Arithmetic made simple

164 Pages·2012·22.11 MB·English

Only $1.95
Arithmetic
Acomprehensive
guide for
Made self-studyand review
Simple
A. P.Sperlingand
Samuel D. Levison

ARITHMETIC
MADE
SIMPLE
By
ABRAHAM
P. SPERLING, PH.D.
And
SAMUEL D. LEVISON, M.S.
MADE SIMPLE BOOKS
DOUBLEDAY & COMPANY, INC.
GARDEN CITY, NEW YORK
©
Copyright 1960byDoubleday 4 Company, Inc.
AllRightsReserved
Printedinthe UnitedStatesofAmerica
ABOUT THIS BOOK
This book is for anyone who wants to learn the fundamentals of
arithmetic—. The reader can work with it himself with a minimum of out-
sidehelp ornoneatall.
Here is a book that can be of great value to parents, tutors and friends
who want to help others to improve their skill in arithmetic. The sub-
ject matter for the examples and problems is sure to be of interest to
the reader. As a unique feature, wherever necessary, the answers are
workedoutindetail.
Since arithmetic is a logical subject, it must be presented step by step
in an orderly and systematic way. In this book you will understand each
stage and topic before continuing on to the next one. Practice Exercises
follow each new topic so that the reader can measure his progress.
Arithmetic Made Simple explains and describes the operations and
—
methods of arithmetic as they are taught in the classroom from grades
1 through 8. Where there is a difference of opinion among educators
regardingthe best method of solving specific problems or examples, alter-
nateexplanationsandsolutionsareoffered.
It is all here for you to study and learn. Whether your interest is in
multi—plication, decimals, fractions or percents, you will find—it in this
book the book that makes arithmetic exciting and enjoyable the book
that shows millions of young people that arithmetic is not only valuable,
butalsofun!
—
ThePublisher
Digitized by the Internet Archive
2012
in
http://archive.org/details/arithmeticmadesiOOabra
...
TABLE OF CONTENTS
About This Book
CHAPTER ONE
LearningtoUse Our NumberSystem ... 9 Numbers to the Left and Right of the
HowThey Counted inEarly Times .... 9 DecimalPoint 11
Early Written Numbers 9 Understanding Place Values 11
Introduction of Hindu-Arabic Numer- Analyzing Numbers According to Place
als 10 Values 12
Reading and Writing Roman Numer- HowtoRead LargeNumbers 12
als 10 GroupingandWritingLargeNumbers . 13
How "Ten" Relates to OurNumber Sys- Rounding OffWhole Numbers 13
tem 11
CHAPTER TWO
AdditionandSubtractionofWholeNum- AddingbyPartialTotals .-y. 18
bers 15 The LanguageofSubtraction 19
The Language ofAddition 15 Subtraction Vocabulary 19
SightTest inMentalAddition 15 TheMethodsofSubtraction 19
Basic One HundredAdditionFacts .... 15 Adeptness in Subtraction RequiresDrill
Usea CardSystemtoPerfect YourMen- as inAddition 20
talAddition 15 SightTestinSubtraction 20
Practice in SightAddition 16 100 Subtraction Facts 20
ColumnAdditiontheModernWay 17 Use Cards to Gain Speed in Subtrac-
Suggestion Aids for Good Habits in tion 21
Adding 17 Subtractionof Three-Place Numbers In-
Gaining Speedin ColumnAddition .... 17 cluding Zero 21
HintsonLearningtoAddMentally 17 TheOldMethodofDoingSubtraction . 21
CopyingNumbersandAdding 18 AddingandSubtractingwithMoney....; 22
CHAPTER THREE
Multiplication and Division of Whole MultiplyingbyaNumberwithaZeroin
Numbers 24 the Multiplier !27j
Learning Multiplication Means Memo- Multiplying by a Number Ending in]
rization 24 Zero 27
Memory Hints for the Multiplication MultiplicationofMoney Numbers 28
Tables 25 Short Cuts inMultiplication 28
MultiplyingTwoandThree-FigureNum- Methods of Checking Results in Multi-
bers 25 plication 29
Learning"Carrying"inMultiplication .. 25 FindingRemainders 30
Multiplyingwith a Zeroin theMultipli- ProcedureinCheckingMultiplicationby
cand 26 CastingOutNines i 30
MultiplyingbyaTwo-FigureNumber .. 26 Division of Whole Numbers 31
Multiplying by a Three-Figure Num- HowWeExplainDivisioninOurSchools
ber 26 Today ........ ;. B2
B
.. ..
ArithmeticMadeSimple
Definitions 32 Handling Zerointhe Quotient 35
WhentheQuotientIsNot Exact 32 Checking Division by Casting Out
Division Drill 33 Nines 36
Study Procedures for Carrying Out Di- Short Division 36
vision 33 Division of Money Numbers 37
LearningAidsforTwo-FigureandThree- Placement of Point for Dollars and
FigureDivision 34 Cents 37
CHAPTER FOUR
AllAboutFractions 39 MultiplyingMixedNumbers 49
TheMeaningofaFraction 39 AShortWayofMultiplyingbyFractions 49
EandsofFractions 39 DivisionofFractions 50
Uses of Fractions 39 Dividinga FractionbyaWholeNumber 50
EquivalentFractions 40 Dividinga WholeNumber byaFraction 51
RaisingFractionstoHigherTerms 40 DividingaFractionbyaFraction 51
ReducingFractionstoLowerTerms .... 41 Dividing When There Are Mixed Num-
Changing Whole Numbers to Fractions 41 bers 51
Importance of the Least Common De- Dividing a Whole Number by a Mixed
nominator 42 Number 51
FindingtheLeastCommonDenominator 43 Dividing a Mixed Number by a Whole
StepstoFindaCommonDenominator.. 43 Number 52
Additionof Fractions 43 Dividing a Mixed Number by a Proper
SubtractionofFractions 44 Fraction 52
MultiplicationofFractions 46 Dividing a Proper Fraction by a Mixed
MultiplyingaFractionbyaWholeNum- Number 52
ber Dividing a Mixed Number by a Mixed
MultiplyingaWholeNumber byaFrac- Number 52
tion CheckingDivisionofFractions 52
Multiplying Whole Numbers by Mixed Finding the Whole When a Fractional
Numbers PartIsGiven 52
MultiplyingaFractionbyaFraction
..
CHAPTER FIVE
LeakntoUseDecimalswithEase 54 Subtractionof Decimals 60
Place Values in Decimals 54 Reminders When Subtracting Decimals 60
WritingDecimals 55 MultiplicationofDecimals 61
ReadingDecimals 55 MultiplyingDecimalsby10, 100,1000 . 62
AnotherWayofReadingDecimals 57 DivisionofNumbersby10, 100,1000 . 62
Comparingthe Values ofDecimals .... 57 A Short WaytoMultiply by .1, .01, .001 63
Interchange of Decimals and Common Division ofDecimals 64
Fractions 57 DividingaDecimalbya WholeNumber 64
HowDecimals Are RelatedtoMoney . 58 DividingaDecimalbyaDecimal 65
Addition of Decimals 59 Rounding Decimals 65
RemindersWhenAddingDecimals 59 Fractionand DecimalRelationships ... 66
AddingDecimalsandFractions 60
CHAPTER SIX
Percentage 68 Popular Percents 69
Memorizing Fractional Equivalents of ComparingPercents 70
Contents ...
Uses ofPercents 70 FindingaNumber WhenaPercent ofit
Percent ofaNumber 71 Is Given 74
ShortCutsforFindingPercentsMentally 72 Rounding OffPercents 75
FindingWhatPercentOneNumberIsof UsingPercentstoShowChanges ......^. 75
Another 73
CHAPTER SEVEN
How Percents are Used in Daily Busi- To FindOriginal Price WhenNetPrice
ness 77 Is Known 79
— —
Discount Commission Profit and Loss 77 FiguringMultipleDiscounts 79
Discount 77 Commission or Brokerage 80
Language ofDiscount 77 LanguageofCommission andBrokerage 81
RateofDiscount 77 Mathematics of Buying and Selling or
Profit and Loss 82
CHAPTER EIGHT
HowMoneyIs UsedtoEarnMoney 87 Applying the 60 Day-6% Method to
Figuring Interest andBank Borrowing . 87 Other Terms 89
Definitions 87 Compound Interest 90
Finding InterestbyFormula 87 How to Use a Compound Interest Table 91
Indirect Cases of Interest 88 CompoundInterestTable 91
The 60 Day-6% Method of Figuring In- BorrowingMoney 92
terest 89 SmallLoans andInstallment Buying ... 93
Installment Buying 93
CHAPTER NINE
Measure of Distance, Weight and Time 95 Subtraction of Denominate Numbers .. 98
Denominate Numbers 95 Multiplication of Denominate Numbers 99
Tables of Measur—es 96 DivisionofDenominateNumbers 99
Linear Measure Measures Lengths or ChangingfromHighertoLower Unitsof
Distances 96 Denominate Numbers 100
Weight Measures 96 The Metric System ofMeasurements .. 101
Liquid Measure 96 LinearMeasureintheMetricSystem .. 102
Dry Measure 96 Metric Tables ofMeasure 103
UnitsofCounting 96 MeasuringWeightsbytheMetricSystem 104
SurfaceMeasureorSquareMeasure .... 97 Finding Time Between Dates 104
Volume Measureor CubicMeasure .... 97 FiguringClockTimeinDifferentPartsof
Time Measure 97 the Country 105
Angle Measure 97 How to Figure Travel and Other Time
EquatingDenominateNumbers 97 Differences 106
—
Applying the FourFundamental Opera- Armed Services Time The 24-Hour
tions with Denominate Numbers .... 98 Clock 107
AdditionofDenominate Numbers 98
CHAPTER TEN
Measures of Lines, Angles and Perime- Angles 109
ters ofPlane Figures 108 Types andSizes of Angles 109
Lines 108 MeasuringAngles 110
—
TheLanguageofLines 108 Triangles Figures with Three Sides . Ill
.
ArithmeticMadeSimple
PartsofaTriangle Ill Perimeter of a Rectangle or Parallelo-
UsingtheSidestoNametheTriangle... Ill gram 116
UsingtheAnglestoNametheTriangle. 112 Perimeter—ofa Trapezoid 116
Figures withFourSides orMore 113 TheCircle ASpecialPlaneFigure .... 117
Quadrilaterals 114 PerimeterofaCircle 118
FindingPerimeters 114 AnExperimentinFindingaFormulafor
PerimeterofaTriangle 114 Circumference 118
PerimeterofaSquare 115
CHAPTER ELEVEN
MeasuringAreasandVolumes 120 MeasuringVolume 127
FindingtheAreaof a Rectangle 121 Another WayofFiguringtheVolumeof
FindingtheAreaofaSquare 121 aRectangularSolid 129
ToFindtheSideofaRectangle 122 Finding the Volume of a Triangular
Finding the AreasofParallelograms ... 123 Prism 129
FindingtheAreasof Triangles 124 FindingtheVolumeofaCylinder 130
FindingAreasofCircles 125
CHAPTER TWELVE
Comparison of Quantities by Ratio and HowtoIndicateRatio 132
Proportion 132 Proportion 133
Ratio 132
CHAPTER THIRTEEN
—
Graphs Pictures of Number Compari- StepstoFollowinConstructingtheLine
sons 135 Graph 137
KindsofGraphs 135 UsingTwoLineGraphsforComparisons 138
Bar Graphs 135 Pictographs 139
Interpretation 136 RectangleGraphs 140
HowtoConstructtheBarGraph 137 HintsforConstructingRectangularorDi-
LineGraphs 137 videdBarGraphs 141
CharacteristicsoftheLineGraph 137 Circle Graphs 141
Howto ConstructaTypicalLineGraph 137
CHAPTER FOURTEEN
Signed Numbers 144 Addition ofSignedNumbers 145
Applying Signed Numbers for Opposite Subtractionof Signed Numbers 146
Directions 144 AlgebraicSums andDifferences 146
Answers 148
Index 152