Financial Mathematics


 Lindsay O’Brien’
 2 years ago
 Views:
Transcription
1 Financial Mathematics For the next few weeks we will study the mathematics of finance. Apart from basic arithmetic, financial mathematics is probably the most practical math you will learn. practical in the everyday sort of sense) After you complete this chapter you should be able to determine how much money you need to save for major purchases like cars, houses, college savings accounts for children, retirement. You should also be able to determine the size of payments on loans. This can help you make more informed decisions when financing a car or a home. If time permits, we will also look into credit card billing and credit ratings. So many people get so deeply in debt simply due to a misunderstanding of how credit cards work. Nearly everything in finance is measured in terms of percent changes, so we will begin reviewing percent increase/ percent decreases. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
2 Percent Increase and Percent Decrease Cent means. For example, cents in a dollar, or years in a century, etc. Percent means per hundred, or out of a hundred. 78 percent just means percent of 200 means which is 156. This can also be thought of as In general, P % of N equals A means 78 = P N = A OR P = A N In applications, any two of P, A, N could be given. The above formula can be used to find the remaining variable. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
3 Percents At a certain high school, 72% of entering freshman earn a diploma. Suppose 306 students finish with a diploma. How large was the entering class? so 72 = 306 N so 72 N = 306 N = The entering class had 425 students = 425 Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
4 Percents Tuition for resident students at a certain university which will remain nameless) was $3, 735 in 2001 and is currently $9, 128. Express the current tuition as a percentage of the 2001 tuition. so P = P = 9128 = % 3735 Thus, the current tuition is % of the 2001 tuition. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
5 Percents Tuition for resident students at a certain university was $3, 735 in 2001 and is currently $9, 128. Express the 2001 tuition as a percentage of the current tuition. so P = P = 3735 = % 9128 Thus, the 2001 tuition is 40.92% of the current tuition. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
6 Setting up the correct percentage The previous two examples used the same data, but a subtle change in wording switched the role of N and A. How can we check if we set up the fractions correctly? The current tuition is more than the 2001 tuition, thus, if the current tuition is expressed as a percentage of the 2001, this percentage had better be greater than % Likewise, the 2001 tuition is less than the current tuition, thus, if the 2001 tuition is expresses as a percentage of the current tuition, this percentage had better be less than %. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
7 Percent Increase / Percent Decrease In applications, it is very common to express only the percent change between two quantities, not the absolute percentages. The current tuition is % of the 2001 tuition, which could be expressed by saying Tuition increased by % If the population of a town was 0 people and the population increased by 25%, what is the new populaton? 25 0 = 250 The population increased by 250 people, therefore the total population is = 1250 Original Population + Increase = New Population) Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
8 Percent Increase / Percent Decrease You buy a new computer. The list price is $1200. You have to pay 6% sales tax. How much do you actually pay? METHOD 1: The amount of tax is = 72. Thus, you pay = $1272. METHOD 2: You pay % for the computer plus 6% for the tax, thus the actual price is + 6) = 106% of the list price. Thus, you pay = $1272 Notice 106 = + 6 = thus, the final price could also be expressed as ) = $1272 Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
9 The Growth Factor of a Percentage Change In the previous example, we saw that adding 6% to the price corresponded to multiplying the price by ) = 1.06) I will refer to this as the growth factor corresponding to the 6% increase. For a percent increase, the growth factor will be greater than 1: A 34% increase corresponds to the growth factor = = A 271% increase corresponds to the growth factor = = For a percent decrease, the growth factor will be bewteen 0 and 1: A 28% decrease corresponds to the growth factor 1 28 = = Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
10 The Growth Factor of a Percentage Change To recover the percent change from a growth factor, first subtract 1, then multiply by i.e., move decimal two places to the right). The percent change is the absolute value of the number you just found. If the number is postive, then the change is a percent increase. If the number if negative, the change is a percent decrease. Find the percent change corresponding to the growth factor 1.74: Subtract 1: = 0.74 Multiply : 0.74 = 74% Since this is positive, this is a 74% increase. Find the percent change corresponding to the growth factor 0.62: Subtract 1: = 0.38 Multiply : 0.38 = 38%. Since this is negative, this is a 38% decrease. When applying a percent change, we can approach the problem in two ways: a) Add the percent increase or subtract the percent decrease b) Multiply by the growth factor The former is simpler in small examples. We ll see that the latter method greatly simplifies longer problems. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
11 Percent Increase / Percent Decrease Your textbook gives these two formulas: If you start with a quantity Q and increase it by x% then you end up with the quantity I, I = 1 + x ) Q If you start with a quantity Q and decrease it by x% then you end up with the quantity D, D = 1 x ) Q You may find it easier to only remember the first quantity and to think of decreases as negative increases. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
12 Percent Increase / Percent Decrease On Monday morning, the price of gold was $ per ounce. On Tuesday morning the price of gold was $ per ounce. Find the percent increase / percent decrease in the price of gold. Using the percent increase formula with Q = 1845 and I = 1841 we find 1841 = 1 + x ) x ) = = x = = x = ) = Thus, the price of gold decreased by %. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
13 Back to where we started? An item typically sells for $.00 but is on sale, at 7% off. The sales tax is 7%. After the sale and the tax, do you pay $.00 for this item? Why or why not? First, deduct 7% from the original price. The sale price is therefore 1 7 ) = $93.00 The price after tax is obtained by adding 7% of the sale price, so the final price is ) = $99.51 Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
14 How did this happen? We subtracted 7% then added 7%. Why isn t this 0%? Shouldn t 7% 7% = 0? We need to pay special attention to the bases of the percentages. In particular, 7% of 7% of IS equal to 0 BUT our problem is concerned with 7% of 93 7% of = 0.49 Thus, the combined effect of the two percent changes was to lower the price by $0.49 Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
15 Using Growth Factors When percent changes are combined, we can add the changes together, provided we remember to attach each percentage to its appropriate base. Alternatively, we can convert each percent change to its corresponding growth factor, then MULTIPLY all of the growth factors together, then convert back to a percent change. This latter method is preferable, since we don t need to keep track of the bases of each of the percentages. In the previous example, 7% off is a 7% decrease, so the corresponding growth factor is = % sales tax is a 7% increase, so the corresponding growth factor is = The net effect of applying the discount and the sales tax is to multiply: = Subtracting 1 from and multiplying by gives the growth factor of 0.49%. The combined effect is a 0.49% decrease in the price. The final price of the item is $.00 = $99.51 so the two percent changes combined to lower the price by $0.49. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
16 A more complex example The Dow Jones Industrial average started the week at points. On Monday it increased 1.9%. On Tuesday it decreased 0.7%. On Wednesday it decreased 3.5%. On Thursday it decreased 2.7%. On Friday it increased 1.4%. What was the total percent change over the week? Is this a percent increase or a percent decrease? The growth factors are ) = add since increase ) = subtract since decrease ) = subtract since decrease ) = subtract since decrease ) = add since increase Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
17 A more complex example The Dow Jones Industrial average started the week at points. On Monday it increased 1.9%. On Tuesday it decreased 0.7%. On Wednesday it decreased 3.5%. On Thursday it decreased 2.7%. On Friday it increased 1.4%. What was the total percent change over the week? Is this a percent increase or a percent decrease? For the whole week, the growth factor is the product = Now, if the percent change over the entire week is x% then 1 + x = x = = x = = 3.66% The percent change is 3.66% and this is a decrease since x is negative. Paul Koester ) MA 111, Percent Increase / Percent Decrease February / 17
The 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 informationAmount, Base, and Rate
The Mathematics 11 Competency Test, Base, and Rate Sorting out a percent problem always involves correctly attaching numbers to three fundamental quantities: the percent (rate), the value to which the
More informationARITHMETIC. Overview. Testing Tips
ARITHMETIC Overview The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental
More information1.3 Order of Operations
1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit
More information2. In solving percent problems with a proportion, use the following pattern:
HFCC Learning Lab PERCENT WORD PROBLEMS Arithmetic  11 Many percent problems can be solved using a proportion. In order to use this method, you should be familiar with the following ideas about percent:
More informationAccuplacer Arithmetic Study Guide
Testing Center Student Success Center 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
More informationWord Problems. Simplifying Word Problems
Word Problems This sheet is designed as a review aid. If you have not previously studied this concept, or if after reviewing the contents you still don t pass, you should enroll in the appropriate math
More informationSimply Math. Everyday Math Skills NWT Literacy Council
Simply Math Everyday Math Skills 2009 NWT Literacy Council Acknowledgement The NWT Literacy Council gratefully acknowledges the financial assistance for this project from the Department of Education, Culture
More informationTHINGS TO REMEMBER CONSUMER MATHEMATICS
PREMIER CURRICULUM SERIES Based on the Sunshine State Standards for Secondary Education, established by the State of Florida, Department of Education THINGS TO REMEMBER CONSUMER MATHEMATICS Copyright 2009
More informationPlans for Monday, May 19, 2014 By: Cheryl Casey
Plans for Monday, May 19, 2014 Students will continue graphing and writing inequalities HW: Graphing and Writing Inequalities, due Tuesday Students will graph and write inequalities HW: Graphing and Writing
More informationWorking with percentages. Introduction. Try these. Think about
Working with percentages Introduction You will have met percentages before. They are very useful because they are easier to work with than fractions and make it easy to compare things, for example, test
More informationMath Refresher. Book #2. Workers Opportunities Resources Knowledge
Math Refresher Book #2 Workers Opportunities Resources Knowledge Contents Introduction...1 Basic Math Concepts...2 1. Fractions...2 2. Decimals...11 3. Percentages...15 4. Ratios...17 Sample Questions...18
More informationMath 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
More informationPart 1 Expressions, Equations, and Inequalities: Simplifying and Solving
Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words
More informationProblem Set 1: Compound Interest Problems
Problem Sets FINA 5170 Fall 2006 Problem Set 1: Compound Interest Problems Prior to attempting problems 137, please review examples 1, 2, 3, 4, and 5 of Lecture Topic 4. 1. Suppose you invest $1,000 on
More informationACCUPLACER Arithmetic Assessment Preparation Guide
ACCUPLACER Arithmetic Assessment 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 at George
More informationIn order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Percentages In this unit we shall look at the meaning of percentages and carry out calculations involving percentages. We will also look at the use of the percentage button on calculators. In order to
More informationCostVolumeProfit Analysis
CostVolumeProfit Analysis Costvolumeprofit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. In performing this analysis, there
More informationTeaching & Learning Plans. Applications of Geometric Sequences and Series. Junior Certificate Syllabus Leaving Certificate Syllabus
Teaching & Learning Plans Applications of Geometric Sequences and Series Junior Certificate Syllabus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what
More information3.4 Multiplication and Division of Rational Numbers
3.4 Multiplication and Division of Rational Numbers We now turn our attention to multiplication and division with both fractions and decimals. Consider the multiplication problem: 8 12 2 One approach is
More informationcount up and down in tenths count up and down in hundredths
Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number
More informationHOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9
HOSPITALITY Math Assessment 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 at George
More informationModule 2: Working with Fractions and Mixed Numbers. 2.1 Review of Fractions. 1. Understand Fractions on a Number Line
Module : Working with Fractions and Mixed Numbers.1 Review of Fractions 1. Understand Fractions on a Number Line Fractions are used to represent quantities between the whole numbers on a number line. A
More informationGRE MATH REVIEW #4. To find 30% of 200, convert 30% to.30. Then multiply 200 by.30, which results in 60. Hence, 60 is 30% of 200.
GRE MATH REVIEW #4 Percentages A percent is just a shorthand way of expressing a fraction whose denominator is 100. Percent means per 100, out of 100, or divided by 100. For example, 25% = 25/100 = 0.25
More informationPreAlgebra Lecture 6
PreAlgebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More informationImproper Fractions and Mixed Numbers
This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All
More informationSummary of Skills and Scores
Skills Assessment Summary of Skills and Scores Applied Mathematics includes the mathematical reasoning, critical thinking and problemsolving techniques used to communicate workrelated information and
More informationSect Exponents: Multiplying and Dividing Common Bases
40 Sect 5.1  Exponents: Multiplying and Dividing Common Bases Concept #1 Review of Exponential Notation In the exponential expression 4 5, 4 is called the base and 5 is called the exponent. This says
More informationGrade 7/8 Math Circles February 910, 2016
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles February 910, 2016 Modular Arithmetic 1 Introduction: The 12hour Clock Question:
More informationClick on the links below to jump directly to the relevant section
Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationAccuplacer Elementary Algebra Study Guide for Screen Readers
Accuplacer Elementary Algebra Study Guide for Screen Readers The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra test. Reviewing these
More informationLESSON SUMMARY. Manipulation of Real Numbers
LESSON SUMMARY CXC CSEC MATHEMATICS UNIT TWO: COMPUTATION Lesson 2 Manipulation of Real Numbers Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1. (Some helpful exercises and page numbers
More informationPercentages. It is quite straightforward to convert a percent into a fraction or decimal (and vice versa) using the following rules:
What do percentages mean? Percentages Academic Skills Advice Percent (%) means per hundred. e.g. 22% means 22 per 00, and can also be written as a fraction ( 22 00 ) or a decimal (0.22) It is quite straightforward
More information$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months?
Simple Interest, Compound Interest, and Effective Yield Simple Interest The formula that gives the amount of simple interest (also known as addon interest) owed on a Principal P (also known as present
More informationChapter 3 Review Math 1030
Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%
More informationAll the examples in this worksheet and all the answers to questions are available as answer sheets or videos.
BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Algebra 1 In this section we will look at  the meaning of symbols  the language of algebra  substituting numbers into algebraic expressions  simplifying
More informationPractice Math Placement Exam
Practice Math Placement Exam The following are problems like those on the Mansfield University Math Placement Exam. You must pass this test or take MA 0090 before taking any mathematics courses. 1. What
More informationNumber Systems and Radix Conversion
Number Systems and Radix Conversion Sanjay Rajopadhye, Colorado State University 1 Introduction These notes for CS 270 describe polynomial number systems. The material is not in the textbook, but will
More informationPERCENTAGES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier
Mathematics Revision Guides ercentages age 1 of 14 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier ERCENTAGES Version: 2.3 Date: 01022014 Mathematics Revision Guides ercentages
More informationCOMPASS Numerical Skills/PreAlgebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13
COMPASS Numerical Skills/PreAlgebra 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
More informationPERCENTS  compliments of Dan Mosenkis
PERCENTS  compliments of Dan Mosenkis Percent Basics: Percents are connected to many ideas: fractions, decimals, proportions, relative amounts, and multiplicative change. You could say they are like the
More informationProject V Building Up Savings and Debt
Project V Building Up Savings and Debt 1 Introduction During the January Workshop, oh so long ago, we talked about compound interest. If you deposit a pincipal P into a savings account with an interest
More informationEQUATIONS. Main Overarching Questions: 1. What is a variable and what does it represent?
EQUATIONS Introduction to Variables, Algebraic Expressions, and Equations (2 days) Overview of Objectives, students should be able to: Main Overarching Questions: 1. Evaluate algebraic expressions given
More informationLesson 1 Order of Operations
Lesson 1 Order of Operations "Operations" means things like add, subtract, multiply, divide Student A solved the following problem: 177 x 2 = 20. Is he correct? Why or why not? Lesson 1 Order of Operations
More informationDecimal 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
More informationMake the denominators the same, convert the numerators by multiplying, then add the numerators.
Experience & Outcome: MNU 207a I have investigated the everyday contexts in which simple fractions, percentages or decimal fractions are used and can carry out the necessary calculations to solve related
More informationIntroduction. Percent Increase/Decrease. Module #1: Percents Bus 130 1
Module #1: Percents Bus 130 1 Introduction In this module, we are going to use the process of excavating soil to demonstrate the mathematical concept of percent changes and problem solving skills. When
More informationPercents. Writing percents as decimals. How to change a percent to a decimal.
Percents Introduction: Percent (%) means per hundred or hundredths. When you read in the newspaper that 80% of the voters voted, it means that 80 out of 100 eligible citizens voted. A percent can be considered
More informationLinear Equations and Inequalities
Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109  Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................
More informationCalculate the amount if you know the total and percentage
Calculate the amount if you know the total and percentage For example, if you purchase a computer for $800 and there is an 8.9% sales tax, how much do you have to pay for the sales tax? In this example,
More informationActivity 2: Arithmetic
Activity 2: Arithmetic Now that you ve written a few programs, let s take a step back and discuss how to do basic arithmetic. But first, there s something important to know about why you re working in
More informationhp calculators HP 30S Solving Problems Involving Percents Percentages Practice Working Problems Involving Percentages
HP 30S Solving Problems Involving Percents Percentages Practice Working Problems Involving Percentages Percentages The percentage is defined as the number of parts for each hundred, and is usually abbreviated
More informationObjectives. 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
More information2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.
Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard
More information7. Finance. Maths for Economics. 1 Finance. Vera L. te Velde. 27. August Effective annual interest rates
Maths for Economics 7. Finance Vera L. te Velde 27. August 2015 1 Finance We now know enough to understand how to mathematically analyze many financial situations. Let s start with a simply bank account
More informationSolving Equations, Formulas, and Proportions
Solving Equations, Formulas, and Proportions Section : Introduction One of the basic goals of algebra is solving equations. An equation is a mathematical statement in which two epressions equal one another.
More informationPersonal Financial Literacy
Personal Financial Literacy 7 Unit Overview Being financially literate means taking responsibility for learning how to manage your money. In this unit, you will learn about banking services that can help
More informationMaths Assessment Year 4: Fractions
Name: Maths Assessment Year : Fractions 1. Recognise and show, using diagrams, families of common equivalent fractions. 2. Count up and down in hundredths. 3. Solve problems involving increasingly harder
More informationparent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE
TM parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE 5 America s schools are working to provide higher quality instruction than ever before. The way we taught students in the past simply does
More informationOrder of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A.
Order of Operations Section 1: Introduction You know from previous courses that if two quantities are added, it does not make a difference which quantity is added to which. For example, 5 + 6 = 6 + 5.
More informationCapital Budgeting Decisions Tools
Management Accounting 217 Capital Budgeting Decisions Tools In many businesses, growth is a major factor to business success. Substantial growth in sales may eventually means a need to expand plant capacity.
More informationAdding and Subtracting Mixed Numbers and Improper Fractions
Just like our counting numbers (1, 2, 3, ), fractions can also be added and subtracted. When counting improper fractions and mixed numbers, we are counting the number wholes and parts. Note: The rules
More informationSection 1. Proportions
Worksheet.5 Percentages Section Proportions A pie is cut into twelve pieces. John eats five pieces, Peter eats one piece and Chris and Michael eat three pieces each. If we ask what proportion of the pie
More informationDECIMALS. The student will be able to:
DECIMALS The student will be able to: 1. Perform basic operations using decimal numbers: addition, subtraction multiplication, and division. Demonstrate an understanding of place value Locate decimal numbers
More informationeday 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
More informationDECIMAL 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
More informationExperience is a hard teacher because she gives the test first, the lesson afterward. Vernon Law DRAFT
! Lesson 24 Ins and Outs 111 Lesson 24 Ins and Outs Learning Objecves 1. Distinguish between inputs (independent variables) and outputs (dependent variables). 2. Evaluate expressions and formulas. 3.
More informationMath News! Focus Area Topic A. 3 rd Grade Math. Grade 3, Module 3, Topic A. Properties of Multiplication and Division
Grade, Module, Topic A rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69 Topic A. Topic A. Properties of Multiplication
More informationBasic Calculations and Percentages
Saturday Xtra XSheet: 1 Basic Calculations and Percentages Key Concepts In this session, we will focus on summarising what you need to know about:  Basic Calculations (revision of earlier work) o Scientific
More information5.4 Solving Percent Problems Using the Percent Equation
5. Solving Percent Problems Using the Percent Equation In this section we will develop and use a more algebraic equation approach to solving percent equations. Recall the percent proportion from the last
More informationTo Multiply Decimals
4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by
More informationDecimals Worksheets. The decimal point separates the whole numbers from the fractional part of a number.
Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 8.09 In a whole number the decimal point is all the way to the right, even if it is not shown in
More informationGrade 6 Math Circles Fall 2012 Applications of Percent
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2012 Applications of Percent A percentage is a way of expressing a number as
More informationLESSON 5  DECIMALS INTRODUCTION
LESSON 5  DECIMALS INTRODUCTION Now that we know something about whole numbers and fractions, we will begin working with types of numbers that are extensions of whole numbers and related to fractions.
More informationWelcome to Basic Math Skills!
Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots
More informationBalancing Chemical Equations
Balancing Chemical Equations A mathematical equation is simply a sentence that states that two expressions are equal. One or both of the expressions will contain a variable whose value must be determined
More informationIntroduction 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
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 (125) 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 information5.1 Simple and Compound Interest
5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?
More informationA fraction is a noninteger quantity expressed in terms of a numerator and a denominator.
1 Fractions Adding & Subtracting A fraction is a noninteger quantity expressed in terms of a numerator and a denominator. 1. FRACTION DEFINITIONS 1) Proper fraction: numerator is less than the denominator.
More informationChapter 3. The Concept of Elasticity and Consumer and Producer Surplus. Chapter Objectives. Chapter Outline
Chapter 3 The Concept of Elasticity and Consumer and roducer Surplus Chapter Objectives After reading this chapter you should be able to Understand that elasticity, the responsiveness of quantity to changes
More informationB. Examples  Use the given conditions to write a system of equations. Solve the system and answer the question.
Math 123  Section 4.4  Problem Solving Using Systems of Equations  Part II  Page 1 Section 4.4 Problem Solving Using Systems of Equations  Part II I. In general A. Remember to 1. Define the variables.
More informationArithmetic Circuits Addition, Subtraction, & Multiplication
Arithmetic Circuits Addition, Subtraction, & Multiplication The adder is another classic design example which we are obliged look at. Simple decimal arithmetic is something which we rarely give a second
More informationChapter 24 Measuring Domestic Output and National Income QUESTIONS. 1. In what ways are national income statistics useful? LO1
Chapter 24 Measuring Domestic Output and National Income QUESTIONS 1. In what ways are national income statistics useful? LO1 Answer: National income accounting does for the economy as a whole what private
More informationSuperSpeed Math, copyright Chris Biffle SuperSpeed Math 2.0
SuperSpeed Math, copyright Chris Biffle SuperSpeed Math. Addition, Subtraction, Multiplication, Division And the Gnarlies!  Special. Bonus: Fractions!!! Chris Biffle WholeBrainTeaching.com ChrisBiffle@WholeBrainTeaching.com
More informationSection 1.5 Exponents, Square Roots, and the Order of Operations
Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.
More informationA percentage is a fraction with a denominator (bottom number) of % = 23
Chapter 5 Percentages We have all seen advertisements on television that use percentages. Shops selling items at a % discount or cereal boxes offering % more than usual for the same price. Percentages
More informationFROM THE SPECIFIC TO THE GENERAL
CONNECT: Algebra FROM THE SPECIFIC TO THE GENERAL How do you react when you see the word Algebra? Many people find the concept of Algebra difficult, so if you are one of them, please relax, as you have
More informationMATH Fundamental Mathematics II.
MATH 10032 Fundamental Mathematics II http://www.math.kent.edu/ebooks/10032/funmath2.pdf Department of Mathematical Sciences Kent State University December 29, 2008 2 Contents 1 Fundamental Mathematics
More informationPERPETUITIES NARRATIVE SCRIPT 2004 SOUTHWESTERN, A THOMSON BUSINESS
NARRATIVE SCRIPT 2004 SOUTHWESTERN, A THOMSON BUSINESS NARRATIVE SCRIPT: SLIDE 2 A good understanding of the time value of money is crucial for anybody who wants to deal in financial markets. It does
More informationName: CONVERTING BEWTEEN FRACTIONS, DECIMALS, AND PERCENTS DIRECTED LEARNING ACTIVITY
Name: CONVERTING BEWTEEN FRACTIONS, DECIMALS, AND PERCENTS DIRECTED LEARNING ACTIVITY Objective: Convert between fractions, decimals, and percents. Activity: You will learn how to convert fractions to
More informationH.C.C.T.P. Highway Construction Careers Training Program. Entrance Exam. Study Guide
H.C.C.T.P. Highway Construction Careers Training Program Entrance Exam Study Guide Entrance Exam Study Guide How to use this study guide: This study guide is to prepare you for the math section on your
More informationhp calculators HP 17bII+ Net Present Value and Internal Rate of Return Cash Flow Zero A Series of Cash Flows What Net Present Value Is
HP 17bII+ Net Present Value and Internal Rate of Return Cash Flow Zero A Series of Cash Flows What Net Present Value Is Present Value and Net Present Value Getting the Present Value And Now For the Internal
More informationRound decimals to the nearest whole number
Round decimals to the nearest whole number Learning Objective Simplifying Fractions Simplified Fractions To simplify a fraction, we find an equivalent fraction which uses the smallest numbers possible.
More informationAccounting & Finance Foundations Math Skills A Review. Place Value Percentages Calculating Interest Discounts Compounding
Accounting & Finance Foundations Math Skills A Review Place Value Percentages Calculating Interest Discounts Compounding Place Value Ten Thousands Thousands Hundredths Tenths Ones Tens Hundreds Thousands
More informationAll the examples in this worksheet and all the answers to questions are available as answer sheets or videos.
BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Numbers 3 In this section we will look at  improper fractions and mixed fractions  multiplying and dividing fractions  what decimals mean and exponents
More informationChapter 15: Spending, Income and GDP
Chapter 15: Spending, Income and GDP By the end of this chapter, you will be able to: Define GDP Calculate GDP by: adding up value added of production. adding up expenditure. adding up income. Distinguish
More informationMaths Workshop for Parents 2. Fractions and Algebra
Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)
More information