# Positive and Negative Integers

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 0.4 Positive and Negative Integers 0.4 OBJECTIVES 1. Represent integers on a number line 2. Order signed numbers 3. Evaluate numerical expressions involving absolute value When numbers are used to represent physical quantities (altitudes, temperatures, and amounts of money are examples), it may be necessary to distinguish between positive and negative quantities. It is convenient to represent these quantities with plus ( ) or minus ( ) signs. For instance, The altitude of Mount Whitney is 14,495 feet (ft) above sea level ( 14,495). 14,495 ft Mount Whitney The altitude of Death Valley is 282 ft below sea level ( 282). 282 ft Death Valley The temperature in Chicago is 10 below zero ( 10 )

2 36 CHAPTER 0 AN ARITHMETIC REVIEW An account could show a gain of \$100 ( 100), or a loss of \$100 ( 100). These numbers suggest the need to extend the whole numbers to include both positive numbers (like 100) and negative numbers (like 282). To represent the negative numbers, we extend the number line to the left of zero and name equally spaced points. Numbers used to name points to the right of zero are positive numbers. They are written with a positive ( ) sign or with no sign at all. +6 and 9 are positive numbers Numbers used to name points to the left of zero are negative numbers. They are always written with a negative ( ) sign. 3 and 20 are negative numbers Read negative 3. Positive and negative numbers considered together are signed numbers. Here is the number line extended to include both positive and negative numbers. NOTE 0 is not considered a signed number. Zero is neither positive nor negative Negative numbers Positive numbers NOTE The dots are called ellipses and indicate that the pattern continues. The numbers used to name the points shown on the number line above are called the integers. The integers consist of the natural numbers, their negatives, and the number 0. We can represent the set of integers by {..., 3, 2, 1, 0, 1, 2, 3,...}

3 POSITIVE AND NEGATIVE INTEGERS SECTION Example 1 Representing Integers on the Number Line Represent the following integers on the number line shown. 3, 12, 8, 15, CHECK YOURSELF 1 Represent the following integers on a number line. 1, 9, 4, 11, 8, The set of numbers on the number line is ordered. The numbers get smaller moving to the left on the number line and larger moving to the right When a set of numbers is written from smallest to largest, the numbers are said to be in ascending order. Example 2 Ordering Signed Numbers Place each set of numbers in ascending order. (a) 9, 5, 8, 3, 7 From smallest to largest, the numbers are 8, 5, 3, 7, 9 Note that this is the order in which the numbers appear on a number line as we move from left to right. (b) 3, 2, 18, 20, 13 From smallest to largest, the numbers are 20, 13, 2, 3, 18 CHECK YOURSELF 2 Place each set of numbers in ascending order. (a) 12, 13, 15, 2, 8, 3 (b) 3, 6, 9, 3, 8

4 38 CHAPTER 0 AN ARITHMETIC REVIEW The least and greatest numbers in a set are called the extreme values. The least element is called the minimum and the greatest element is called the maximum. Example 3 Labeling Extreme Values For each set of numbers, determine the minimum and maximum values. (a) 9, 5, 8, 3, 7 From our previous ordering of these numbers, we see that 8, the least element, is the minimum, and 9, the greatest element, is the maximum. (b) 3, 2, 18, 20, is the minimum and 18 is the maximum. CHECK YOURSELF 3 For each set of numbers, determine the minimum and maximum values. (a) 12, 13, 15, 2, 8, 3 (b) 3, 6, 9, 3, 8 Integers are not the only kind of signed numbers. Decimals and fractions can also be thought of as signed numbers. Example 4 Identifying Signed Numbers that are Integers Which of the following signed numbers are also integers? (a) 145 is an integer. (b) 28 is an integer. (c) 0.35 is not an integer. (d) 2 3 is not an integer. CHECK YOURSELF 4 Which of the following signed numbers are also integers? Sometimes we refer to the negative of a number as its opposite. But what is the opposite of the opposite of a number? It is the number itself. The next example illustrates.

5 POSITIVE AND NEGATIVE INTEGERS SECTION Example 5 Find the Opposite for Each Number (a) 5 The opposite of 5 is 5. (b) 9 The opposite of 9 is 9. CHECK YOURSELF 5 Find the opposite for each number. (a) 17 (b) 12 An important idea for our work in this chapter is the absolute value of a number. This represents the distance of the point named by the number from the origin on the number line. 5 units 5 units The absolute value of 5 is 5. The absolute value of 5 is also 5. The absolute value of a positive number or zero is itself. The absolute value of a negative number is its opposite. In symbols we write 5 5 and 5 5 Read the absolute Read the absolute value of 5. value of negative 5. The absolute value of a number does not depend on whether the number is to the right or to the left of the origin, but on its distance from the origin. Example 6 Simplifying Absolute Value Expressions (a) 7 7 (b) 7 7 (c) 7 7 This is the negative, or opposite, of the absolute value of negative 7. (d) Absolute value bars serve as another set of grouping symbols, so do the operation inside first. (e) (f) Here, evaluate the absolute values, then subtract.

6 40 CHAPTER 0 AN ARITHMETIC REVIEW CHECK YOURSELF 6 Evaluate. (a) 8 (b) 8 (c) 8 (d) 9 4 (e) 9 4 (f) 9 4 CHECK YOURSELF ANSWERS (a) 13, 8, 3, 2, 12, 15 (b) 9, 3, 3, 6, (a) minimum is 13; maximum is 15 (b) minimum is 9; maximum is , 1054, 0, and (a) 17; (b) (a) 8; (b) 8; (c) 8; (d) 13; (e) 5; (f ) 5

7 Name 0.4 Exercises Section Date Represent each quantity with a signed number. 1. An altitude of 400 feet (ft) above sea level 2. An altitude of 80 ft below sea level 3. A loss of \$ A profit of \$ A decrease in population of 25, An increase in population of 12,500 Represent the integers on the number lines shown. ANSWERS , 15, 18, 8, , 4, 5, 13, 9 Which numbers in the following sets are integers? , 2, 175, 234, , 0.35, 3, 700, 26 5 Place each of the following sets in ascending order , 5, 2, 0, 7, 1, , 7, 1, 8, 6, 1, , 2, 11, 4, 6, 1, , 18, 5, 11, 15, 14, , 7, 7, 6, 3, , 13, 14, 14, 15, For each set, determine the maximum and minimum values , 6, 0, 10, 3, 15, 1, , 1, 3, 11, 4, 2, 5, , 15, 0, 7, 9, 16, 3, , 0, 22, 31, 18, 5, , 0, 1, 2, 5, 4, , 7, 3, 5, 10, 5 Find the opposite of each number

9 ANSWERS Label each statement as true or false. 53. All whole numbers are integers. 54. All nonzero integers are signed numbers. 55. All integers are whole numbers. 56. All signed numbers are integers. 57. All negative integers are whole numbers. 58. Zero is neither positive nor negative. Place absolute value bars in the proper location on the left side of the expression so that the equation is true ( 2) ( 3) ( 2) ( 3) 11 Represent each quantity with a signed number. 63. Soil erosion. The erosion of 5 centimeters (cm) of topsoil from an Iowa corn field. 64. Soil formation. The formation of 2.5 cm of new topsoil on the African savanna. 65. Checking accounts. The withdrawal of \$50 from a checking account. 66. Saving accounts. The deposit of \$200 in a savings account. 67. Temperature. The temperature change pictured F F 1:00 P.M. 2:00 P.M. 68. Stocks. An increase of 75 points in the Dow-Jones average. JUNE JULY 43

10 ANSWERS Baseball. An eight-game losing streak by the local baseball team. 70. Population. An increase of 25,000 in the population of the city. 71. Positive trade balance. A country exported \$90,000,000 more than it imported, creating a positive trade balance. 72. Negative trade balance. A country exported \$60,000,000 less than it imported, creating a negative trade balance. For each collection of numbers given in exercises 73 to 76, answer the following: (a) Which number is smallest? (b) Which number lies farthest from the origin? (c) Which number has the largest absolute value? (d) Which number has the smallest absolute value? 73. 6, 3, 8, 7, , 3, 5, 4, , 6, 1, 0, 2, , 0, 2, 3, Simplify each of the following: ( 7) ( ( 7)) ( ( ( 7))) Based on your answers, generalize your results. Answers or ( 400) , , 175, , 5, 1, 0, 2, 3, , 6, 2, 1, 4, 5, , 6, 3, 3, 6, Max: 15; Min: Max: 21, Min: Max: 5; Min: True 55. False 57. False ( 2) F ,000, ; 8; 8; ; 6; 6;

### INTEGERS AND ALGEBRA. chapter CHAPTER 2 OUTLINE INTRODUCTION

hut6236_ch2_a.qxd 9/22/8 9:55 AM Page 119 chapter 2 INTEGERS AND INTRODUCTION INTRODUCTION TO ALGEBRA CHAPTER 2 OUTLINE Section 2.1 Introduction to Integers page 121 Section 2.2 Addition of Integers page

### For any two different places on the number line, the integer on the right is greater than the integer on the left.

Positive and Negative Integers Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5,.... Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5,. We

### MULTIPLYING AND DIVIDING INTEGERS Guided Notes

Notes Name: Date: Period: MULTIPLYING AND DIVIDING INTEGERS Guided Notes Target Objective 1: Multiply, and divide integers Target Objective 2: Describe situations involving arithmetic operations with integers

### Study Guide For use with pages 5 9

1.1 GOAL For use with pages 5 9 Evaluate and write variable expressions. VOCABULARY A numerical expression consists of numbers and operations. For example, the expression 10 4 is a numerical expression.

### 25 Integers: Addition and Subtraction

25 Integers: Addition and Subtraction Whole numbers and their operations were developed as a direct result of people s need to count. But nowadays many quantitative needs aside from counting require numbers

### 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

### 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

### MULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.

1.4 Multiplication and (1-25) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with

### Multiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20

SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed

### Table of Content of Algebra I. Chapter I. Rational Numbers

Table of Content of Algebra I Chapter I. Rational Numbers 1.1. Introducing the negative numbers 1.2. Integers and rational numbers 1.3. The number axis 1.4. Opposite numbers and absolute values 1.5. Comparing

### Addition and Subtraction of Integers

Addition and Subtraction of Integers Integers are the negative numbers, zero, and positive numbers Addition of integers An integer can be represented or graphed on a number line by an arrow. An arrow pointing

### Adding and Subtracting Positive and Negative Numbers

Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number

### UNIT 3 VOCABULARY: INTEGERS

1º ESO Bilingüe Page 1 UNIT 3 VOCABULARY: INTEGERS 3.1. Some uses of negative numbers There are many situations in which you need to use negative numbers. POSITIONS A submarine which is sailing 700 m below

### Exponents. Exponents tell us how many times to multiply a base number by itself.

Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,

### Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.

INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe

### 1.1 THE REAL NUMBERS. section. The Integers. The Rational Numbers

2 (1 2) Chapter 1 Real Numbers and Their Properties 1.1 THE REAL NUMBERS In this section In arithmetic we use only positive numbers and zero, but in algebra we use negative numbers also. The numbers that

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### Subtracting Negative Integers

Subtracting Negative Integers Notes: Comparison of CST questions to the skill of subtracting negative integers. 5 th Grade/65 NS2.1 Add, subtract, multiply and divide with decimals; add with negative integers;

### 3-4 Multiply Integers. Multiply. 1. 8( 12) SOLUTION: The integers have different signs. The product is negative. So, 8( 12) = 96.

Multiply. 1. 8( 12) The integers have different signs. The product is negative. So, 8( 12) = 96. 96 2. 15( 4) The integers have the same sign. The product is positive. So, 15( 4) = 60. 60 3. ( 6) 2 36

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Training Manual. Pre-Employment Math. Version 1.1

Training Manual Pre-Employment Math Version 1.1 Created April 2012 1 Table of Contents Item # Training Topic Page # 1. Operations with Whole Numbers... 3 2. Operations with Decimal Numbers... 4 3. Operations

### OPERATIONS AND PROPERTIES

CHAPTER OPERATIONS AND PROPERTIES Jesse is fascinated by number relationships and often tries to find special mathematical properties of the five-digit number displayed on the odometer of his car. Today

### SIMPLIFYING ALGEBRAIC FRACTIONS

Tallahassee Community College 5 SIMPLIFYING ALGEBRAIC FRACTIONS In arithmetic, you learned that a fraction is in simplest form if the Greatest Common Factor (GCF) of the numerator and the denominator is

### Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW

Name Period Date 8-1 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW 1.1 Integer Operations: Patterns Explore the meaning of integer addition, subtraction, multiplication, and division.

### ALGEBRA READINESS DIAGNOSTIC TEST PRACTICE

1 ALGEBRA READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the examples, work the problems, then check your answers at the end of each topic. If you don t get the answer given, check your work and

### Operations on Decimals

Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal

### Domain Essential Question Common Core Standards Resources

Middle School Math 2016-2017 Domain Essential Question Common Core Standards First Ratios and Proportional Relationships How can you use mathematics to describe change and model real world solutions? How

### How To Math Properties

CLOSURE a + b is a real number; when you add 2 real numbers, the result is also a real number. and 5 are both real numbers, + 5 8 and the sum, 8, is also a real number. a b is a real number; when you subtract

### Introduction to the Practice Exams

Introduction to the Practice Eams The math placement eam determines what math course you will start with at North Hennepin Community College. The placement eam starts with a 1 question elementary algebra

### Recall the process used for adding decimal numbers. 1. Place the numbers to be added in vertical format, aligning the decimal points.

2 MODULE 4. DECIMALS 4a Decimal Arithmetic Adding Decimals Recall the process used for adding decimal numbers. Adding Decimals. To add decimal numbers, proceed as follows: 1. Place the numbers to be added

### 11-5 Dividing Polynomials. Find each quotient. 1. (8a a) 4a ANSWER: 2a (4z 3 + 1) 2z ANSWER: 3. (12n 3 6n ) 6n ANSWER:

Find each quotient. 1. (8a 2 + 20a) 4a 2a + 5 9. (4y 2 + 8y + 3) (y + 2) 2. (4z 3 + 1) 2z 10. (4h 3 + 6h 2 3) (2h + 3) 3. (12n 3 6n 2 + 15) 6n 11. (9n 3 13n + 8) (3n 1) 4. (t 2 + 5t + 4) (t + 4) t + 1

### a) b) -4 + ( -5) c) d) 2 - ( -2) f)

CLASS VII New Integers A 1. The integer consist of, and numbers 2. The numbers less than zero are called integer. 3. All the numbers which are less than zero have sign. 4. Zero is greater than integer.

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 5 Subtracting Integers

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 5 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

### Hundreds Chart. Vocabulary. Place Value

Addition plus, sum, addend Subtraction minus, difference Multiplication times, product, factor Division quotient, divisor, dividend Hundreds Chart SYMBOLS Addition: + Subtraction: Multiplication: x * Division:

### Introduction to Signed Numbers

Worksheet 1.6 Signed Numbers Section 1 Introduction to Signed Numbers Signed numbers are positive and negative numbers. So far in the worksheets we have mainly talked about the counting numbers, which

### Lesson Plan -- Integers, Opposites, Absolute Value

Lesson Plan -- Integers, Opposites, Absolute Value Chapter Resources - Lesson 3-1 Integers and the Number Line - Lesson 3-1 Integers and the Number Line Answers - Lesson 3-2 Opposites and Absolute Value

### MAT 0950 Course Objectives

MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. Identify

### A Short Guide to Significant Figures

A Short Guide to Significant Figures Quick Reference Section Here are the basic rules for significant figures - read the full text of this guide to gain a complete understanding of what these rules really

### Ways We Use Integers. Negative Numbers in Bar Graphs

Ways We Use Integers Problem Solving: Negative Numbers in Bar Graphs Ways We Use Integers When do we use negative integers? We use negative integers in several different ways. Most of the time, they are

### Solutions of Linear Equations in One Variable

2. Solutions of Linear Equations in One Variable 2. OBJECTIVES. Identify a linear equation 2. Combine like terms to solve an equation We begin this chapter by considering one of the most important tools

### Example 1: If the sum of seven and a number is multiplied by four, the result is 76. Find the number.

EXERCISE SET 2.3 DUE DATE: STUDENT INSTRUCTOR: 2.3 MORE APPLICATIONS OF LINEAR EQUATIONS Here are a couple of reminders you may need for this section: perimeter is the distance around the outside of the

### Scientific Notation Notes

Scientific Notation Notes Scientific notation is a short way to write very large or very small numbers. It is written as the product of a number between 1 and 10 and a power of 10. TO CONVERT A NUMBER

### Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10.

Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign + 6 + + 5 = + - 8 + - 2 = - 0 Different signs: Subtract & take sign of larger value + 9 + - 5 = + 4-6

### Q N R. Sep 5 7:55 AM THE NUMBER SYSTEM

Q W I TITLE: Q N R Sep 5 7:55 AM THE NUMBER SYSTEM N NATURAL NUMBERS All positive non zero numbers; in other words, all positive numbers. This does not include zero. These are the numbers we use to count.

### 1.2. Adding and Subtracting Integers Changing Elevations. My Notes ACTIVITY

Adding and Subtracting Integers SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Think/Pair/Share, Interactive Word Wall Ms. Flowers, a math teacher at Rachel Carson Middle School, plans a field

Subtract. 1. 0 10 10 2. 9 5 14 3. 4 8 12 4. 31 48 17 5. 25 5 30 esolutions Manual - Powered by Cognero Page 1 6. 44 41 85 7. 4 ( 19) 23 8. 11 ( 42) 31 9. 52 ( 52) 104 Evaluate each expression if f = -6,

### 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

### 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

### Algebra 1. Practice Workbook with Examples. McDougal Littell. Concepts and Skills

McDougal Littell Algebra 1 Concepts and Skills Larson Boswell Kanold Stiff Practice Workbook with Examples The Practice Workbook provides additional practice with worked-out examples for every lesson.

### The collection of numbers 0, +1, 1, +2, 2, +3, 3,... is called integers. NCERT. The integers are represented on the number line as follows :

MATHEMATICS UNIT 3 INTEGERS (A) Main Concepts and Results The collection of numbers 0, +1, 1, +2, 2, +3, 3,... is called integers. The numbers +1, +2, +3, +4,... are referred to as positive integers. The

### 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.

### MATH-0910 Review Concepts (Haugen)

Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,

### 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,

### 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

### Accentuate the Negative: Homework Examples from ACE

Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),

### 5 1 d. 2.5? t. 10 more than the. the sum of 10x and 7z quotient of x and 4. product of 3 and x

- Practice Form G Variables and Expressions Write an algebraic expression for each word phrase.. 0 less than x. 5 more than d x 0 5 d. 7 minus f. the sum of and k 7 f k 5. x multiplied by 6 6. a number

### The Addition Property of Equality. The Addition Property of Equality. Adding the same number to both sides Solve x 3 7. x 3 7

dug508_ch0a.qxd 8/9/0 :55 PM Page 66 66 ( ) Chapter Linear Equations in One Variable In this helpful section The Addition Property of Equality The Multiplication Property of Equality Variables on Both

### Grade 7 Unit 1: Add, Subtract, Multiply and Divide Rational Numbers (6 Weeks)

Grade 7 Unit : Add, Subtract, Multiply and Divide Rational Numbers (6 Weeks) Stage Desired Results Established Goals Unit Description Apply and extend previous understandings of operations with fractions

### 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

### 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

### Fractions and Decimals (pages 62 66)

A Fractions and Decimals (pages 6 66) A decimal that ends, such as 0., is a terminating decimal. All terminating decimals are rational numbers. 0.,000 A decimal that repeats, such as 0. is a repeating

### Decimal and Fraction Review Sheet

Decimal and Fraction Review Sheet Decimals -Addition To add 2 decimals, such as 3.25946 and 3.514253 we write them one over the other with the decimal point lined up like this 3.25946 +3.514253 If one

### 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.

Task Model 1 Graphing DOK Level 2 7.NS.A.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a

### Rational Numbers Subtracting Rational Numbers ~ Lesson Plan

Rational Numbers Subtracting Rational Numbers Lesson Plan I. Topic: Subtracting Rational Numbers II. III. Goals and Objectives: A. The student will learn how to subtract rational numbers with the same

### Objectives. By the time the student is finished with this section of the workbook, he/she should be able

QUADRATIC FUNCTIONS Completing the Square..95 The Quadratic Formula....99 The Discriminant... 0 Equations in Quadratic Form.. 04 The Standard Form of a Parabola...06 Working with the Standard Form of a

### Chapter 4. Fractions, Decimals, Percent s Worksheets. Name: Class::

Chapter 4 Fractions, Decimals, Percent s Worksheets Name: Class:: Rounding Worksheet NAME: Thousands Hundreds Tens Units Decimal. Tenths Hundredths Thousandths Use the table provided to help you round

### Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

### Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = -7 + m = m 15 = m = 7 + m 8 = = 8

Bell Ringer Solve each equation. Show you work. the solution. 1. 8 = 7 + m 8 = -7 + m 8 + 7 = -7 + 7 + m 15 = m 8 = -7 + m 8 = -7 + 15 8 = 8 Answers to Homework Worksheet 2-1 Today s Objectives Solving

### MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

### January 22. Interest Rates

January 22 Interest Rates Compound Interest If you put \$100 in a bank account at 5% interest per year, you will have \$105 after one year. You earn \$5 in interest. How much do you have after two years if

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### Measurement with Ratios

Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

### Foundations for Middle School 6 th Grade Syllabus

Unit 1:, and Percents (Lessons 0 19) and Percents (Lessons 0 19) Foundations for Middle School 6 th Grade Syllabus Solving for every variable Foundations for Middle School 6 th Grade Syllabus 1 Unit 1:

### Section 1.4 Notes Page Linear Equations in Two Variables and Linear Functions., x

Section. Notes Page. Linear Equations in Two Variables and Linear Functions Slope Formula The slope formula is used to find the slope between two points ( x, y ) and ( ) x, y. x, y ) The slope is the vertical

### Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

### Math 0306 Final Exam Review

Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire

### Pre-Algebra Curriculum Map 8 th Grade Unit 1 Integers, Equations, and Inequalities

Key Skills and Concepts Common Core Math Standards Unit 1 Integers, Equations, and Inequalities Chapter 1 Variables, Expressions, and Integers 12 days Add, subtract, multiply, and divide integers. Make

### ascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.

SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom

### Integers (pages 294 298)

A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write

### 2014 Summer Math Packet

Academir Charter School Middle Rh RT CE, 2014 Summer Math Packet )( MOE Academir Charter School Middle is committed to fostering continuous student learning, development and achievement. This commitment

### Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities

Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.

### Answer Key for California State Standards: Algebra I

Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.

### DECIMAL REVIEW. 2. Change to a fraction Notice that =.791 The zero in front of the decimal place is not needed.

DECIMAL REVIEW A. INTRODUCTION TO THE DECIMAL SYSTEM The Decimal System is another way of expressing a part of a whole number. A decimal is simply a fraction with a denominator of 10, 100, 1 000 or 10

### Rules of Signs for Decimals

CHAPTER 6 C Rules of Signs for Decimals c GOAL Apply the rules of signs for calculating with decimals. You will need number lines a calculator with a sign change key Learn about the Math Positive and negative

### COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13

COMPASS Numerical Skills/Pre-Algebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre

### Grade 7 Math The Number System Grade 7 Math Grade 7 Math Start Date: August 30, 2012 End Date : September 28, 2012

Unit Overview Students will be able to: describe real life situations for quantities that combine to make zero understand the distance between two on a number line show how opposites have a sum of zero

### 100 Math Facts 6 th Grade

100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

### Maths Module 1. An Introduction to Mathematics. This module covers concepts such as:

Maths Module 1 An Introduction to Mathematics This module covers concepts such as: basic arithmetic rounding order of operations mental computation strategies www.jcu.edu.au/students/learning-centre Module

### 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

### eday Lessons Mathematics Grade 8 Student Name:

eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards- Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times