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

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Περιεχόμενα

Zero
25
Absolute and relative values of every digit
28
Table to illustrate their values
29
Examples in Numeration
30
Examples in Notation
31
Roman Notation
32
Illustrations
33
ARTICLE
34
Uses of Roman characters
35
Exercises in Numeration
36
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
Definition of Addition
43
The Sum 46 Explanation of + and
46
Preparatory exercises
47
The operation of Addition shortened
48
Numbers to be added up must be of the same kind
49
Method of proving operation in Addition
50
Exercises
51
Subtraction Remainder Difference or Excess
52
Definition of Subtraction Minuend and Subtrahend
53
Explanation
54
Preparatory Exercises
55
The operation of Subtraction explained
56
Inference drawn from
57
155 To divide an integer by a fraction
58
The process of Subtraction shortened
59
Second Definition of Subtraction
60
Methods of proving an operation in Subtraction
61
Exercises
63
Multiplication
64
Definition of Multiplication Product Multiplicand and Multiplier
65
Terms or Factors
66
Preparatory Exercises
67
Exercises
68
Prime Numbers Multiples 70 Table of Prime Numbers and Multiples with the Factors from 1
69
to 74 Process of Multiplication explained and shortened
71
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 divided by the same number
102
Exercises
103
Common factor or common measute When a fraction is in its lowest terms Greatest common measure
104
Multiple
105
Reduction of fractions 107 Observations on numbers divisible by 2 3
108
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
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
46 To multiply a mixed quantity by another 147 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
A Decimal is not altered in value by annexing ciphers on its right
171
Advantages of Decimals
172
Every cipher affixed to the left hand of a Decimal after the point decreases its value tenfold
173
Equation of payments Correct method 304 Method used
175
Multiplication and Division of Decimals by 10 100
176
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 dccimal 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
Multiplication of Decimals Three cases
194
When both fractions are terminating
195
When one factor is finite and the other recurring
196
When both factors are recurring
197
Contracted multiplication of decimals
198
Arbitration of exchange Examples
199
Exercises
200
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
Alligation First consideration 317 Second consideration 318 Inference from articles 316 and 317
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
Formula derived from squaring numbers 330 Application of that formula 331 332 Explanation of the extraction of the square root 333 Exercises
217
Extraction of the square root approximately
226
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
Third To divide a compound quantity by another Note
260
Miscellaneous exercises
261
Reduction of concrete quantities as fractions of others 1st case To express a given quantity in terms of or as the fraction of another given quantity
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
Exercises 251 2nd case To multiply a compound quantity by a fraction or by a mixed quantity 252 Exercises 253 3rd case To multiply a compound ...
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 Bapkers 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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Σελίδα 244 - ... one grain of wheat for the first square, two for the second, four for the third, and so on, doubling...
Σελίδα 44 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Σελίδα 244 - Sessa requested that he might be allowed one grain of wheat for the first square on the chess board, 2 for the second, 4 for the third, and so on, doubling continually, to 64, the whole number of squares. Now, supposing, a pint to contain 7680 of these grains, and one quarter or 8 bushels to be worth yja 6d, it is required to compute the value of all the corn ? Ans.
Σελίδα 134 - XV — 24, as shown in the operation. 2. 5 compositors, in 16 days, of 14 hours each, can compose 20 sheets of 24 pages in each sheet, 50 lines in a page, and 40 letters in a line; in...
Σελίδα 292 - The real resistance to a plane, from a fluid acting in a direction perpendicular to its face, is equal to the weight of a column of the fluid, whose base is the plane...
Σελίδα 57 - Multiply the numerator of the dividend by the denominator of the divisor...
Σελίδα 52 - To Multiply a Fraction by a Whole Number. Multiply the numerator by the whole number and divide the product by the denominator.
Σελίδα 47 - Divide the given number by any prime factor ; divide the quotient in the same manner, and so continue the division until the quotient is a prime number. The several divisors and the last quotient will be the prime factors required.

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