5.4 Solving Percent Problems Using the Percent Equation


 Mercy Cummings
 5 years ago
 Views:
Transcription
1 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 section: percent 100 = percentage base Considering that percent 100 of it in the equation: is merely a percent divided by 100, we can consider the decimal form percent = percentage base base percent = base percentage base This last statement is called the percent equation. Remember that the term percent refers to the decimal (or fraction) form, which has already been divided by 100. This percent equation involves the familiar quantities from the past section: percent, base, and percentage. Once identified, the method of solving the equation utilizes our steps for solving equations from Chapter. Suppose we are asked to find 18% of 50. The percent is 18% = 0.18 (converted to a decimal), and the base is 50. x = x = 5 Thus 18% of 50 is 5. Let s use this approach to resolve Example 1 from the last section. Example 1 Find the following percentages. a. 8% of 10 b. 5% of 86 c. 7.5% of 1500 d % of 00 e. 150% of
2 Solution a. The percent is 8% = 0.8 (converted to decimal) and the base is 10. x = x = 57.6 Thus 8% of 10 is b. The percent is 5% = 0.5 (converted to decimal) and the base is 86. x = x = 18.7 Thus 5% of 86 is c. The percent is 7.5% = (converted to decimal) and the base is x = x = Thus 7.5% of 1500 is d. The percent is 15 1 % = 15.5% = (converted to decimal) and the base is 00. x = x = 37 Thus 15 1 % of 00 is 37. e. The percent is 150% = 1.50 (converted to decimal) and the base is 60. x = x = 390 Thus 150% of 60 is
3 The second type of percent problem involved one in which the percentage is given and the base is unknown. Suppose we know that 68% of a number is 0. The percent is 68% = 0.68, converted to a decimal. This time the percentage is 0, and the base is unknown. Using the percent equation: 0.68x = 0 x = = 300 Thus 68% of 300 is 0. Note that the percent equation provides an easy check of our answer, since = 0, verifying our answer. As more practice, let s resolve Example from the last section. Example Solve the following percent problems. a. % of what number is equal to 10? b. 35% of what number is equal to 51.8? c. 7.5% of what number is equal to 70? d. 6 1 %of what number is equal to 75? e. 15% of what number is equal to 800? Solution a. The percent is % = 0. (converted to decimal) and the percentage is x = 10 x = = 500 Thus % of 500 is 10. Checking the value: = 10. b. The percent is 35% = 0.35 (converted to decimal) and the percentage is x = 51.8 x = = 18 Thus 35% of 18 is Checking the value: =
4 c. The percent is 7.5% = (converted to decimal) and the percentage is x = 70 x = = 3600 Thus 7.5% of 3600 is 70. Checking the value: = 70. d. The percent is 6 1 % = 6.5% = (converted to decimal) and the percentage is x = 75 x = = 00 Thus 6 1 % of 00 is 75. Checking the value: = 75. e. The percent is 15% = 1.5 (converted to decimal) and the percentage is x = 800 x = = 60 Thus 15% of 60 is 800. Checking the value: = 800. The third type of percent problem is where both the percentage and base are given, but the percent is unknown. Suppose we want to know what percent 08 represents out of 30. The percentage is 08, the base is 30, and the percent is unknown. p 30 = 08 p = p = 0.65 = 65% 398
5 Thus 08 represents 65% of 30. Again note that we can check the equation: = 08. Note the use of the variable p in this equation. It was used as a reminder that p represents a percent, and thus must be converted back to a percent for the final step. This is a good habit to get into in solving percent equations. Now let s resolve Example 3 from the last section. Example 3 Find the following percents. a. 36 is what percent of 80? b. 13 is what percent of 165? c. 10 is what percent of 180? d. 00 is what percent of 160? Solution a. The percentage is 36, the base is 80, and the percent is unknown. p 80 = 36 p = p = 0.5 = 5% Thus 36 is 5% of 80. Checking the value: = 36. b. The percentage is 13, the base is 165, and the percent is unknown. p 165 = 13 p = p = 0.80 = 80% Thus 13 is 80% of 165. Checking the value: = 13. c. The percentage is 10, the base is 180, and the percent is unknown. p 180 = 10 p = p = 3 = 66 3 % 399
6 Thus 10 is 66 % of 180. Note in this problem we did not convert to a 3 decimal, since a repeating decimal would have resulted. Checking the value: 180 = d. The percentage is 00, the base is 160, and the percent is unknown. p 160 = 00 p = p = 1.5 = 15% Thus 00 is 15% of 160. Checking the value: = 00. Often students find the percent equation easier to use than the proportion method. Keep in mind that both methods require you to recognize the percent, the base, and the percentage. We will resolve Example from the previous section, however this time we use the percent equation approach, rather than percent proportions. Example Solve the following percent problems. a. 1 %of 60 is what number? b. 35% of what number is 30.1? c. 11 is what percent of 10? d. 97 represents 5% of what number? e. 19.8% of 100 is what number? f. 0 represents what percent of 180? 00
7 Solution a. The percent, base, and percentage are: percent = 1 % =.5% = 0.05 base = 60 percentage = x (unknown) x = x = 7.9 Thus 1 % of 60 is 7.9. b. The percent, base, and percentage are: percent = 35% = 0.35 base = x (unknown) percentage = x = 30.1 x = = 86 Thus 35% of 86 is Checking the value: = c. The percent, base, and percentage are: percent = p (unknown) base = 10 percentage = 11 p 10 = 11 p = p = 0.80 = 80% Thus 11 is 80% of 10. Checking the value: =
8 d. The percent, base, and percentage are: percent = 5% = 0.5 base = x (unknown) percentage = x = 97 x = = 660 Thus 97 represents 5% of 660. Checking the value: = 97. e. The percent, base, and percentage are: percent = 19.8% = base = 100 percentage = x (unknown) x = x = 37.6 Thus 19.8% of 100 is f. The percent, base, and percentage are: percent = p (unknown) base = 180 percentage = 0 p 180 = 0 p = p = 3 = % Thus 0 represents % of 180. Checking the value: 180 = 0 3 Note again we used fractions here to avoid using repeating decimals. 0
9 Terminology percent equation Exercise Set 5. Solve the following percent problems. Remember that you will need to recognize the percent, the base, and the percentage in order to set up the percent equation % of 00 is what number?. 65% of 18 is what number? 3. 35% of what number is 80?. 55% of what number is 75? is what percent of 160? is what percent of 00? 7. 37% of 150 is what number? 8. 56% of 10 is what number? 9. 5 is what percent of 60? is what percent of 50? % of what number is 109.6? 1. 57% of what number is 86.5? % of,000 is what number? % of 1,300 is what number? % of what number is 37.5? % of what number is 316.8? is what percent of 7? is what percent of 900? %of 900 is what number? %of 800 is what number? 1. 10% of what number is 91?. 160% of what number is 83.? is what percent of 150?. 500 is what percent of 360? % of 100 is what number? %of 80 is what number? % of what number is 8.075? %of what number is 90.3? is what percent of 0? is what percent of 50? % of 30 is what number? 3. 8% of 50 is what number? %of what number is 100? 3. 9 % of what number is 17.9? is what percent of 86? is what percent of 70? % of 80 is what number? % of 6 is what number? % of what number is 0? 0. 0% of what number is 1? 03
Chapter 1: Order of Operations, Fractions & Percents
HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain
More information3.3 Addition and Subtraction of Rational Numbers
3.3 Addition and Subtraction of Rational Numbers In this section we consider addition and subtraction of both fractions and decimals. We start with addition and subtraction of fractions with the same denominator.
More informationThree Types of Percent Problems
6.4 Three Types of Percent Problems 6.4 OBJECTIVES. Find the unknown amount in a percent problem 2. Find the unknown rate in a percent problem 3. Find the unknown base in a percent problem From your work
More information5 Systems of Equations
Systems of Equations Concepts: Solutions to Systems of EquationsGraphically and Algebraically Solving Systems  Substitution Method Solving Systems  Elimination Method Using Dimensional Graphs to Approximate
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 information5.2 Percent: Converting Between Fractions, Decimals, and Percents
5.2 Percent: Converting Between Fractions, Decimals, and Percents The concept of percent permeates most common uses of mathematics in everyday life. We pay taes based on percents, many people earn income
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 informationEquations, Inequalities & Partial Fractions
Contents Equations, Inequalities & Partial Fractions.1 Solving Linear Equations 2.2 Solving Quadratic Equations 1. Solving Polynomial Equations 1.4 Solving Simultaneous Linear Equations 42.5 Solving Inequalities
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 information1.5 Greatest Common Factor and Least Common Multiple
1.5 Greatest Common Factor and Least Common Multiple This chapter will conclude with two topics which will be used when working with fractions. Recall that factors of a number are numbers that divide into
More informationUseful Number Systems
Useful Number Systems Decimal Base = 10 Digit Set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Binary Base = 2 Digit Set = {0, 1} Octal Base = 8 = 2 3 Digit Set = {0, 1, 2, 3, 4, 5, 6, 7} Hexadecimal Base = 16 = 2
More informationPreliminary Mathematics
Preliminary Mathematics The purpose of this document is to provide you with a refresher over some topics that will be essential for what we do in this class. We will begin with fractions, decimals, and
More informationConversions between percents, decimals, and fractions
Click on the links below to jump directly to the relevant section Conversions between percents, decimals and fractions Operations with percents Percentage of a number Percent change Conversions between
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 information3.1. Solving linear equations. Introduction. Prerequisites. Learning Outcomes. Learning Style
Solving linear equations 3.1 Introduction Many problems in engineering reduce to the solution of an equation or a set of equations. An equation is a type of mathematical expression which contains one or
More informationMACMILLAN/McGRAWHILL. MATH CONNECTS and IMPACT MATHEMATICS WASHINGTON STATE MATHEMATICS STANDARDS. ESSENTIAL ACADEMIC LEARNING REQUIREMENTS (EALRs)
MACMILLAN/McGRAWHILL MATH CONNECTS and IMPACT MATHEMATICS TO WASHINGTON STATE MATHEMATICS STANDARDS ESSENTIAL ACADEMIC LEARNING REQUIREMENTS (EALRs) And GRADE LEVEL EXPECTATIONS (GLEs) / Edition, Copyright
More informationSolving Systems of Two Equations Algebraically
8 MODULE 3. EQUATIONS 3b Solving Systems of Two Equations Algebraically Solving Systems by Substitution In this section we introduce an algebraic technique for solving systems of two equations in two unknowns
More informationIrrational Numbers. A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers.
Irrational Numbers A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers. Definition: Rational Number A rational number is a number that
More informationActivity 1: Using base ten blocks to model operations on decimals
Rational Numbers 9: Decimal Form of Rational Numbers Objectives To use base ten blocks to model operations on decimal numbers To review the algorithms for addition, subtraction, multiplication and division
More informationRatio and Proportion Study Guide 12
Ratio and Proportion Study Guide 12 Ratio: A ratio is a comparison of the relationship between two quantities or categories of things. For example, a ratio might be used to compare the number of girls
More informationCOMP 250 Fall 2012 lecture 2 binary representations Sept. 11, 2012
Binary numbers The reason humans represent numbers using decimal (the ten digits from 0,1,... 9) is that we have ten fingers. There is no other reason than that. There is nothing special otherwise about
More informationFractions to decimals
Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of
More informationTrigonometric Functions and Triangles
Trigonometric Functions and Triangles Dr. Philippe B. Laval Kennesaw STate University August 27, 2010 Abstract This handout defines the trigonometric function of angles and discusses the relationship between
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 informationSolving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
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 informationLINEAR EQUATIONS IN TWO VARIABLES
66 MATHEMATICS CHAPTER 4 LINEAR EQUATIONS IN TWO VARIABLES The principal use of the Analytic Art is to bring Mathematical Problems to Equations and to exhibit those Equations in the most simple terms that
More informationFinancial Mathematics
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
More information3.6. Partial Fractions. Introduction. Prerequisites. Learning Outcomes
Partial Fractions 3.6 Introduction It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions. For 4x + 7 example it can be shown that x 2 + 3x + 2 has the same
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 informationPartial Fractions. (x 1)(x 2 + 1)
Partial Fractions Adding rational functions involves finding a common denominator, rewriting each fraction so that it has that denominator, then adding. For example, 3x x 1 3x(x 1) (x + 1)(x 1) + 1(x +
More informationNUMBER SYSTEMS. William Stallings
NUMBER SYSTEMS William Stallings The Decimal System... The Binary System...3 Converting between Binary and Decimal...3 Integers...4 Fractions...5 Hexadecimal Notation...6 This document available at WilliamStallings.com/StudentSupport.html
More informationEquations Involving Fractions
. Equations Involving Fractions. OBJECTIVES. Determine the ecluded values for the variables of an algebraic fraction. Solve a fractional equation. Solve a proportion for an unknown NOTE The resulting equation
More informationSolution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together
Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a
More informationBinary Adders: Half Adders and Full Adders
Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order
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 informationAlgebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.
Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear
More informationFactoring Trinomials using Algebra Tiles Student Activity
Factoring Trinomials using Algebra Tiles Student Activity Materials: Algebra Tiles (student set) Worksheet: Factoring Trinomials using Algebra Tiles Algebra Tiles: Each algebra tile kits should contain
More informationMATH0910 Review Concepts (Haugen)
Unit 1 Whole Numbers and Fractions MATH0910 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 informationConfidence Intervals for One Standard Deviation Using Standard Deviation
Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from
More informationBuoyant Force. Goals and Introduction
Buoyant Force Goals and Introduction When an object is placed in a fluid, it either floats or sinks. While the downward gravitational force, F g, still acts on the object, an object in a fluid is also
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 informationDesigner: Nathan Kimball. Stage 1 Desired Results
Interpolation Subject: Science, math Grade: 68 Time: 4 minutes Topic: Reading Graphs Designer: Nathan Kimball Stage 1 Desired Results Lesson Overview: In this activity students work with the direct linear
More informationUsing Proportions to Solve Percent Problems I
RP71 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving
More informationMultiplying Fractions
. Multiplying Fractions. OBJECTIVES 1. Multiply two fractions. Multiply two mixed numbers. Simplify before multiplying fractions 4. Estimate products by rounding Multiplication is the easiest of the four
More informationDecimal Notations for Fractions Number and Operations Fractions /4.NF
Decimal Notations for Fractions Number and Operations Fractions /4.NF Domain: Cluster: Standard: 4.NF Number and Operations Fractions Understand decimal notation for fractions, and compare decimal fractions.
More informationHow To Understand Algebraic Equations
Please use the resources below to review mathematical concepts found in chemistry. 1. Many Online videos by MiraCosta Professor Julie Harland: www.yourmathgal.com 2. Text references in red/burgundy and
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 informationNumeracy Preparation Guide. for the. VETASSESS Test for Certificate IV in Nursing (Enrolled / Division 2 Nursing) course
Numeracy Preparation Guide for the VETASSESS Test for Certificate IV in Nursing (Enrolled / Division Nursing) course Introduction The Nursing course selection (or entrance) test used by various Registered
More informationPartial Fractions. Combining fractions over a common denominator is a familiar operation from algebra:
Partial Fractions Combining fractions over a common denominator is a familiar operation from algebra: From the standpoint of integration, the left side of Equation 1 would be much easier to work with than
More informationEVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING Revised For ACCESS TO APPRENTICESHIP
EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING For ACCESS TO APPRENTICESHIP MATHEMATICS SKILL OPERATIONS WITH INTEGERS AN ACADEMIC SKILLS MANUAL for The Precision Machining And Tooling Trades
More informationGMAT.cz GMAT (Graduate Management Admission Test) Preparation Course Syllabus
Lesson Overview of Lesson Plan Key Content Covered Numbers 1&2 An introduction to GMAT. GMAT introduction Handing over Princeton Review Book and GMAT.cz Package DVD from the course book and an insight
More informationLesson 7 ZScores and Probability
Lesson 7 ZScores and Probability Outline Introduction Areas Under the Normal Curve Using the Ztable Converting Zscore to area area less than z/area greater than z/area between two zvalues Converting
More informationis identically equal to x 2 +3x +2
Partial fractions 3.6 Introduction It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions. 4x+7 For example it can be shown that has the same value as 1 + 3
More information6.4 Normal Distribution
Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under
More information5.5. Solving linear systems by the elimination method
55 Solving linear systems by the elimination method Equivalent systems The major technique of solving systems of equations is changing the original problem into another one which is of an easier to solve
More informationCalculator Notes for the TINspire and TINspire CAS
INTRODUCTION Calculator Notes for the Getting Started: Navigating Screens and Menus Your handheld is like a small computer. You will always work in a document with one or more problems and one or more
More informationMultiplying and Dividing Algebraic Fractions
. Multiplying and Dividing Algebraic Fractions. OBJECTIVES. Write the product of two algebraic fractions in simplest form. Write the quotient of two algebraic fractions in simplest form. Simplify a comple
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 PRETEST
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 informationMatrices 2. Solving Square Systems of Linear Equations; Inverse Matrices
Matrices 2. Solving Square Systems of Linear Equations; Inverse Matrices Solving square systems of linear equations; inverse matrices. Linear algebra is essentially about solving systems of linear equations,
More informationPartial Fractions. p(x) q(x)
Partial Fractions Introduction to Partial Fractions Given a rational function of the form p(x) q(x) where the degree of p(x) is less than the degree of q(x), the method of partial fractions seeks to break
More informationGeorgia Milestones Content Weights for the 20142015 School Year
Grade 3 Operations and Algebraic Thinking 25% Number and Operations 35% Measurement and Data 30% Geometry 10% Earth 34% Life 33% Physical 33% History 30% Geography 20% Government/Civics 30% Economics 20%
More informationPercent, Sales Tax, & Discounts
Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase
More information23. RATIONAL EXPONENTS
23. RATIONAL EXPONENTS renaming radicals rational numbers writing radicals with rational exponents When serious work needs to be done with radicals, they are usually changed to a name that uses exponents,
More information9.2 Summation Notation
9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a
More information2.6 Exponents and Order of Operations
2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated
More informationGMAT SYLLABI. Types of Assignments  1 
GMAT SYLLABI The syllabi on the following pages list the math and verbal assignments for each class. Your homework assignments depend on your current math and verbal scores. Be sure to read How to Use
More informationRelative and Absolute Change Percentages
Relative and Absolute Change Percentages Ethan D. Bolker Maura M. Mast September 6, 2007 Plan Use the credit card solicitation data to address the question of measuring change. Subtraction comes naturally.
More informationTo give it a definition, an implicit function of x and y is simply any relationship that takes the form:
2 Implicit function theorems and applications 21 Implicit functions The implicit function theorem is one of the most useful single tools you ll meet this year After a while, it will be second nature to
More informationActivities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median
Activities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median 58 What is a Ratio? A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a
More informationPricing I: Linear Demand
Pricing I: Linear Demand This module covers the relationships between price and quantity, maximum willing to buy, maximum reservation price, profit maximizing price, and price elasticity, assuming a linear
More informationTest 4 Sample Problem Solutions, 27.58 = 27 47 100, 7 5, 1 6. 5 = 14 10 = 1.4. Moving the decimal two spots to the left gives
Test 4 Sample Problem Solutions Convert from a decimal to a fraction: 0.023, 27.58, 0.777... For the first two we have 0.023 = 23 58, 27.58 = 27 1000 100. For the last, if we set x = 0.777..., then 10x
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 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 informationSYSTEMS OF EQUATIONS AND MATRICES WITH THE TI89. by Joseph Collison
SYSTEMS OF EQUATIONS AND MATRICES WITH THE TI89 by Joseph Collison Copyright 2000 by Joseph Collison All rights reserved Reproduction or translation of any part of this work beyond that permitted by Sections
More information2.2 Scientific Notation: Writing Large and Small Numbers
2.2 Scientific Notation: Writing Large and Small Numbers A number written in scientific notation has two parts. A decimal part: a number that is between 1 and 10. An exponential part: 10 raised to an exponent,
More informationSequences. A sequence is a list of numbers, or a pattern, which obeys a rule.
Sequences A sequence is a list of numbers, or a pattern, which obeys a rule. Each number in a sequence is called a term. ie the fourth term of the sequence 2, 4, 6, 8, 10, 12... is 8, because it is the
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 informationPartial Fractions Decomposition
Partial Fractions Decomposition Dr. Philippe B. Laval Kennesaw State University August 6, 008 Abstract This handout describes partial fractions decomposition and how it can be used when integrating rational
More informationSolve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers
More informationMBA Jump Start Program
MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right
More information47 Numerator Denominator
JH WEEKLIES ISSUE #22 20122013 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 informationSecond Order Linear Nonhomogeneous Differential Equations; Method of Undetermined Coefficients. y + p(t) y + q(t) y = g(t), g(t) 0.
Second Order Linear Nonhomogeneous Differential Equations; Method of Undetermined Coefficients We will now turn our attention to nonhomogeneous second order linear equations, equations with the standard
More informationFree PreAlgebra Lesson 55! page 1
Free PreAlgebra 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 informationStanford Math Circle: Sunday, May 9, 2010 SquareTriangular Numbers, Pell s Equation, and Continued Fractions
Stanford Math Circle: Sunday, May 9, 00 SquareTriangular Numbers, Pell s Equation, and Continued Fractions Recall that triangular numbers are numbers of the form T m = numbers that can be arranged in
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 information1. Annuity a sequence of payments, each made at equally spaced time intervals.
Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology
More information5.1 Identifying the Target Parameter
University of California, Davis Department of Statistics Summer Session II Statistics 13 August 20, 2012 Date of latest update: August 20 Lecture 5: Estimation with Confidence intervals 5.1 Identifying
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 informationMath Circle Beginners Group October 18, 2015
Math Circle Beginners Group October 18, 2015 Warmup problem 1. Let n be a (positive) integer. Prove that if n 2 is odd, then n is also odd. (Hint: Use a proof by contradiction.) Suppose that n 2 is odd
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 realworld and mathematical
More informationGeometry Notes RIGHT TRIANGLE TRIGONOMETRY
Right Triangle Trigonometry Page 1 of 15 RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right
More information1.7 Graphs of Functions
64 Relations and Functions 1.7 Graphs of Functions In Section 1.4 we defined a function as a special type of relation; one in which each xcoordinate was matched with only one ycoordinate. We spent most
More information1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes
Arithmetic of Algebraic Fractions 1.4 Introduction Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an algebraic fraction.
More informationQuestions. Strategies August/September Number Theory. What is meant by a number being evenly divisible by another number?
Content Skills Essential August/September Number Theory Identify factors List multiples of whole numbers Classify prime and composite numbers Analyze the rules of divisibility What is meant by a number
More informationCONVERT QUADRATIC FUNCTIONS FROM ONE FORM TO ANOTHER (Standard Form <==> Intercept Form <==> Vertex Form) (By Nghi H Nguyen Dec 08, 2014)
CONVERT QUADRATIC FUNCTIONS FROM ONE FORM TO ANOTHER (Standard Form Intercept Form Vertex Form) (By Nghi H Nguyen Dec 08, 2014) 1. THE QUADRATIC FUNCTION IN INTERCEPT FORM The graph of the quadratic
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 informationSQUARES AND SQUARE ROOTS
1. Squares and Square Roots SQUARES AND SQUARE ROOTS In this lesson, students link the geometric concepts of side length and area of a square to the algebra concepts of squares and square roots of numbers.
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 information