Art. 8. The cipher, when standing alone, or at the left hand of another figure, signifies nothing, as 05, 005, is five in either case, because it still occupies the unit's place. But when placed at the right hand of another figure, it increases its value in a tenfold ratio, by removing the figure farther from the unit's place. This may be seen by the following— TABLE II. 0 Nothing. 20 Twenty. 200 Two hundred. 2,000 Two thousand. 20,000 Twenty thousand. 200,000 Two hundred thousand. 2,000,000 Two millions. Art. 9. To know the value of any number of figures. ing units, tens, hundreds, &c., as in the Table. 2. To the simple value of each figure join the name of its place, reading from the left hand to the righ. TABLE III. Period Millions. Period Units. 783 694 542 987|562|714|923|610|782|184|542|365|987|963 HHHHHHM The first division of the foregoing Table is according to the French method, into periods of three figures each: the name of the period is superadded. The second division is according to the English method, into periods of six figures each. The name of each period is subjoined. The two divisions of the QUESTIONS.-20. How may the value of any number be found? 21. What are the two methods of numeration in the third table? 22. In what respect do they differ? the same. Table agree for the first nine figures-beyond that they as sume different names. The principles of Notation in both are In the former method the names, units, tens, hundreds, are repeated in each period; in the latter method, thousands, tens of thousands, hundreds of thousands, are repeated with the name of the period. If the sum be not expressed in figures, it is necessary to know the method of notation employed. Art. 10.-Let the scholar point the following numbers into periods, and read them. 3445 67891 983452 5437643 67821356 436543897 5678923412 96754329876 1234678901263 Art. 11.-Express the following numbers in figures. 1. Twenty-three. 2. Thirty-five. 3. One hundred and twenty. 4. One hundred and twenty-six. 5. Ten thousand three hundred and twenty. 6. Four millions four thousand and four. 7. One hundred and seventeen millions, one hundred and two. 8. Three billions, three millions, seventeen thousand and ten. 9. One hundred billions, one hundred thousand, two hundred and fifty. 10. Twenty billions and twenty. 11. Seven billions, seven thousand and seventeen. 12. One hundred and seven billions, twenty-seven thousand and one. 13. Five hundred and four trillions, two billions, ten millions, ten thousand and ten. 14. Forty-five trillions, forty billions and thirteen. 15. Two millions, two thousand, three hundred and three. 16. Thirty quadrillions, fifty millions, four thousand, three hundred and forty-eight. 17. Four hundred and four quadrillions, seven hundred and seven thousand, two hundred and two. 18. Four quintillions, thirty-five quadrillions, three trillions, two billions, twenty-seven millions, three hundred and forty thousand, four hundred and seventeen. ADDITION TABLE. Art. 12.-Signs.-A cross + is the sign of addition. It shows that the numbers between which added. Two parallel horizontal lines Thus: 3+4=7 is read, 3 added to 4, or 3 Latin word, which signifies more) is equal to 7. is placed are to be signify equality. plus 4 (plus is a The following TABLE may be read thus: 2 and 0 are two; 2 and 1 are 3, &c. QUESTIONS.-Two and 0-how many? 2. Two and 1--how many? 3. Two and 2-how many? The scholar should be questioned in this manner, until he is familiar with the above table. The scholar should be well versed in Notation and Numeration, before proceeding to the following questions. EXERCISES. Art. 13.—1. If John has 6 apples, and his brother gives him 3 more, how many will he have? 2. James being on a visit at his uncle's, one of his cousins gave him 3 walnuts, another 4, and his uncle gave him 9; how many did he receive? 3. Samuel bought a book for 15 cents, and a slate for 17; how many cents did he give for both? 4. If a boy pay 15 cents for a book, 10 for a knife, and 6 for a dozen of apples, how many cents does he pay in all ? 5. If an inkstand cost 10 cents, an orange 5, a lemon 3, and a dozen of quills 14 cents, what is the cost of the whole? 6. A man bought of a drover 3 sheep and a cow; for one of the sheep he paid 4 dollars, for the other two he paid 3 dollars apiece, for the cow he paid 20 dollars; how many dollars did he pay for the whole? 7. Joseph bought a sled for 25 cents, a yoke for 12 cents, and a whip for 6 cents; what did the whole cost him? 8. If I pay 6 dollars for a hat, 8 for a cap, 4 for a vest, and 14 for a coat, what do I pay for the whole? 9 If I owe one man 6 dollars, another 8, another 12, another 20, how much do I owe in all ? 10. The scholars in a certain school are divided into 4 classes; in the first class there are 10 scholars, in the second 12, in the third 9, and in the fourth 14; how many in all? 11. If from my library I lend to one man 5 books, to another 10, to another 8, to another 12, to another 20, how many do I lend in all? 12. In my garden there are 6 apple-trees, 8 pear-trees, 10 peach-trees, 18 plum-trees; how many trees are there in all? 13. In a certain school 10 study music, 12 French, 14 Spanish; how many are there in all these studies? 14. Eliza had 4 finger-rings, Mary had 10, and Susan had 7; how many had they in all? 15. A certain man had 4 boarders; for two he received 3 dollars each per week, for one 2 dollars, for another 5; how much did he receive per week for the whole? 16. A young lady bought two dresses; for one she paid 7 dollars, for the other 9 dollars; how much did she pay for both? ADDITION. Art. 14.-ADDITION is the putting together of two or more numbers so as to make but one. The number thus obtained, is called their sum or amount. Art. 15.-SIMPLE ADDITION is the putting together of two or more numbers of the same kind. OBS.-It is called Simple Addition, because the numbers are all of one denomination; that is, all dollars, or all cents. When the numbers are pounds, shillings, pence, &c., the denominations are different. If one man owe me 25 dollars, another 22,-to find the amount of what both owe, I write the sums in the following manner, units under units, tens under tens, and add them together, thus: 25 22 Tens. Units. or thus, 2 + 5 47 amount. 2+2 4 + 7 47. Illustration.-Beginning at the right hand, or unit's place, I say 2 and 5 are 7; then, in the second place, or place of tens, I say 2 and 2 are 4-which is 4 tens, or 40. 2. A man has three fields; one contains 31 acres, another 25, another 42; how many acres are there in all? Operation. 31 25 Illustration.—Having written the numbers according to the directions, units under units, tens under tens, &c., we begin at the right hand to add, and find the amount to be 8 units, which we place under the column of units. Ans. 98 amount of the second column, or column of tens, we find to be 9 tens, or 90. The answer, then, is 9 tens and 8 units, or 98. 42 The 3. What will a carriage, horse and harness cost, if the carriage cost 102 dollars, the horse 80 dollars, and the harness 16 dollars? Ans. 198. 4. If a wagon cost 78 dollars, and a yoke of oxen 96 dollars, what will be the cost of both? QUESTIONS.-1. What is Addition? 2. What is Simple Addition? 3. How are the numbers to be added written? 4. By what number do you carry? 5. Why? 6. What is the number called arising from the operation? 7. What is the sign of Addition? 8. Sign of Equality? 9. Sign of Subtraction? 10. What does plus signify? |