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? 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. Annual Interest PAGE 205 207 209 215 . . . SECTION IX. SECTION VI. Measures of Value PAGE 124 124 126 127 128 129 130 131 132 133 133 134 142 143 145 145 146 147 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 INVOLUTION AND EVOLU- 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 . 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 10 is ten units or 1 ten, called ten. 14 is 1 ten and 4 units, or fourteen. And so on to 19, or nineteen. 20 is 2 tens, called twenty. 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 ? |