Positive and Negative Integers
|
|
- Matthew Barker
- 7 years ago
- Views:
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
8 ANSWERS Evaluate
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;
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
More informationAdding 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
More informationAddition 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
More informationUNIT 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
More informationMultiplying 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
More informationIntegers 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
More informationMULTIPLICATION 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
More informationHow 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
More informationLesson 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
More informationExponents. 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,
More informationSolutions 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
More informationTraining 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
More informationSubtracting 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;
More informationA 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
More informationMATH-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,
More informationRecall 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
More informationInteger 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.
More informationSquare Roots and the Pythagorean Theorem
4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate
More informationAnswer 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.
More informationSIMPLIFYING 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
More informationIntegers (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
More informationWays 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
More informationMeasurement 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
More informationLINEAR INEQUALITIES. less than, < 2x + 5 x 3 less than or equal to, greater than, > 3x 2 x 6 greater than or equal to,
LINEAR INEQUALITIES When we use the equal sign in an equation we are stating that both sides of the equation are equal to each other. In an inequality, we are stating that both sides of the equation are
More informationGrade 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
More informationAccentuate 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),
More informationAlgebra 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.
More informationUnit 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
More informationMATH 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 informationProperties 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 informationCONTENTS. Please note:
CONTENTS Introduction...iv. Number Systems... 2. Algebraic Expressions.... Factorising...24 4. Solving Linear Equations...8. Solving Quadratic Equations...0 6. Simultaneous Equations.... Long Division
More informationThe 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 informationQuick 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
More information1.2 Linear Equations and Rational Equations
Linear Equations and Rational Equations Section Notes Page In this section, you will learn how to solve various linear and rational equations A linear equation will have an variable raised to a power of
More informationVocabulary 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
More informationNegative Exponents and Scientific Notation
3.2 Negative Exponents and Scientific Notation 3.2 OBJECTIVES. Evaluate expressions involving zero or a negative exponent 2. Simplify expressions involving zero or a negative exponent 3. Write a decimal
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationA Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
More informationAnswer: The relationship cannot be determined.
Question 1 Test 2, Second QR Section (version 3) In City X, the range of the daily low temperatures during... QA: The range of the daily low temperatures in City X... QB: 30 Fahrenheit Arithmetic: Ranges
More informationMath 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
More informationExponents. Learning Objectives 4-1
Eponents -1 to - Learning Objectives -1 The product rule for eponents The quotient rule for eponents The power rule for eponents Power rules for products and quotient We can simplify by combining the like
More informationMath 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
More information47 Numerator Denominator
JH WEEKLIES ISSUE #22 2012-2013 Mathematics Fractions Mathematicians often have to deal with numbers that are not whole numbers (1, 2, 3 etc.). The preferred way to represent these partial numbers (rational
More informationThe Mathematics 11 Competency Test Percent Increase or Decrease
The Mathematics 11 Competency Test Percent Increase or Decrease The language of percent is frequently used to indicate the relative degree to which some quantity changes. So, we often speak of percent
More information5.1 Introduction to Decimals, Place Value, and Rounding
5.1 Introduction to Decimals, Place Value, and Rounding 5.1 OBJECTIVES 1. Identify place value in a decimal fraction 2. Write a decimal in words 3. Write a decimal as a fraction or mixed number 4. Compare
More information0.8 Rational Expressions and Equations
96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions - that is, algebraic fractions - and equations which contain them. The reader is encouraged to
More informationCOMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh
BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or
More informationLogarithmic and Exponential Equations
11.5 Logarithmic and Exponential Equations 11.5 OBJECTIVES 1. Solve a logarithmic equation 2. Solve an exponential equation 3. Solve an application involving an exponential equation Much of the importance
More informationAbsolute Value Equations and Inequalities
. Absolute Value Equations and Inequalities. OBJECTIVES 1. Solve an absolute value equation in one variable. Solve an absolute value inequality in one variable NOTE Technically we mean the distance between
More informationFree Pre-Algebra Lesson 55! page 1
Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can
More informationFormulas and Problem Solving
2.4 Formulas and Problem Solving 2.4 OBJECTIVES. Solve a literal equation for one of its variables 2. Translate a word statement to an equation 3. Use an equation to solve an application Formulas are extremely
More information5.1 Radical Notation and Rational Exponents
Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots
More informationLesson 4: Efficiently Adding Integers and Other Rational Numbers
Classwork Example 1: Rule for Adding Integers with Same Signs a. Represent the sum of 3 + 5 using arrows on the number line. i. How long is the arrow that represents 3? ii. iii. How long is the arrow that
More informationMath Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important
More informationGrade 6 Mathematics Performance Level Descriptors
Limited Grade 6 Mathematics Performance Level Descriptors A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Grade 6 Mathematics. A student at this
More informationNegative Integral Exponents. If x is nonzero, the reciprocal of x is written as 1 x. For example, the reciprocal of 23 is written as 2
4 (4-) Chapter 4 Polynomials and Eponents P( r) 0 ( r) dollars. Which law of eponents can be used to simplify the last epression? Simplify it. P( r) 7. CD rollover. Ronnie invested P dollars in a -year
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationSolving Equations by the Multiplication Property
2.2 Solving Equations by the Multiplication Property 2.2 OBJECTIVES 1. Determine whether a given number is a solution for an equation 2. Use the multiplication property to solve equations. Find the mean
More informationALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite
ALGEBRA Pupils should be taught to: Generate and describe sequences As outcomes, Year 7 pupils should, for example: Use, read and write, spelling correctly: sequence, term, nth term, consecutive, rule,
More informationMethod To Solve Linear, Polynomial, or Absolute Value Inequalities:
Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with
More informationMcDougal Littell California:
McDougal Littell California: Pre-Algebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California Pre-Algebra Components: Pupil Edition (PE), Teacher s Edition (TE),
More informationFigure 1. A typical Laboratory Thermometer graduated in C.
SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES
More informationGrade 7 Mathematics. Unit 2. Integers. Estimated Time: 15 Hours
Grade 7 Mathematics Integers Estimated Time: 15 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade
More informationA.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents
Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationSample Problems. Practice Problems
Lecture Notes Quadratic Word Problems page 1 Sample Problems 1. The sum of two numbers is 31, their di erence is 41. Find these numbers.. The product of two numbers is 640. Their di erence is 1. Find these
More informationNegative Integer Exponents
7.7 Negative Integer Exponents 7.7 OBJECTIVES. Define the zero exponent 2. Use the definition of a negative exponent to simplify an expression 3. Use the properties of exponents to simplify expressions
More informationTemperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.
Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is
More informationSimplifying 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 informationObjective. Materials. TI-73 Calculator
0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI-73 Calculator Integer Subtraction What s the Difference? Teacher
More informationMath Workshop October 2010 Fractions and Repeating Decimals
Math Workshop October 2010 Fractions and Repeating Decimals This evening we will investigate the patterns that arise when converting fractions to decimals. As an example of what we will be looking at,
More informationLESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to:
LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to: 1. Change fractions to decimals. 2. Change decimals to fractions. 3. Change percents to decimals.
More informationLecture 2. Binary and Hexadecimal Numbers
Lecture 2 Binary and Hexadecimal Numbers Purpose: Review binary and hexadecimal number representations Convert directly from one base to another base Review addition and subtraction in binary representations
More informationMathematics. Steps to Success. and. Top Tips. Year 5
Pownall Green Primary School Mathematics and Year 5 1 Contents Page 1. Multiplication and Division 3 2. Positive and Negative Numbers 4 3. Decimal Notation 4. Reading Decimals 5 5. Fractions Linked to
More informationMathematics. Mathematical Practices
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with
More informationInequalities - Absolute Value Inequalities
3.3 Inequalities - Absolute Value Inequalities Objective: Solve, graph and give interval notation for the solution to inequalities with absolute values. When an inequality has an absolute value we will
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More informationPre-Algebra - Order of Operations
0.3 Pre-Algebra - Order of Operations Objective: Evaluate expressions using the order of operations, including the use of absolute value. When simplifying expressions it is important that we simplify them
More informationLesson 2. Operations with Integers. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 2 Operations with Integers Objectives Add and subtract integers Determine the absolute value of a number Solve word problems that involve adding
More informationTo Evaluate an Algebraic Expression
1.5 Evaluating Algebraic Expressions 1.5 OBJECTIVES 1. Evaluate algebraic expressions given any signed number value for the variables 2. Use a calculator to evaluate algebraic expressions 3. Find the sum
More informationPREPARATION 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 informationAdding & Subtracting Integers
WARDEN AVE P.S. Adding & Subtracting Integers Number Sense & Numeration Unit #1 Grade 7 Math 2014-2015 School Year This mini-unit will run from September 15-26 and must be handed in on Friday Sept. 26th
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares
More informationGEOMETRIC SEQUENCES AND SERIES
4.4 Geometric Sequences and Series (4 7) 757 of a novel and every day thereafter increase their daily reading by two pages. If his students follow this suggestion, then how many pages will they read during
More informationFlorida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower
Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including
More informationIn this this review we turn our attention to the square root function, the function defined by the equation. f(x) = x. (5.1)
Section 5.2 The Square Root 1 5.2 The Square Root In this this review we turn our attention to the square root function, the function defined b the equation f() =. (5.1) We can determine the domain and
More informationSession 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers:
Session 9 Scientific Notation and Laws of Exponents If you have ever taken a Chemistry class, you may have encountered the following numbers: There are approximately 60,4,79,00,000,000,000,000 molecules
More informationPrime Factorization 0.1. Overcoming Math Anxiety
0.1 Prime Factorization 0.1 OBJECTIVES 1. Find the factors of a natural number 2. Determine whether a number is prime, composite, or neither 3. Find the prime factorization for a number 4. Find the GCF
More informationWorksheet 1. What You Need to Know About Motion Along the x-axis (Part 1)
Worksheet 1. What You Need to Know About Motion Along the x-axis (Part 1) In discussing motion, there are three closely related concepts that you need to keep straight. These are: If x(t) represents the
More information3.1. 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 informationSummer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students
Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Studies show that most students lose about two months of math abilities over the summer when they do not engage in
More informationIntegers, I, is a set of numbers that include positive and negative numbers and zero.
Grade 9 Math Unit 3: Rational Numbers Section 3.1: What is a Rational Number? Integers, I, is a set of numbers that include positive and negative numbers and zero. Imagine a number line These numbers are
More information26 Integers: Multiplication, Division, and Order
26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue
More informationSOLVING EQUATIONS WITH RADICALS AND EXPONENTS 9.5. section ( 3 5 3 2 )( 3 25 3 10 3 4 ). The Odd-Root Property
498 (9 3) Chapter 9 Radicals and Rational Exponents Replace the question mark by an expression that makes the equation correct. Equations involving variables are to be identities. 75. 6 76. 3?? 1 77. 1
More informationMATH 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 informationSolving Linear Equations in One Variable. Worked Examples
Solving Linear Equations in One Variable Worked Examples Solve the equation 30 x 1 22x Solve the equation 30 x 1 22x Our goal is to isolate the x on one side. We ll do that by adding (or subtracting) quantities
More information2.3 Solving Equations Containing Fractions and Decimals
2. Solving Equations Containing Fractions and Decimals Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Solve equations containing fractions
More informationCopy 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 informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More information