The course of arithmetic as taught in the Pestalozzian school, Worksop. [With] Answers

Front Cover
1854

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Page xv
... length of a line . Perimeter . 395 The diameter of a circle being given , to find the circumference . 396 397 Method of measuring angles . Protractor . Exercises . 398 Mensuration of surfaces . Definition of the superficial unit . 399 ...
Page xvii
... length of the foot . One foot is here called the unit or unity . Suppose a piece of cloth contain twelve yards ; here one yard is the unit ; in a basket there are eight pebbles , one pebble is the unit , and so on . 5. Therefore , in ...
Page 1
... length of the foot . One foot is here called the unit or unity . Suppose a piece of cloth contain twelve yards ; here one yard is the unit ; in a basket there are eight pebbles , one pebble is the unit , and so on . 5. Therefore , in ...
Page 58
... length , and 173 in breadth . Find its area , or the number of square feet in its floor . DIVISION OF FRACTIONS . 154. We are enabled to make as many cases in division as were made in multiplication . 1st , to divide an integer by a ...
Page 61
... length . 19. A can perform a piece of work in 5 days , B in 7 days , and C in 9 days . In how many days will the three do it together ? 20. It is required to place five persons , A , B , C , D , and E , according to their statures ; A ...

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Contents

Used almost by all nations
20
Sextuple period
21
Signs used to express numbers and their origin
22
to 27 Method of expressing every numerical quantity Cipher
24
Zero
25
Absolute and relative values of every digit
28
Table to illustrate their values
29
Examples in Numeration
30
Examples in Notation
31
Illustrations
33
ARTICLE
34
Uses of Roman characters Exercises in Numeration
35
Exercises in Notation
37
Exercises in Roman Notation
38
Express Roman Notation in Arabic Figures
39
ADDITION SUBTRACTION MULTIPLICATION AND DIVISION 40 In what every process in Arithmetic consists
40
Four fundamental processes
41
Addition Subtraction Multiplication and Division
42
Table of Prime Numbers and Multiples with the Factors from 1
53
Definition of angles
54
Method of simplifying certain fractional expressions 152 The product of two quantities is sometimes less than either quantity 153 Exercises
57
155 To divide an integer by a fraction 156 To divide a fraction by au integer 157 To divide an integer by a mixed quantity 158 To divide a mixed q...
58
To divide a mixed qurntity by another mixed quantity 163 Exercises
60
PART IV
63
to 74 Process of Multiplication explained and shortened
71
195 When both fractions are terminating 196 When one factor is finite and the other recurring 197 When both factors are recurring 198 199 Contra...
72
How to prove an operation in Multiplication
75
Exercises
76
Division
77
Definition of Division
78
Dividend Divisor Quotient Explanation of
79
Preparatory Exercises
80
to 86 Process of Division explained and shortened
82
How to prove a process in division
87
Exercises
88
PART III
89
Definition of a Fraction
90
How Fractions are expressed Numerator and Denominator or the terms of a Fraction
92
Observations
94
Fractions in connexion with each other must be parts of the same unit
95
How fractions increase and decrease
96
Proper and Improper fractions
97
Method of multiplying a fraction by a whole number
98
Method of dividing a fraction by a whole number
99
Exercises
100
Fractions not altered in value when the terms are multiplied or 103 divided by the same number Exercises
102
The vertical line drawn from a point to a line measures their distance
103
Common factor or common measure lowest terms
104
Multiple When a fraction is in
105
Reduction of fractions
106
Observations on numbers divisible by 2 3
108
If any number measures another number it measures any multiple of the latter
111
Every number which measures both the dividend and the divisor measures likewise the remainder
112
Method to find the greatest common measure of two numbers
113
Common measure of two numbers one of which is a prime number
115
Numbers which have no common measure except 1
117
Method of finding approximate values of fractions Explanation of and
118
Examples
119
Exercises
121
Mixed quantities
122
Exercises on the reduction of fractions to whole numbers
123
Reduction of mixed quantities to improper fractions
124
Exercises
125
Recapitulation Exercises
126
Addition of fractions
127
Examples
128
Definition of the least common denominator
130
132 133 Reduction of fractions to the least common denominator
131
Examples
133
Exercises in addition of fractions
134
Subtraction of fractions
135
Examples
136
Exercises
138
Multiplication of fractions Eight cases
139
To multiply a fraction by a whole number
140
To multiply an integer by a fraction
141
Contractions in the previous cases cancelling
142
To multiply a mixed quantity by a whole number
143
To multiply a whole number by a mixed quantity
144
To multiply a fraction by a fraction
145
To multiply a mixed quantity by another
146
To multiply a mixed quantity by a fraction or to multiply a fraction by a mixed quantity
147
The word of connecting two fractions is equivalent to X
149
Stocks General remarks 295 Jointstock associations Examples
159
Exercises
160
Annuities Examples 298 Exercises 299 Partnership or Fellowship Examples
164
The numerator and the denominator of a decimal
167
Reduction of vulgar fractions to decimals
177
Exercises
178
Recurring repeating or circulating Decimals Period or repetend Pure and mixed
179
Simplification of the process for finding Decimals with long periods
180
Exercises
181
To convert a terminating Decimal to a Vulgar Fraction
182
Exercises
183
Reduction of a pure circulating decimal to a common fraction 185 Transformation of a mixed circulating decimal into a common fraction 186 Algeb...
184
Algebraical method of
185
Exercises
188
Addition of Decimals
189
Addition of recurring decimals
190
Subtraction of decimals
191
Subtraction of recurring decimals
192
Exercises in addition and subtraction of decimals
193
Exercises
197
Arbitration of exchange Examples
199
Division of decimals Three cases
201
1st When the dividend is a decimal and the divisor an integer
202
2nd When the dividend is an integer and the divisor a decimal
203
3rd When both divisor and dividend are decimals
204
Examples
205
Observations on the division of recurring decimals Examples
206
Contracted division of whole numbers and decimals
207
Examples 320 Exercises
208
Exercises
209
Reduction of any decimals of a given quantity
210
Exercises
211
Reduction of a given quantity to the decimal of another quantity
212
Exercises
213
Miscellaneous exercises in decimals PART V
214
Observations
215
QUANTITIES
217
Extraction of the square root approximately 335 Extraction of the square root of mixed numbers 336 Extraction of the square root of vulgar fraction...
219
Cube root Formation of the cube of numbers Consequence 339 Formula derived from cubing numbers Extraction of the cube root 340 Second meth...
228
to 231 Tables of money weights measures
232
Reduction descending
233
Reduction ascending
234
Observation
235
Exercises
236
Compound addition
237
Examples
238
Exercises
239
Subtraction of compound quantities Example
240
Exercises
241
Compound multiplication Three cases
242
1st To multiply a compound quantity by an integer Exercises
243
Abbreviations of 243 1st method
244
Exercises
245
Abbreviations of 243 2nd method
246
Exercises
247
Abbreviation of 243 3rd method commonly called practice
248
Observations on practice Aliquot parts
249
Compound division Three cases
255
First To divide a composite number by a simple number
256
Exercises
257
Second To divide a composite number by a mixed number or by a fraction
258
Exercises
259
2nd case To multiply a compound quantity by a fraction or
260
Miscellaneous exercises
261
a mixed quantity Exercises
262
Exercises
263
Second case To express a fraction of one given quantity as the fraction of another
264
Exercises
265
Miscellaneous exercises in fractions
266
Observations Examples
267
Remarks on the preceding examples Rule of three
268
Double rule of three or rule of five
270
271 272 273 Interest Definitions of interest rate principal and amount
271
3rd case To multiply a compound quantity by another Miscellaneous exercises
274
Definitions of simple and compound interest
275
Four cases considered in simple interest
276
First case To find the interest when the principal the rate and the time are known Examples
278
Second case To find the rate when the principal the interest and the time are given Examples
279
Third case To find the time when the rate the principal and the amount are given Examples
280
Fourth case To find the principal when the time the interest and the rate are known
281
Exercises
282
Compound interest Four methods explained
283
Exercises
284
Discount
285
True discount Bankers discount
286
Discount is mostly applied to the payment of bille
288
Days of grace
289
Tradesmen allow a discount Examples
290
Exercises
291
Observations on commission brokerage insurance and statistics Examples
292
Exercises
293

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The Course of Arithmetic as Taught in the Pestalozzian School, Worksop
J. L. Ellenberger
Full view - 1854
The Course of Arithmetic as Taught in the Pestalozzian School, Worksop ...
J L Ellenberger
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Common terms and phrases

1st method 2nd method acres amount annum avoirdupois bought bushel called cent ciphers circumference common difference common fraction compound quantity contained cost cube root cubic inches decimal places denominator diameter discount divide a fraction dividend division divisor dwts equal example exchange EXERCISES Express factors farthings feet Find the number Find the sum Find the value florins francs gain gallon given greatest common measure guinea Hence hundreds improper fraction integer interest logarithms miles minutes mixed quantity months multiplicand number of terms operation paid pence performed person piastres piece pounds present worth principal quotient receive recurring decimal Reduce remainder result Rix-dollars rubles selling share shillings sold square root sterling subtracted tare tens thousandths Troy weight units vulgar fractions weight whole number Worksop yards of cloth

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Bibliographic information

TitleThe course of arithmetic as taught in the Pestalozzian school, Worksop. [With] Answers
The course of arithmetic as taught in the Pestalozzian school, Worksop. [With] Answers, J L. Ellenberger
AuthorJ L. Ellenberger
Published1854
Original fromOxford University
Digitized7 Sep 2006
  
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