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SECTION II.

FUNDAMENTAL PROCESSES.

ADDITION.

ORAL EXERCISES.

12.-1. A class has 4 boys and 9 girls in it; how many pupils in the class ?

2. Horace is 5 years old; how old will he be in 8 years ? In 9 years? In 6 years? In 5 years ?

3. A farmer has 6 cows; how many will he have if he buys 5 more? 8 more? 7 more? 6 more? 9 more?

4. Arthur has 7 marbles; how many will he have if he buys 5 more? 6 more? 9 more? 8 more? 7 more?

5. Ruth has 8 cents; how many will she have if May gives her 6 more? 5 more? 9 more? 8 more? 7 more?

6. A teacher has 9 pupils in arithmetic; if 9 more are added, how many

will there be in the class? If 8 more? If 7 more? If 6 more? If 5 more? If 4 more? 7. How many are

8 and 5 ? 9 and 9? 6 and 9? 4 and 7?
7 and 6? 8 and 9? 9 and 7? 8 and 7?
5 and 9? 7 and 8? 6 and 8? 9 and 8?
4 and 8? 8 and 8? 6 and 7 ? 7 and 7 ?

8. Count by 2's from 2 to 30. From 30 to 60. From 1 to 31. From 31 to 61. 9. Count by 3's from 3 to 45. From 1 to 46. From 2 to 47.

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Annual Interest
Compound Interest .
Discount
Stocks and Bonds

PAGE 205 207 209 215

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SECTION IX.

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SECTION VI.
DENOMINATE NUMBERS

Measures of Value
Measures of Weight
Measures of Length
Measures of Surface
Measures of Volume
Measures of Capacity
Measures of Time
Angular Measure
Miscellaneous Tables
Miscellaneous Measures .
Reduction .
Addition
Subtraction
Multiplication
Division
Longitude.
Longitude and Time

PAGE 124 124 126 127 128 129 130 131 132 133 133 134 142 143 145 145 146 147

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SECTION VII. PRACTICAL MEASUREMENTS. 154 Measures of Surfaces

151 Painting, Papering, Plastering, etc. .

159 Measures of Volume

161 Bins, Tanks, and Cisterns . 164 Boards and Timber .

165 Masonry and Brickwork

167

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INVOLUTION AND EVOLU-
TION

240 Involution

240 Squaring Numbers Geometrically

242 Cubing Numbers Geometrically

243 Evolution.

244 Evolution by Factoring - 246 Square Root .

247 Of Decimals

249 Of Imperfect Squares .

250 Of Fractions

251 Applications of Square Root

251 The Square

251 The Right Triangle 252 Similar Figures

254 Cube Root

255 Short Method

259 Of Decimals

260 Of Imperfect Cubes 261 Of Fractions

261 Applications of Cube Root. 262 The Cube.

262 Similar Volumes .

263

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ARITHMETIC.

SECTION I.

NUMERATION AND NOTATION.

1. If we desire to know how many trees there are in a certain grove, we must count them; thus, one, two, three, four, five, six, seven, eight, nine, etc., until all have been counted.

These expressions, one, two, three, etc., are called Whole Numbers, or Integers.

2. Notation is the method of representing numbers by means of characters.

Numeration is the method of reading numbers when expressed by characters.

ARABIC SYSTEM OF NOTATION. 3. Ten characters, called Figures, are used to represent numbers. They are

FIGURES, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, Names,

one, two, three, four, five, six, seven, eight, nine, zero. These ten characters are also called Digits. A figure standing alone expresses ones, or Units.

4. Numbers greater than nine are expressed by writing two or more of these figures side by side.

If we add one more to nine, we shall have ten. To express
this, we write 1 in the second place and zero in the first place.
Hence
A figure standing in the second place expresses Tens. Thus,

10 is ten units or 1 ten, called ten.
11 is 1 ten and 1 unit, or eleven.
12 is 1 ten and 2 units, or twelve.
13 is 1 ten and 3 units, or thirteen.

14 is 1 ten and 4 units, or fourteen. And so on to 19, or nineteen.

20 is 2 tens, called twenty.
21 is 2 tens and 1 unit, or twenty-one.
22 is 2 tens and 2 units, or twenty-two.

23 is 2 tens and 3 units, or twenty-three. And so on to 29, or twenty-nine.

In like manner we have 30, 40, 50, 60, 70, 80, 90, with the intervening numbers.

EXERCISES.

1. Write neatly in figures the numbers from ten to twenty; from thirty to forty; from fifty to sixty; from seventy to eighty; from thirty-four to fifty-six ; from sixty-six to eighty-six. How many tens and units in2. 3.

5. 6. 7. 8. 14? 15?

25 ? 37 ? 40 ? 50 ? 99 ? 26 ? 32 ? 39? 59 ? 72 ? 79? 80? 35? 47 ? 54 ? 60? 88 ? 77? 21 ?

9. What is the largest number that can be expressed by two figures? What is the smallest ?

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