1.8 Intro to Variables, Algebraic Expressions, and Equations

Size: px
Start display at page:

Download "1.8 Intro to Variables, Algebraic Expressions, and Equations"

Transcription

1 1.8 Intro to Variables, Algebraic Expressions, and Equations Professor Tim Busken M.S. Applied Mathematics with a Concentration in Dynamical Systems San Diego State University 2011 Southwestern College Math Faculty February 18, 2012

2 Talk Outline 1 Objective A: Evaluate Algebraic Expressions.

3 Talk Outline 1 Objective A: Evaluate Algebraic Expressions. 2 Objective B: Identify Solutions of Equations.

4 Talk Outline 1 Objective A: Evaluate Algebraic Expressions. 2 Objective B: Identify Solutions of Equations. 3 Objective C: Translate Phrases into Variable Expressions.

5 Section 1 Objective A: Evaluate Algebraic Expressions.

6 Definition +,,, and are called the arithmetic operations

7 Definition +,,, and are called the arithmetic operations Definition A variable is a symbol or letter used to represent a number, or set of numbers.

8 Definition +,,, and are called the arithmetic operations Definition A variable is a symbol or letter used to represent a number, or set of numbers. Definition A combination of arithmetic operations on variables and numbers is called an algebraic expression or expression.

9 If two variables or a number and a variable are next to each other, with no operations sign between them, the operation is multiplication. For example, 2x means 2 x and xy or x(y) means x y

10 Also, the meaning of an exponent remains the same when the base is a variable.

11 Also, the meaning of an exponent remains the same when the base is a variable. For example, x 2 = x }{{} x and y 5 = y y y y y }{{} 2 factors of x 5 factors of y

12 Also, the meaning of an exponent remains the same when the base is a variable. For example, x 2 = x }{{} x and y 5 = y y y y y }{{} 2 factors of x 5 factors of y Algebraic expressions such as 4x have different values depending on replacement values for x.

13 Also, the meaning of an exponent remains the same when the base is a variable. For example, x 2 = x }{{} x and y 5 = y y y y y }{{} 2 factors of x 5 factors of y Algebraic expressions such as 4x have different values depending on replacement values for x. For instance, if x = 3, then 4x becomes 4x = 4 3 = 12.

14 If x = 5, then 4x becomes 4x = 4 5 = 20.

15 If x = 5, then 4x becomes 4x = 4 5 = 20. Definition Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression for the variable.

16 If x = 5, then 4x becomes 4x = 4 5 = 20. Definition Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression for the variable. When finding the value of an expression, remember to follow the Order of Operations.

17 The Order of the Arithmetic Operations When evaluating or simplifying an algebraic or arithmetic expression, we always use the ORDER OF OPERATIONS. In other words we evaluate the expression in the following order: P Parenthesis E Exponents M Multiplication D Division A Addition S Subtraction The operations +,,, must be performed from left to right! The acronym PEMDAS helps us to recall the ORDER OF OPERATIONS.

Lesson 1: Arithmetic Review

Lesson 1: Arithmetic Review In this lesson we step back and review several key arithmetic topics that are extremely relevant to this course. Before we work with algebraic expressions and equations, it is important to have a good

More information

Working with Algebraic Expressions

Working with Algebraic Expressions 2 Working with Algebraic Expressions This chapter contains 25 algebraic expressions; each can contain up to five variables. Remember that a variable is just a letter that represents a number in a mathematical

More information

The Order of Operations. Unit 1 Lesson 3

The Order of Operations. Unit 1 Lesson 3 Unit 1 Lesson 3 Students will be able to: Perform arithmetic operations, including those involving whole-number exponents, in the conventional order. Key Vocabulary: Parentheses, exponents, multiplication,

More information

Lesson 1: Arithmetic Review

Lesson 1: Arithmetic Review Lesson 1: Arithmetic Review Topics and Objectives: Order of Operations Fractions o Improper fractions and mixed numbers o Equivalent fractions o Fractions in simplest form o One and zero Operations on

More information

Algebra 1 Review. Properties of Real Numbers. Algebraic Expressions

Algebra 1 Review. Properties of Real Numbers. Algebraic Expressions Algebra 1 Review Properties of Real Numbers Algebraic Expressions Real Numbers Natural Numbers: 1, 2, 3, 4,.. Numbers used for counting Whole Numbers: 0, 1, 2, 3, 4,.. Natural Numbers and 0 Integers:,

More information

Summer Assignment Glossary

Summer Assignment Glossary Algebra 1.1 Summer Assignment Name: Date: Hour: Directions: Show all work for full credit using a pencil. Circle your final answer. This assignment is due the first day of school. Use the summer assignment

More information

Exponents. Reteach. Write each expression in exponential form (0.4)

Exponents. Reteach. Write each expression in exponential form (0.4) 9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,

More information

Mini-Lesson 1. Section 1.1: Order of Operations PEMDAS

Mini-Lesson 1. Section 1.1: Order of Operations PEMDAS Name: Date: 1 Section 1.1: Order of Operations PEMDAS If we are working with a mathematical expression that contains more than one operation, then we need to understand how to simplify. The acronym PEMDAS

More information

SAMLab Tip Sheet #1 Translating Mathematical Formulas Into Excel s Language

SAMLab Tip Sheet #1 Translating Mathematical Formulas Into Excel s Language Translating Mathematical Formulas Into Excel s Language Introduction Microsoft Excel is a very powerful calculator; you can use it to compute a wide variety of mathematical expressions. Before exploring

More information

Algebraic Expressions & Models L1.2. Welcome Back! Get your stuff out and be ready to go when the bell rings!

Algebraic Expressions & Models L1.2. Welcome Back! Get your stuff out and be ready to go when the bell rings! Welcome Back! Get your stuff out and be ready to go when the bell rings! 1 2 Variable: 3 Variable: Letter that represents one or more numbers 4 Variable: Letter that represents one or more numbers Expression:

More information

Section 3.1 Variables, Expressions and Order of Operations

Section 3.1 Variables, Expressions and Order of Operations Section.1 Variables, Expressions and Order of Operations A variable is a symbol, usually a letter of the alphabet that represents some varying or undetermined number. An algebraic expression is a mathematical

More information

2.2 Order of Operations

2.2 Order of Operations 2.2 Order of Operations Learning Objectives Evaluate algebraic expressions with grouping symbols. Evaluate algebraic expressions with fraction bars. Evaluate algebraic expressions using a graphing calculator.

More information

Watkins Mill High School. Algebra 2. Math Challenge

Watkins Mill High School. Algebra 2. Math Challenge Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking

More information

TI-84+ GC 3: Order of Operations, Additional Parentheses, Roots and Absolute Value

TI-84+ GC 3: Order of Operations, Additional Parentheses, Roots and Absolute Value Rev 6--11 Name Date TI-84+ GC : Order of Operations, Additional Parentheses, Roots and Absolute Value Objectives: Review the order of operations Observe that the GC uses the order of operations Use parentheses

More information

George Hartas, MS. Educational Assistant for Mathematics Remediation. MAT 025 Instructor. Table of Contents

George Hartas, MS. Educational Assistant for Mathematics Remediation. MAT 025 Instructor. Table of Contents Last Updated: 6/14/18 SIGNED NUMBERS WORKBOOK By George Hartas, MS Educational Assistant for Mathematics Remediation MAT 025 Instructor Table of Contents Page Introduction 2 Anatomy of a Signed Number

More information

2. If x = 3, then what is the. 1. If x = 4, then what is the value of x 2? We will evaluate 1 expressions by using the order of operations.

2. If x = 3, then what is the. 1. If x = 4, then what is the value of x 2? We will evaluate 1 expressions by using the order of operations. Learning Objective We will evaluate 1 expressions by using the order of operations. Name: February 18, 2014 Per: Common Core 7.AF1.2 Activate Prior Knowledge CFU Substitution means to replace a variable

More information

7th Grade Math Unit 1 Algebraic Reasoning

7th Grade Math Unit 1 Algebraic Reasoning 7th Grade Math Unit 1 Algebraic Reasoning Name: Period: Common Core State Standards CC.7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers;

More information

Chapter 1: Foundations for Algebra

Chapter 1: Foundations for Algebra Chapter 1: Foundations for Algebra Dear Family, The student will follow the order of operations, a set of rules that standardize how to simplify expressions. Order of Operations 1. Perform operations within

More information

ALGEBRA I Summer Packet

ALGEBRA I Summer Packet ALGEBRA I Summer Packet 2018-2019 Name 7 th Grade Math Teacher: Objectives for Algebra I Summer Packet I. Variables and translating (Problems #1 5) Write Algebraic Expressions Writing Algebraic Equations

More information

CCBC Math 081 Order of Operations Section 1.7. Step 2: Exponents and Roots Simplify any numbers being raised to a power and any numbers under the

CCBC Math 081 Order of Operations Section 1.7. Step 2: Exponents and Roots Simplify any numbers being raised to a power and any numbers under the CCBC Math 081 Order of Operations 1.7 1.7 Order of Operations Now you know how to perform all the operations addition, subtraction, multiplication, division, exponents, and roots. But what if we have a

More information

How to Do Word Problems. Building the Foundation

How to Do Word Problems. Building the Foundation Building the Foundation The notion that Mathematics is a language, is held by many mathematicians and is being expressed on frequent occasions. Mathematics is the language of science. It is unique among

More information

Think: 5 5 5, or 25. Think: Think: Evaluate Multiply. So, when s 2, the value of. 5(s 3) is 125. Then divide.

Think: 5 5 5, or 25. Think: Think: Evaluate Multiply. So, when s 2, the value of. 5(s 3) is 125. Then divide. 7 Multiply first. Think: 9 8 Then divide. Think: 8 Finally, subtract. Think: Replace a with 9. o, when a 9, the value of a is. 8 9 a ubtract.. Replace a with 5. The value of a is a a 5 b Add. is Divide.

More information

Welcome to 5 th Grade Math Review Properties of Operations

Welcome to 5 th Grade Math Review Properties of Operations Welcome to 5 th Grade Math Review Properties of Operations What do you notice in this chart? Are there any patterns? Powers of Ten Strategy Time Interactive Math Journal Today s Lesson: Review of Properties

More information

Key Terms. Writing Algebraic Expressions. Example

Key Terms. Writing Algebraic Expressions. Example Chapter 6 Summary Key Terms variable (6.1) algebraic expression (6.1) evaluate an algebraic expression (6.1) Distributive Property of Multiplication over Addition (6.2) Distributive Property of Multiplication

More information

Equations and Problem Solving with Fractions. Variable. Expression. Equation. A variable is a letter used to represent a number.

Equations and Problem Solving with Fractions. Variable. Expression. Equation. A variable is a letter used to represent a number. MAT 040: Basic Math Equations and Problem Solving with Fractions Variable A variable is a letter used to represent a number. Expression An algebraic expression is a combination of variables and/or numbers

More information

Shell Script Programming

Shell Script Programming C h a p t e r 5 Programming In this chapter, you will learn the following to World Class standards: 1. s 2. Variables 3. Operations 4. Creating an Executable 5-1 Introduction to s A shell script is a text

More information

Pre-Algebra Notes Unit One: Variables, Expressions, and Integers

Pre-Algebra Notes Unit One: Variables, Expressions, and Integers Pre-Algebra Notes Unit One: Variables, Expressions, and Integers Evaluating Algebraic Expressions Syllabus Objective: (.) The student will evaluate variable and numerical expressions using the order of

More information

Power Standard 5 Practice Test

Power Standard 5 Practice Test Name Date 1) Variable a. A symbol that is used to represent a number. b. A symbol that is used to represent another symbol. c. A number that is used to represent a symbol. 2) Expression Power Standard

More information

The Distributive Property and Expressions Understand how to use the Distributive Property to Clear Parenthesis

The Distributive Property and Expressions Understand how to use the Distributive Property to Clear Parenthesis Objective 1 The Distributive Property and Expressions Understand how to use the Distributive Property to Clear Parenthesis The Distributive Property The Distributive Property states that multiplication

More information

Fractions. There are several terms that are commonly used when working with fractions.

Fractions. There are several terms that are commonly used when working with fractions. Chapter 0 Review of Arithmetic Fractions There are several terms that are commonly used when working with fractions. Fraction: The ratio of two numbers. We use a division bar to show this ratio. The number

More information

Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework

Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework 1 T 8/30 Introductions Operations on Decimals Converting Decimals

More information

GUIDELINES FOR COMPLETING THE ASSIGNMENT

GUIDELINES FOR COMPLETING THE ASSIGNMENT RAHWAY HIGH SCHOOL MATHEMATICS DEPARTMENT Algebra 1 Summer Assignment packet Summer 2018 Due date: September 7th GUIDELINES FOR COMPLETING THE ASSIGNMENT This packet was created to help you succeed in

More information

Only to be used for arranged hours. Order of Operations

Only to be used for arranged hours. Order of Operations Math 84 Activity # 1 Your name: Order of Operations Goals: 1) Evaluate Real numbers with Exponents. ) Use the Order of Operations to Evaluate Expressions. ) Review Exponents and Powers of Ten Integer exponents

More information

Due Date: Friday, September 9 th Attached is your summer review packet for the Algebra 1 course.

Due Date: Friday, September 9 th Attached is your summer review packet for the Algebra 1 course. Due Date: Friday, September 9 th Attached is your summer review packet for the Algebra 1 course. This is your first Graded HW grade. You MUST SHOW WORK in order to receive credit. This means if you typed

More information

Section 1.8. Simplifying Expressions

Section 1.8. Simplifying Expressions Section 1.8 Simplifying Expressions But, first Commutative property: a + b = b + a; a * b = b * a Associative property: (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) Distributive property: a * (b

More information

1.1 Review of Place Value

1.1 Review of Place Value 1 1.1 Review of Place Value Our decimal number system is based upon powers of ten. In a given whole number, each digit has a place value, and each place value consists of a power of ten. Example 1 Identify

More information

Project 2: How Parentheses and the Order of Operations Impose Structure on Expressions

Project 2: How Parentheses and the Order of Operations Impose Structure on Expressions MAT 51 Wladis Project 2: How Parentheses and the Order of Operations Impose Structure on Expressions Parentheses show us how things should be grouped together. The sole purpose of parentheses in algebraic

More information

Course PJL. Arithmetic Operations

Course PJL. Arithmetic Operations Outline Oman College of Management and Technology Course 503200 PJL Handout 5 Arithmetic Operations CS/MIS Department 1 // Fig. 2.9: Addition.java 2 // Addition program that displays the sum of two numbers.

More information

Prefix/Infix/Postfix Notation

Prefix/Infix/Postfix Notation Prefix/Infix/Postfix Notation One commonly writes arithmetic expressions, such as 3 + 4 * (5-2) in infix notation which means that the operator is placed in between the two operands. In this example, the

More information

Objective Simplify expressions using the properties of exponents.

Objective Simplify expressions using the properties of exponents. Pre-Algebra: Exponent Properties Objective Simplify expressions using the properties of exponents. Exponents are used to simplify expressions. For example, a*a*a*a*a*a*a is the expanded expression of a

More information

Algebra II Chapter 6: Rational Exponents and Radical Functions

Algebra II Chapter 6: Rational Exponents and Radical Functions Algebra II Chapter 6: Rational Exponents and Radical Functions Chapter 6 Lesson 1 Evaluate nth Roots and Use Rational Exponents Vocabulary 1 Example 1: Find nth Roots Note: and Example 2: Evaluate Expressions

More information

MAT 003 Brian Killough s Instructor Notes Saint Leo University

MAT 003 Brian Killough s Instructor Notes Saint Leo University MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample

More information

Lesson 2b Functions and Function Operations

Lesson 2b Functions and Function Operations As we continue to work with more complex functions it is important that we are comfortable with Function Notation, opertions on Functions and opertions involving more than one function. In this lesson,

More information

Algebraic Expressions

Algebraic Expressions P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation Objectives: Evaluate algebraic expressions, find intersection and unions of sets, simplify algebraic

More information

1.1 evaluating expressions 2017 ink.notebook. August 18, page 7 page 8 Unit 1 Basic Equations and Inequalities. 1.1 Order of Operations.

1.1 evaluating expressions 2017 ink.notebook. August 18, page 7 page 8 Unit 1 Basic Equations and Inequalities. 1.1 Order of Operations. 1.1 evaluating expressions 2017 ink.notebook page 7 page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 page 10 Lesson Objectives Standards 1.1 Order of Operations Press the tabs

More information

1-6 Order of Operations

1-6 Order of Operations 1-6 Order of Operations Warm Up Lesson Presentation Lesson Quiz 2 pts 3 pts Bell Quiz 1-6 Find each square root. 1. 25 Write all classifications that apply to each real number. 3. -55 5 pts possible Questions

More information

Math 1 Variable Manipulation Part 2 Exponents & Roots

Math 1 Variable Manipulation Part 2 Exponents & Roots Math 1 Variable Manipulation Part 2 Exponents & Roots 1 PRE-ALGEBRA REVIEW: WORKING WITH EXPONENTS Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts

More information

Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties

Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties Chapter 3: Arithmetic Properties CHAPTER 3: ARITHMETIC PROPERTIES Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Arithmetic Properties Date: Lesson: Learning Log Title:

More information

MAT 1033C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade)

MAT 1033C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade) MAT 0C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade) Name Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers

More information

MAT 090 Brian Killough s Instructor Notes Strayer University

MAT 090 Brian Killough s Instructor Notes Strayer University MAT 090 Brian Killough s Instructor Notes Strayer University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample

More information

ARITHMETIC EXPRESSION

ARITHMETIC EXPRESSION Section 1: Expression & Terms MATH LEVEL 2 LESSON PLAN 1 ARITHMETIC EXPRESSION 2017 Copyright Vinay Agarwala, Revised: 10/31/17 1. An arithmetic expression is made up of numbers joined by addition (+),

More information

Fraction to Percents Change the fraction to a decimal (see above) and then change the decimal to a percent (see above).

Fraction to Percents Change the fraction to a decimal (see above) and then change the decimal to a percent (see above). PEMDAS This is an acronym for the order of operations. Order of operations is the order in which you complete problems with more than one operation. o P parenthesis o E exponents o M multiplication OR

More information

Module 7 Highlights. Mastered Reviewed. Sections ,

Module 7 Highlights. Mastered Reviewed. Sections , Sections 5.3 5.6, 6.1 6.6 Module 7 Highlights Andrea Hendricks Math 0098 Pre-college Algebra Topics Degree & leading coeff. of a univariate polynomial (5.3, Obj. 1) Simplifying a sum/diff. of two univariate

More information

College Prep Algebra II Summer Packet

College Prep Algebra II Summer Packet Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When

More information

3. Replace any row by the sum of that row and a constant multiple of any other row.

3. Replace any row by the sum of that row and a constant multiple of any other row. Math Section. Section.: Solving Systems of Linear Equations Using Matrices As you may recall from College Algebra or Section., you can solve a system of linear equations in two variables easily by applying

More information

Working with Rational Expressions

Working with Rational Expressions Working with Rational Expressions Return to Table of Contents 4 Goals and Objectives Students will simplify rational expressions, as well as be able to add, subtract, multiply, and divide rational expressions.

More information

Solution Guide for Chapter 2

Solution Guide for Chapter 2 Solution Guide for Chapter 2 Here are the solutions for the Doing the Math exercises in Kiss My Math! DTM from p.27 2. 39 + (39 + 58) =? The only operation here is addition (that negative sign is not subtraction,

More information

Beginning and Intermediate Algebra Chapter 0: Arithmetic

Beginning and Intermediate Algebra Chapter 0: Arithmetic Beginning and Intermediate Algebra Chapter 0: Arithmetic An open source (CC-BY) textbook by Tyler Wallace 1 ? Beginning and Intermediate Algebra by Tyler Wallace is licensed under a Creative Commons Attribution

More information

Section 2 0: The Rectangular Coordinate System. The Coordinate System

Section 2 0: The Rectangular Coordinate System. The Coordinate System Section 2 : The Rectangular Coordinate System The rectangular coordinate system is based on two number lines. A horizontal line called the x axis and a vertical line called the y axis. Each axis has marks

More information

Using Variables to Write Pattern Rules

Using Variables to Write Pattern Rules Using Variables to Write Pattern Rules Goal Use numbers and variables to represent mathematical relationships. 1. a) What stays the same and what changes in the pattern below? b) Describe the pattern rule

More information

The simplest way to evaluate the expression is simply to start at the left and work your way across, keeping track of the total as you go:

The simplest way to evaluate the expression is simply to start at the left and work your way across, keeping track of the total as you go: ck 12 Chapter 1 Order of Operations Learning Objectives Evaluate algebraic expressions with grouping symbols. Evaluate algebraic expressions with fraction bars. Evaluate algebraic expressions with a graphing

More information

Meeting 1 Introduction to Functions. Part 1 Graphing Points on a Plane (REVIEW) Part 2 What is a function?

Meeting 1 Introduction to Functions. Part 1 Graphing Points on a Plane (REVIEW) Part 2 What is a function? Meeting 1 Introduction to Functions Part 1 Graphing Points on a Plane (REVIEW) A plane is a flat, two-dimensional surface. We describe particular locations, or points, on a plane relative to two number

More information

Evaluating Expressions Using the Order of Operations

Evaluating Expressions Using the Order of Operations Section 6. PRE-ACTIVITY PREPARATION Evaluating Expressions Using the Order of Operations Sales of admission tickets to the family concert were as follows: 50 adult tickets sold for $5 each, 00 youth tickets

More information

Hi. I m a three. I m always a three. I never ever change. That s why I m a constant.

Hi. I m a three. I m always a three. I never ever change. That s why I m a constant. Lesson 1-1: 1 1: Evaluating Expressions Hi. I m a three. I m always a three. I never ever change. That s why I m a constant. 3 Real life changes, though. So to talk about real life, math needs things that

More information

Operations and Properties

Operations and Properties . Operations and Properties. OBJECTIVES. Represent the four arithmetic operations using variables. Evaluate expressions using the order of operations. Recognize and apply the properties of addition 4.

More information

1 Basic Mathematical Operations

1 Basic Mathematical Operations 1 Basic Mathematical Operations Recall the basic operations of addition, substraction, multiplication, and division. Consider evaluating the following expression: 2+3 5 Do we add 2 and 3 first or do we

More information

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 15 Dividing Expressions

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 15 Dividing Expressions Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Please watch Section 15 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item67.cfm

More information

Odd-Numbered Answers to Exercise Set 1.1: Numbers

Odd-Numbered Answers to Exercise Set 1.1: Numbers Odd-Numbered Answers to Exercise Set.: Numbers. (a) Composite;,,, Prime Neither (d) Neither (e) Composite;,,,,,. (a) 0. 0. 0. (d) 0. (e) 0. (f) 0. (g) 0. (h) 0. (i) 0.9 = (j). (since = ) 9 9 (k). (since

More information

Lecture 3 Operators MIT AITI

Lecture 3 Operators MIT AITI Lecture 3 Operators MIT AITI - 2004 What are Operators? Operators are special symbols used for mathematical functions assignment statements logical comparisons Examples: 3 + 5 // uses + operator 14 + 5

More information

!"!!!"!!"!! = 10!!!!!(!!) = 10! = 1,000,000

!!!!!!!! = 10!!!!!(!!) = 10! = 1,000,000 Math Review for AP Chemistry The following is a brief review of some of the math you should remember from your past. This is meant to jog your memory and not to teach you something new. If you find you

More information

1. Variables 2. Arithmetic 3. Input and output 4. Problem solving: first do it by hand 5. Strings 6. Chapter summary

1. Variables 2. Arithmetic 3. Input and output 4. Problem solving: first do it by hand 5. Strings 6. Chapter summary Topic 2 1. Variables 2. Arithmetic 3. Input and output 4. Problem solving: first do it by hand 5. Strings 6. Chapter summary Arithmetic Operators C++ has the same arithmetic operators as a calculator:

More information

(2 1) What does evaluate to? What does evaluate to? What does evaluate to?

(2 1) What does evaluate to? What does evaluate to? What does evaluate to? Order of Operations (Time 20 minutes) Math is a language, just like English, Spanish, or any other language. We use nouns, like "bread", "tomato", "mustard" and "cheese" to describe physical objects. Math

More information

Advanced Algebra I Simplifying Expressions

Advanced Algebra I Simplifying Expressions Page - 1 - Name: Advanced Algebra I Simplifying Expressions Objectives The students will be able to solve problems using order of operations. The students will identify expressions and write variable expressions.

More information

Learning Packet. Lesson 6 Exponents and Rational Functions THIS BOX FOR INSTRUCTOR GRADING USE ONLY

Learning Packet. Lesson 6 Exponents and Rational Functions THIS BOX FOR INSTRUCTOR GRADING USE ONLY Learning Packet Student Name Due Date Class Time/Day Submission Date THIS BOX FOR INSTRUCTOR GRADING USE ONLY Mini-Lesson is complete and information presented is as found on media links (0 5 pts) Comments:

More information

Math 154 :: Elementary Algebra

Math 154 :: Elementary Algebra Math 4 :: Elementary Algebra Section 8. Section 8. Section 8. Section 8.4 Section 8. Section 8.6 Math 4 :: Elementary Algebra Section 8. Fraction Review. This answer should be in your own words.. This

More information

NUMBER SENSE AND OPERATIONS. Competency 0001 Understand the structure of numeration systems and multiple representations of numbers.

NUMBER SENSE AND OPERATIONS. Competency 0001 Understand the structure of numeration systems and multiple representations of numbers. SUBAREA I. NUMBER SENSE AND OPERATIONS Competency 0001 Understand the structure of numeration systems and multiple representations of numbers. Prime numbers are numbers that can only be factored into 1

More information

Lesson 6a Exponents and Rational Functions

Lesson 6a Exponents and Rational Functions Lesson 6a Eponents and Rational Functions In this lesson, we put quadratics aside for the most part (not entirely) in this lesson and move to a study of eponents and rational functions. The rules of eponents

More information

Doing Math: Scientific Notation Scientific notation is a way to show (and do math with) very small or very large numbers b 10 c

Doing Math: Scientific Notation Scientific notation is a way to show (and do math with) very small or very large numbers b 10 c Doing Math: Scientific Notation Scientific notation is a way to show (and do math with) very small or very large numbers b 10 c b = a decimal number between 1.0 and 9.99... c =anexponentof10 Example: 1.53

More information

Table of Contents. Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1

Table of Contents. Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1 Table of Contents Table of Contents Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1 Chapter 1: Real Numbers...5 Real Numbers...5 Checking Progress: Real Numbers...8

More information

ISA 563 : Fundamentals of Systems Programming

ISA 563 : Fundamentals of Systems Programming ISA 563 : Fundamentals of Systems Programming Variables, Primitive Types, Operators, and Expressions September 4 th 2008 Outline Define Expressions Discuss how to represent data in a program variable name

More information

Hello, World and Variables

Hello, World and Variables Hello, World and Variables Hello, World! The most basic program in any language (Python included) is often considered to be the Hello, world! statement. As it s name would suggest, the program simply returns

More information

Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions

Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions Variable is a letter or symbol that represents a number. Variable (algebraic)

More information

MATH REVIEW SUPPLEMENT. For The ARITHMETIC SECTION. of the. ACCUPLACER Entry Assessment

MATH REVIEW SUPPLEMENT. For The ARITHMETIC SECTION. of the. ACCUPLACER Entry Assessment Assessment Center MATH REVIEW SUPPLEMENT For The ARITHMETIC SECTION of the ACCUPLACER Entry Assessment Visit The Assessment Center At http://www.stlcc.cc.mo.us/mc/services/assess/index.html This document

More information

Algebra2go: Working with Fractions and Mixed Numbers

Algebra2go: Working with Fractions and Mixed Numbers Algebrago: Working with Fractions and Mixed Numbers Algebrago Review of Fractions. Understand Fractions on a Number Line Fractions are used to represent quantities between the whole numbers on a number

More information

6th Grade Math. Lindsay Law - Curriculum Facilitator (ext. 2085)

6th Grade Math. Lindsay Law - Curriculum Facilitator (ext. 2085) 6th Grade Math Purpose Students will become flexible thinkers and complex problem solvers by applying essential mathematical ideas and concepts through a rigorous, focused, and relevant curriculum. Philosophy

More information

MONTHLY SYLLABUS SESSION CLASS-VII SUBJECT : MATHEMATICS TERM-I (PRATIBHA)

MONTHLY SYLLABUS SESSION CLASS-VII SUBJECT : MATHEMATICS TERM-I (PRATIBHA) MONTHLY SYLLABUS SESSION-2017-18 CLASS-VII SUBJECT : MATHEMATICS MONTH TERM-I (PRATIBHA) April 2017 May 2017 July 2017 Chapter 1: Integers Introduction, Recall, Properties of addition and subtraction of

More information

Chapter 0, Pre-Algebra from Beginning and Intermediate Algebra by Tyler Wallace is available under a Creative Commons Attribution 3.

Chapter 0, Pre-Algebra from Beginning and Intermediate Algebra by Tyler Wallace is available under a Creative Commons Attribution 3. Chapter 0, Pre-Algebra from Beginning and Intermediate Algebra by Tyler Wallace is available under a Creative Commons Attribution 3.0 Unported license. 2010. 0.1 Pre-Algebra - Integers Objective: Add,

More information

Fundamentals of Programming CS-110. Lecture 3

Fundamentals of Programming CS-110. Lecture 3 Fundamentals of Programming CS-110 Lecture 3 Operators Operators Operators are words or symbols that cause a program to do something to variables. OPERATOR TYPES: Type Operators Usage Arithmetic + - *

More information

Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008

Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008 MATH-LITERACY MANUAL Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008 1 Real Numbers 1.1 Sets 1 1.2 Constants and Variables; Real Numbers 7 1.3 Operations with Numbers

More information

Introduction to TURING

Introduction to TURING Introduction to TURING Comments Some code is difficult to understand, even if you understand the language it is written in. To that end, the designers of programming languages have allowed us to comment

More information

Is the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd

Is the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd Is the statement sufficient? If both x and y are odd, is xy odd? Is x < 0? 1) xy 2 < 0 Positives & Negatives Answer: Yes, xy is odd Odd numbers can be represented as 2m + 1 or 2n + 1, where m and n are

More information

Values & Variables 1

Values & Variables 1 Values & Variables 1 Properties of variables Should have a type Stores data Case sensitive Their names can not start with a number Reserved keywords can not be used as variable names 2 Keywords 3 How to

More information

Hundred-thousands. Millions. Ten-thousands

Hundred-thousands. Millions. Ten-thousands Place Value, Names for Numbers, and Reading Tables The digits used to write numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Unit 1 Lesson 1a Natural numbers are positive numbers only {1, 2, 3, 4, 5, 6, 7,

More information

Class#9 in the Pre-Core Mathematics Program. It s time to pass along a stack of tips related to using the ALEKS system and .

Class#9 in the Pre-Core Mathematics Program. It s time to pass along a stack of tips related to using the ALEKS system and  . Class#9 in the Pre-Core Mathematics Program It s time to pass along a stack of tips related to using the ALEKS system and email. 1 ALEKS Tip #1 Let s start with the # ALEKS calculator. # Did you know that

More information

Chapter 1 Operations With Numbers

Chapter 1 Operations With Numbers Chapter 1 Operations With Numbers Part I Negative Numbers You may already know what negative numbers are, but even if you don t, then you have probably seen them several times over the past few days. If

More information

CS 135 Lab Assignments Week 1

CS 135 Lab Assignments Week 1 CS 135 Lab Assignments Week 1 Professor: Matt B. Pedersen This handout is the assignment that you must finish for the lab portion of the course in week 1. You must finish the assignments yourself; if you

More information

Note: The last command (10-5) will generate an error message. Can you see why the calculator is having difficulty deciphering the command?

Note: The last command (10-5) will generate an error message. Can you see why the calculator is having difficulty deciphering the command? Arithmetic on the TI 8/84 Your calculator is incredibly powerful and relatively easy to use. This activity will touch on a small part of its capabilities. There are two keys that look very much alike,

More information

Calculations with Sig Figs

Calculations with Sig Figs Calculations with Sig Figs When you make calculations using data with a specific level of uncertainty, it is important that you also report your answer with the appropriate level of uncertainty (i.e.,

More information

YOGYAKARTA STATE UNIVERSITY MATHEMATICS AND NATURAL SCIENCES FACULTY MATHEMATICS EDUCATION STUDY PROGRAM

YOGYAKARTA STATE UNIVERSITY MATHEMATICS AND NATURAL SCIENCES FACULTY MATHEMATICS EDUCATION STUDY PROGRAM YOGYAKARTA STATE UNIVERSITY MATHEMATICS AND NATURAL SCIENCES FACULTY MATHEMATICS EDUCATION STUDY PROGRAM TOPIC 1 INTRODUCING SOME MATHEMATICS SOFTWARE (Matlab, Maple and Mathematica) This topic provides

More information