all have same variable part x, 4x all have same variable part 6x 3 y z 5, 7x 3 y z 5 all have same variable part FYI: The cool thing about like terms is that we can combine them. Combining Like Terms: To combine like terms, add or subtract their coefficients and keep the same variables with the same exponents. Example 3: Simplify. No calculators allowed. a. 6m m + 5m 8m + 37 b. 3 x 9x 6x + 9x c. (3a + 5a 4) c (3a + 5a 4) can be seen as... means what is the opposite of 3a + 5a 4? (3a + 5a 4) 3a 5a d. 5 x 4 x 7 6 e. n 4n 3 Ans: 4x + 45 Ans: 7 3 n 5 30 (end of Section.6/.7 combo unit, so.6 and.7 are assigned for homework today yay!) CH LECTURE Notes by M. Torres Pg Math 60 Beginning Algebra

3 (Sections.6 and.7, continued ) Are you looking for more math action? Then work on the next page: Math Pizzazz E-6 Prealgebra Review (just in case you wanted to brush up on your prealgebra skills) Sets of Numbers: The set of NATURAL NUMBERS (aka counting numbers) is given by {,, 3, 4, 5, 6, 7, 8, 9, 0,,, 3, 4,, 99, 00, 0, 0, 03,, 099, 00, 0, } The set of WHOLE NUMBERS include the set of natural numbers and 0. {0,,, 3, 4, 5, 6, 7, 8, 9, 0,,, 3,, 99, 00, 0, 0, 03,, 099, 00, 0, } The set of INTEGERS includes the set of whole numbers and their opposites. { 0, 0, 00, 99,, 7, 6, 5, 4, 3,,, 0,,, 3, 4, 5, 6, 7,, 99, 00, 0, 0} Properties of real Numbers If a, b, and c are real numbers, then we have: Commutative Property of Addition: Commutative Property of Multiplication: a + b = b + a e.g. 3 + = + 3 (The order in which we add does not matter) Associative Property of Addition: a + (b + c) = (a + b) + c e.g. + (3 + 4) = ( + 3) + 4 a b = b a e.g. 3 = 3 (The order in which we multiply does not matter) Associative Property of Multiplication: a (b c) = (a b) c e.g. (3 4) = ( 3) 4 The way in which the numbers are grouped does not change their sum Additive Identity: (aka Identity Property of Addition) a + 0 = a, where 0 is the additive identity e.g = = 3 Additive Inverse: (aka Inverse Property of Addition) a + ( a) = 0, where a is the additive inverse e.g. 3 + ( 3) = = 0 Distributive Property (over addition): Note: additive inverse is code for opposite a(b + c) = ab + ac e.g. (x + 3) = x + 3 = x + 6 The way in which the numbers are grouped does not change their product Multiplicative Identity: (aka Identity Property of Multiplication) a = a, where is the multiplicative identity e.g. 3 = 3 3 = 3 Multiplicative Inverse: (aka Inverse Property of Multiplication) a a =, where a e.g. 3 3 = -4 - = 4 Distributive Property (over subtraction): is the multiplicative inverse Note: multiplicative inverse is code for reciprocal a(b c) = ab ac e.g. (x 3) = x 3 = x 6 CH LECTURE Notes by M. Torres Pg 3 Math 60 Beginning Algebra

4 Remember to read the textbook before attempting to do your homework. Bonus Material for Chapter : Translating Verbal Expressions into Variable Expressions (Textbook reference: Section.) Tip: Key terms that you need to feel very comfortable with. Words that are code for... Addition Subtraction Multiplication Division add sum plus more than increased by subtract (from) difference minus less than decreased by less multiply product times twice twice: code for times of divide quotient with fractions and percent The word and is your friend! Why? Because that word separates the terms that you are adding, subtracting, multiplying, or dividing. Warning: Since subtraction is not commutative, you need to be very careful when writing expressions involving subtraction. Whenever you see the word difference, you need to subtract the terms in the order in which they are given. Warning: Since division is not commutative, you need to be very careful when writing expressions involving division. Whenever you see the word quotient, you need to divide the terms in the order in which they are given. Example : Write the algebraic expression described. Let x represent the unknown number. a. Five-ninths of the number e. Eighteen less than a number b. The quotient of eight and a number f. Four less than five times a number c. The sum of twice a number and seven. g. Twenty-six more than ten times a number d. The difference of twelve and fourteen h. The difference of one and twice a number CH LECTURE Notes by M. Torres Pg 4 Math 60 Beginning Algebra

5 Example : Write the algebraic expression described. Let x represent the unknown number. a. Twice the difference of six and a number b. Three times the sum of a number and five c. Six less than twice the difference between a number and seven. d. Eight more than four times the difference of three times a number and negative five. e. The sum of one-eighth of a number and one-twelfth of the number. (You ve reached the official end of Chapter how exciting!!!) Don t forget to start working on today s homework in a timely manner that way you ll be on track to getting the grade that you are willing to earn. You can check out the textbook for FREE through the Library s Reserve System. Instructor also has extra copies of the textbook for you to use during her office times. Wait! Are you looking for more fun? Then work on the attached sheet: Pre-Alg. 4 CH LECTURE Notes by M. Torres Pg 5 Math 60 Beginning Algebra

troduction to Algebra

troduction to Algebra Chapter Three Solving Equations and Problem Solving Section 3.1 Simplifying Algebraic Expressions In algebra letters called variables represent numbers. The addends of an algebraic expression are called

More information

Algebra 1: Topic 1 Notes

Algebra 1: Topic 1 Notes Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating

More information

Sect Properties of Real Numbers and Simplifying Expressions

Sect Properties of Real Numbers and Simplifying Expressions Sect 1.6 - Properties of Real Numbers and Simplifying Expressions Concept #1 Commutative Properties of Real Numbers Ex. 1a.34 + 2.5 Ex. 1b 2.5 + (.34) Ex. 1c 6.3(4.2) Ex. 1d 4.2( 6.3) a).34 + 2.5 = 6.84

More information

A rational number is a number that can be written as where a and b are integers and b 0.

A rational number is a number that can be written as where a and b are integers and b 0. S E L S O N Rational Numbers Goal: Perform operations on rational numbers. Vocabulary Rational number: Additive inverse: A rational number is a number that can be a written as where a and b are integers

More information

Computing with Signed Numbers and Combining Like Terms

Computing with Signed Numbers and Combining Like Terms Section. Pre-Activity Preparation Computing with Signed Numbers and Combining Like Terms One of the distinctions between arithmetic and algebra is that arithmetic problems use concrete knowledge; you know

More information

Section 1.9 Algebraic Expressions: The Distributive Property

Section 1.9 Algebraic Expressions: The Distributive Property Section 1.9 Algebraic Expressions: The Distributive Property Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Apply the Distributive Property.

More information

R.5 Algebraic Expressions

R.5 Algebraic Expressions Section R. Algebraic Expressions 39 R. Algebraic Expressions OBJECTIVES Translate English Expressions into the Language of Mathematics Evaluate Algebraic Expressions 3 Simplify Algebraic Expressions by

More information

MATH REFRESHER I. Notation, Solving Basic Equations, and Fractions. Rockefeller College MPA Welcome Week 2016

MATH REFRESHER I. Notation, Solving Basic Equations, and Fractions. Rockefeller College MPA Welcome Week 2016 MATH REFRESHER I Notation, Solving Basic Equations, and Fractions Rockefeller College MPA Welcome Week 2016 Lucy C. Sorensen Assistant Professor of Public Administration and Policy 1 2 Agenda Why Are You

More information

1.4 Variable Expressions

1.4 Variable Expressions 1.4 Variable Expressions Now that we can properly deal with all of our numbers and numbering systems, we need to turn our attention to actual algebra. Algebra consists of dealing with unknown values. These

More information

Chapter Exam Review for MAT098 - Prealgebra Chapters 1-2: Whole Numbers and Introduction to Algebra & Integers and Introduction to Solving Equations

Chapter Exam Review for MAT098 - Prealgebra Chapters 1-2: Whole Numbers and Introduction to Algebra & Integers and Introduction to Solving Equations Chapter Exam Review for MAT098 - Prealgebra Chapters 1-2: Whole Numbers and Introduction to Algebra & Integers and Introduction to Solving Equations Chapters 1-2 Learning Objectives: In chapter 1 students

More information

4.2 Algebraic Properties: Combining Expressions

4.2 Algebraic Properties: Combining Expressions 4.2 Algebraic Properties: Combining Expressions We begin this section with a summary of the algebraic properties of numbers. Property Name Property Example Commutative property (of addition) Commutative

More information

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form. Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard

More information

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions. Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

More information

3.1. RATIONAL EXPRESSIONS

3.1. RATIONAL EXPRESSIONS 3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers

More information

MATH 90 CHAPTER 1 Name:.

MATH 90 CHAPTER 1 Name:. MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.

More information

The Properties of Signed Numbers Section 1.2 The Commutative Properties If a and b are any numbers,

The Properties of Signed Numbers Section 1.2 The Commutative Properties If a and b are any numbers, 1 Summary DEFINITION/PROCEDURE EXAMPLE REFERENCE From Arithmetic to Algebra Section 1.1 Addition x y means the sum of x and y or x plus y. Some other words The sum of x and 5 is x 5. indicating addition

More information

Summer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2

Summer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2 Summer Math Packet Student Name: Say Hello to Algebra 2 For Students Entering Algebra 2 This summer math booklet was developed to provide students in middle school an opportunity to review grade level

More information

Using the Properties in Computation. a) 347 35 65 b) 3 435 c) 6 28 4 28

Using the Properties in Computation. a) 347 35 65 b) 3 435 c) 6 28 4 28 (1-) Chapter 1 Real Numbers and Their Properties In this section 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS The properties of the real numbers can be helpful when we are doing computations. In this

More information

Algebra 1A and 1B Summer Packet

Algebra 1A and 1B Summer Packet Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the

More information

Math Help and Additional Practice Websites

Math Help and Additional Practice Websites Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade-7 http://www.softschools.com/grades/6th_and_7th.jsp

More information

1.1. Basic Concepts. Write sets using set notation. Write sets using set notation. Write sets using set notation. Write sets using set notation.

1.1. Basic Concepts. Write sets using set notation. Write sets using set notation. Write sets using set notation. Write sets using set notation. 1.1 Basic Concepts Write sets using set notation. Objectives A set is a collection of objects called the elements or members of the set. 1 2 3 4 5 6 7 Write sets using set notation. Use number lines. Know

More information

Placement Test Review Materials for

Placement Test Review Materials for Placement Test Review Materials for 1 To The Student This workbook will provide a review of some of the skills tested on the COMPASS placement test. Skills covered in this workbook will be used on the

More information

Anticipatory Set: Students should know how to add, subtract, multiply and divide positive and negative integers.

Anticipatory Set: Students should know how to add, subtract, multiply and divide positive and negative integers. Lesson Plan Subject: Pre Algebra The Distributive Property Grade Level: 9th Grade Length: 20 minute session Common Core Standards: CCSS.Math.Content.6.EE.A.3 Apply the properties of operations to generate

More information

USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS

USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS 5 (1 5) Chapter 1 Real Numbers and Their Properties 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS In this section The properties of the real numbers can be helpful when we are doing computations. In

More information

USING THE PROPERTIES

USING THE PROPERTIES 8 (-8) Chapter The Real Numbers 6. (xy) (x)y Associative property of multiplication 66. (x ) x Distributive property 67. 4(0.) Multiplicative inverse property 68. 0. 9 9 0. Commutative property of addition

More information

1-2 Properties of Real Numbers

1-2 Properties of Real Numbers 1-2 Properties of Real Numbers Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Simplify. 1. 5+5 0 2. 1 3. 1.81 4. Find 10% of $61.70. $6.17 5. Find the reciprocal of 4. Objective Identify and use properties

More information

CAHSEE on Target UC Davis, School and University Partnerships

CAHSEE on Target UC Davis, School and University Partnerships UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

More information

Simplifying Radical Expressions

Simplifying Radical Expressions In order to simplifying radical expression, it s important to understand a few essential properties. Product Property of Like Bases a a = a Multiplication of like bases is equal to the base raised to the

More information

Equations, Inequalities, Solving. and Problem AN APPLICATION

Equations, Inequalities, Solving. and Problem AN APPLICATION Equations, Inequalities, and Problem Solving. Solving Equations. Using the Principles Together AN APPLICATION To cater a party, Curtis Barbeque charges a $0 setup fee plus $ per person. The cost of Hotel

More information

Algebra I Notes Review Real Numbers and Closure Unit 00a

Algebra I Notes Review Real Numbers and Closure Unit 00a Big Idea(s): Operations on sets of numbers are performed according to properties or rules. An operation works to change numbers. There are six operations in arithmetic that "work on" numbers: addition,

More information

Sect Exponents: Multiplying and Dividing Common Bases

Sect Exponents: Multiplying and Dividing Common Bases 40 Sect 5.1 - Exponents: Multiplying and Dividing Common Bases Concept #1 Review of Exponential Notation In the exponential expression 4 5, 4 is called the base and 5 is called the exponent. This says

More information

1.3 Polynomials and Factoring

1.3 Polynomials and Factoring 1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.

More information

Expressions and Equations

Expressions and Equations Expressions and Equations Standard: CC.6.EE.2 Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y.

More information

MATH Fundamental Mathematics II.

MATH Fundamental Mathematics II. MATH 10032 Fundamental Mathematics II http://www.math.kent.edu/ebooks/10032/fun-math-2.pdf Department of Mathematical Sciences Kent State University December 29, 2008 2 Contents 1 Fundamental Mathematics

More information

P.E.R.T. Math Study Guide

P.E.R.T. Math Study Guide A guide to help you prepare for the Math subtest of Florida s Postsecondary Education Readiness Test or P.E.R.T. P.E.R.T. Math Study Guide www.perttest.com PERT - A Math Study Guide 1. Linear Equations

More information

Summer Math Packet. Number Sense & Math Skills For Students Entering Pre-Algebra. No Calculators!!

Summer Math Packet. Number Sense & Math Skills For Students Entering Pre-Algebra. No Calculators!! Summer Math Packet Number Sense & Math Skills For Students Entering Pre-Algebra No Calculators!! Within the first few days of your Pre-Algebra course you will be assessed on the prerequisite skills outlined

More information

Algebraic Expressions and Equations: Applications I: Translating Words to Mathematical Symbols

Algebraic Expressions and Equations: Applications I: Translating Words to Mathematical Symbols OpenSta-CNX module: m35046 1 Algebraic Epressions and Equations: Applications I: Translating Words to Mathematical Symbols Wade Ellis Denny Burzynski This work is produced by OpenSta-CNX and licensed under

More information

Advanced Algebra Chapter 1. Date Assignment Extra info

Advanced Algebra Chapter 1. Date Assignment Extra info Advanced Algebra Chapter 1 Date Assignment Extra info Expectations/Getting to know you sheets Pg. 9 #16-34(E), 38-48(E), 54, 58 Pg. 15 #19-27 all, 49-62all Pg. 15 #28-35(E), 40-48(E), 72-73 Pg. 24#20-34(E),

More information

Use your TI-84 graphing calculator to check as many problems as possible.

Use your TI-84 graphing calculator to check as many problems as possible. Name: Date: Period: Dear Future Algebra Honors student, We hope that you enjoy your summer vacation to the fullest. We look forward to working with you next year. As you enter your new math class, you

More information

Chapter 1.1 Rational and Irrational Numbers

Chapter 1.1 Rational and Irrational Numbers Chapter 1.1 Rational and Irrational Numbers A rational number is a number that can be written as a ratio or the quotient of two integers a and b written a/b where b 0. Integers, fractions and mixed numbers,

More information

Unit 2 Chapter 2 Section 2 Simplifying Expressions.notebook. October 22, Bellringer. Jul 26 12:38 PM. Jun 6 7:28 PM.

Unit 2 Chapter 2 Section 2 Simplifying Expressions.notebook. October 22, Bellringer. Jul 26 12:38 PM. Jun 6 7:28 PM. Bellringer 1. Get a calculator. Write down tonight's HW. 3. Take out last night's HW Unit packet p. 15 4. Write a variable expression that represents each phrase. Check Your Homework - p.15 a) Eleven more

More information

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

More information

Operations with positive and negative numbers - see first chapter below. Rules related to working with fractions - see second chapter below

Operations with positive and negative numbers - see first chapter below. Rules related to working with fractions - see second chapter below INTRODUCTION If you are uncomfortable with the math required to solve the word problems in this class, we strongly encourage you to take a day to look through the following links and notes. Some of them

More information

Chapter 4 Fractions and Mixed Numbers

Chapter 4 Fractions and Mixed Numbers Chapter 4 Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers Parts of a Fraction Whole numbers are used to count whole things. To refer to a part of a whole, fractions are used.

More information

Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is

More information

MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

More information

Order of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A.

Order of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A. Order of Operations Section 1: Introduction You know from previous courses that if two quantities are added, it does not make a difference which quantity is added to which. For example, 5 + 6 = 6 + 5.

More information

1.6 The Order of Operations

1.6 The Order of Operations 1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

More information

Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.

Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations. Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating

More information

( ) 4, how many factors of 3 5

( ) 4, how many factors of 3 5 Exponents and Division LAUNCH (9 MIN) Before Why would you want more than one way to express the same value? During Should you begin by multiplying the factors in the numerator and the factors in the denominator?

More information

A fraction is a noninteger quantity expressed in terms of a numerator and a denominator.

A fraction is a noninteger quantity expressed in terms of a numerator and a denominator. 1 Fractions Adding & Subtracting A fraction is a noninteger quantity expressed in terms of a numerator and a denominator. 1. FRACTION DEFINITIONS 1) Proper fraction: numerator is less than the denominator.

More information

HFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES

HFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES HFCC Math Lab Beginning Algebra 1 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES Before being able to solve word problems in algebra, you must be able to change words, phrases, and sentences

More information

3. Power of a Product: Separate letters, distribute to the exponents and the bases

3. Power of a Product: Separate letters, distribute to the exponents and the bases Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same

More information

For Students Entering Algebra 1

For Students Entering Algebra 1 Summer Math Packet Student Name: 1 For Students Entering Algebra 1 This summer math booklet was developed to provide students in middle school an opportunity to review grade level math objectives and to

More information

All you have to do is THINK!

All you have to do is THINK! Mathematician s Notes BE A MATHEMATICIAN! All you have to do is THINK! Imagination is more important than knowledge. Albert Einstein We only think when confronted with a problem. John Dewey It s not that

More information

Pre-Algebra Notes: , Absolute Value and Integers. Name: Block: Date: Z = {, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, }

Pre-Algebra Notes: , Absolute Value and Integers. Name: Block: Date: Z = {, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, } Name: Block: Date: Section 2.1: Integers and Absolute Value We remember from our previous lesson that the set Z of integers looks like: Z = {, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, } Why do we care about

More information

Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.

Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}

More information

Improper Fractions and Mixed Numbers

Improper Fractions and Mixed Numbers This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All

More information

Unit 3 Polynomials Study Guide

Unit 3 Polynomials Study Guide Unit Polynomials Study Guide 7-5 Polynomials Part 1: Classifying Polynomials by Terms Some polynomials have specific names based upon the number of terms they have: # of Terms Name 1 Monomial Binomial

More information

MANCHESTER COLLEGE Department of Education. Length: 25 minutes Grade Intended: Pre-Algebra (7 th )

MANCHESTER COLLEGE Department of Education. Length: 25 minutes Grade Intended: Pre-Algebra (7 th ) LESSON PLAN by: Kyler Kearby Lesson: Multiplying and dividing integers MANCHESTER COLLEGE Department of Education Length: 25 minutes Grade Intended: Pre-Algebra (7 th ) Academic Standard: 7.2.1: Solve

More information

Polynomial Identification and Properties of Exponents

Polynomial Identification and Properties of Exponents 2 MODULE 4. INTEGER EXPONENTS AND POLYNOMIALS 4a Polynomial Identification and Properties of Exponents Polynomials We begin with the definition of a term. Term. A term is either a single number (called

More information

Algebra Concept-Readiness Test, Form A

Algebra Concept-Readiness Test, Form A Algebra Concept-Readiness Test, Form A Concept : The Distributive Property Study the concept, and then answer the test questions on the net page. You can use the distributive property to simplify an epression

More information

Expressions Chapter Questions

Expressions Chapter Questions Expressions Chapter Questions 1. Explain how distribution can simplify a problem. 2. What are like terms? 3. How do you combine like terms? NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org Expressions

More information

Properties of Real Numbers

Properties of Real Numbers 16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should

More information

Solving a System of Equations

Solving a System of Equations 11 Solving a System of Equations 11-1 Introduction The previous chapter has shown how to solve an algebraic equation with one variable. However, sometimes there is more than one unknown that must be determined

More information

Radicals - Multiply and Divide Radicals

Radicals - Multiply and Divide Radicals 8. Radicals - Multiply and Divide Radicals Objective: Multiply and divide radicals using the product and quotient rules of radicals. Multiplying radicals is very simple if the index on all the radicals

More information

Chapter 15 Radical Expressions and Equations Notes

Chapter 15 Radical Expressions and Equations Notes Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify

More information

SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS

SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS (Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic

More information

Sierra Verde STEM Academy 8 th Grade Summer Math Packet

Sierra Verde STEM Academy 8 th Grade Summer Math Packet Sierra Verde STEM Academy 8 th Grade Summer Math Packet Dear Incoming 8 th Graders, Please complete this summer math packet prior to the beginning of the 2015-2016 school year. The purpose of the math

More information

Word Problems. Simplifying Word Problems

Word Problems. Simplifying Word Problems Word Problems This sheet is designed as a review aid. If you have not previously studied this concept, or if after reviewing the contents you still don t pass, you should enroll in the appropriate math

More information

Fractions and Linear Equations

Fractions and Linear Equations Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

More information

Radicals - Rational Exponents

Radicals - Rational Exponents 8. Radicals - Rational Exponents Objective: Convert between radical notation and exponential notation and simplify expressions with rational exponents using the properties of exponents. When we simplify

More information

MAT Mathematical Concepts and Applications

MAT Mathematical Concepts and Applications MAT.1180 - Mathematical Concepts and Applications Chapter (Aug, 7) Number Theory: Prime and Composite Numbers. The set of Natural numbers, aka, Counting numbers, denoted by N, is N = {1,,, 4,, 6,...} If

More information

Grade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad

Grade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad Lesson 1&2 6/12/2015 Lesson 3 7/12/2015 Lesson 4 8/12/2015 Lesson 5&6 9/12/2015 Grade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad Date Class Work Home Work 2-1 -find the absolute

More information

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials Algebra Unit 6 Syllabus revised /7/13 1 Objective: Multiply monomials. Simplify expressions involving powers of monomials. Pre-assessment: Exponents, Fractions, and Polynomial Expressions Lesson: Pages

More information

Date: Section P.2: Exponents and Radicals. Properties of Exponents: Example #1: Simplify. a.) 3 4. b.) 2. c.) 3 4. d.) Example #2: Simplify. b.) a.

Date: Section P.2: Exponents and Radicals. Properties of Exponents: Example #1: Simplify. a.) 3 4. b.) 2. c.) 3 4. d.) Example #2: Simplify. b.) a. Properties of Exponents: Section P.2: Exponents and Radicals Date: Example #1: Simplify. a.) 3 4 b.) 2 c.) 34 d.) Example #2: Simplify. a.) b.) c.) d.) 1 Square Root: Principal n th Root: Example #3: Simplify.

More information

Mathematics Placement

Mathematics Placement Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

More information

Actually, if you have a graphing calculator this technique can be used to find solutions to any equation, not just quadratics. All you need to do is

Actually, if you have a graphing calculator this technique can be used to find solutions to any equation, not just quadratics. All you need to do is QUADRATIC EQUATIONS Definition ax 2 + bx + c = 0 a, b, c are constants (generally integers) Roots Synonyms: Solutions or Zeros Can have 0, 1, or 2 real roots Consider the graph of quadratic equations.

More information

MATH 65 NOTEBOOK CERTIFICATIONS

MATH 65 NOTEBOOK CERTIFICATIONS MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1

More information

Simplifying Algebraic Fractions

Simplifying Algebraic Fractions 5. Simplifying Algebraic Fractions 5. OBJECTIVES. Find the GCF for two monomials and simplify a fraction 2. Find the GCF for two polynomials and simplify a fraction Much of our work with algebraic fractions

More information

Clifton High School Mathematics Summer Workbook Algebra 1

Clifton High School Mathematics Summer Workbook Algebra 1 1 Clifton High School Mathematics Summer Workbook Algebra 1 Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature: Parent Signature:

More information

PREPARATION FOR MATH TESTING at CityLab Academy

PREPARATION FOR MATH TESTING at CityLab Academy PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRE-TEST

More information

Multiply and Divide Mixed Numbers and Complex Fractions

Multiply and Divide Mixed Numbers and Complex Fractions OpenStax Staging module: m00 Multiply and Divide Mixed Numbers and Complex Fractions Words Numbers This work is produced by OpenStax Staging and licensed under the Creative Commons Attribution License.0

More information

IV. ALGEBRAIC CONCEPTS

IV. ALGEBRAIC CONCEPTS IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other

More information

Exponents, Polynomials and Functions. Copyright Cengage Learning. All rights reserved.

Exponents, Polynomials and Functions. Copyright Cengage Learning. All rights reserved. Exponents, Polynomials and Functions 3 Copyright Cengage Learning. All rights reserved. 3.1 Rules for Exponents Copyright Cengage Learning. All rights reserved. Rules for Exponents The basic concept of

More information

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers HFCC Math Lab Arithmetic - Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.

More information

Algebra Cheat Sheets

Algebra Cheat Sheets Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts

More information

Algebra I Teacher Notes Expressions, Equations, and Formulas Review

Algebra I Teacher Notes Expressions, Equations, and Formulas Review Big Ideas Write and evaluate algebraic expressions Use expressions to write equations and inequalities Solve equations Represent functions as verbal rules, equations, tables and graphs Review these concepts

More information

GRE MATH REVIEW #5. 1. Variable: A letter that represents an unknown number.

GRE MATH REVIEW #5. 1. Variable: A letter that represents an unknown number. GRE MATH REVIEW #5 Eponents and Radicals Many numbers can be epressed as the product of a number multiplied by itself a number of times. For eample, 16 can be epressed as. Another way to write this is

More information

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

More information

CAHSEE on Target UC Davis, School and University Partnerships

CAHSEE on Target UC Davis, School and University Partnerships UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

More information

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

More information

Linear Equations in One Variable

Linear Equations in One Variable Linear Equations in One Variable MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this section we will learn how to: Recognize and combine like terms. Solve

More information

Combined Operations 150 UNIT 5 COMBINED OPERATIONS. This yacht is propelled by a sail, a motor, or both.

Combined Operations 150 UNIT 5 COMBINED OPERATIONS. This yacht is propelled by a sail, a motor, or both. UNIT 5 Combined Operations This yacht is propelled by a sail, a motor, or both. 150 UNIT 5 COMBINED OPERATIONS Many yachts can be powered by the wind, by a gas engine, or both. A hybrid automobile can

More information

Free Pre-Algebra Lesson 24 page 1

Free Pre-Algebra Lesson 24 page 1 Free Pre-Algebra Lesson page 1 Lesson Equations with Negatives You ve worked with equations for a while now, and including negative numbers doesn t really change any of the rules. Everything you ve already

More information

Chapter 13: Polynomials

Chapter 13: Polynomials Chapter 13: Polynomials We will not cover all there is to know about polynomials for the math competency exam. We will go over the addition, subtraction, and multiplication of polynomials. We will not

More information

equals equals equals equals

equals equals equals equals Addition of Integers Rules Same Sign ---------------- Add --------------- Keep the Sign Different Signs -------- Subtract ------- Take the sign of the integer with the larger absolute value plus plus plus

More information

Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4)

Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) Chapter 2: Functions and Linear Functions 1. Know the definition of a relation. Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) 2. Know the definition of a function. 3. What

More information

MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006

MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006 MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions Created January 7, 2006 Math 092, Elementary Algebra, covers the mathematical content listed below. In order

More information