2. Observe always to supply those places with ciphers, which are omitted in the question, in their proper order. EXAMPLES. Write, in figures, the following numbers. 1. Two hundred and five. We begin at the right hand and write units in the place of units; thus, 5; there are no tens, therefore we supply the place with a cipher, 05; next we write down the hundreds, 205. 2. Thirty-three. 3. Eight hundred and thirty-three. 4. One thousand eight hundred and thirty-three. 5. Forty-five thousand six hundred. 6. Three hundred and forty-five thousand six hundred. 7. Nine millions four thousand one hundred and twentyeight. 8. Eighty-seven millions, nine hundred thousand. 9. Nine hundred and seventy-eight millions, three hundred and sixty-five. When numbers, consisting of many figures, are given to be read, it wil be found convenient to divide them into periods of six figures each, calling the first or right hand period that of units; the second that of millions; the third billions; the fourth trillions, &c. as in the following Period of Trilions. Period of Billions. Period of Millions. Period of Units The foregoing number is read thus, 465 thousand 219 trillions, 678 thou and 391 billions, 543 thousand 675 millions, 213 thousand four hundred and twenty-eight. Trillions is succeeded by Quatrillions, Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, &c. N. B. Billions is substituted for millions of millions; trillions for miltions of millions of millions; quatrillions for millions of millions of millions of millions, &c. Questions. 1. What is Arithmetic? How many principal rules has it for operation? 2. What does numeration teach? 3. What is a single or individual thing called? 4. What are the characters made use of in computation? 5. What are the nine first of these characters called; and what values have they? 6. When standing separately or alone, what value do they express? 7. When placed or located with other figures what value have they? 8. What does any figure in the first place; or place of units express? What, in second place or place of tens? What in the third place? 9. What does the cipher signify or represent? 10. What is the rule for reading numbers ? 11. What is the rule for writing numbers? ADDITION. 1. If you have two apples in one hand, and one in the other, how many have you in both? 2. If you have four pins in one hand, and James puts in three more, how many will you then have ? 3. If James has five apples, and George has four, how 'many have they both together? 4. Thomas gave nine cents for a purse, and had five cents left to put into it; how many cents had he at first? 5. A boy paid twelve cents for paper, and five cents for quills; what was the amount paid for both? 6. If you had twelve cents, and should find six more, how many would you then have ? 7. Peter bought a book for ten cents, and sold it again so as to gain six cents; how much did he get for it? 8. A farmer sold seven cows, and had nine left; how many had he at first? 9. A man bought 12 bushels of corn for nine dollars, and 10 bushels of rye for seven dollars, how much did he pay for both? 10. If you have three cents in one hand, two cents in the other hand, and five cents in your pocket, how many do they all make? 11. If you give twelve cents for a knife, eight cents for an ink stand, and five cents for quills, how many cents do they all come to ? How many are 12, 8, and 5? SIMPLE ADDITION Simple Addition teaches to collect, or put together, several smaller numbers of the same denomination into one sum; as $8 and $4 in one sum are $12. RULE. 1. Write the numbers, units under units, tens under tens, &c. and draw a line under them. 2. Begin at the right hand, or column of units, and add up every figure in that column, and if the amount does not exceed nine, write it under the column; but if the amount be greater than nine, set down the right hand figure or units, and carry the left hand figure or figures, which are tens, to the next column of tens: proceed in the same manner through every column or row, and set down the whole amount of the last. PROOF. Begin at the top of the sum and reckon the figures downwards; or, cut off the upper line of figures, and find the amount of the rest, then if the amount and upper line, when added, be equal to the sum total, the work is supposed to be right. EXAMPLES. 1. What is the whole sum of 312 dollars, 32 dollars, 511 dollars, and 123 dollars? Operation. wHunds. Units. w-Tens. 3 2 5 1 1 1 2 3 Ans. 9 7 8 We write the numbers one under another, so that units may stand under units, tens under tens, &c. We then add up the column of units, thus, 3 and 1 are 4 and 2 are 6 and 2 are 8, which we set down under the column of units. We next proceed to add up the column of tens. 2 and 1 are 3 and 3 are 6 and 1 are 7, which we write under the tens. We then add up the column of hundreds in the same manner and find the amount to be 9, which we set down, and the work is done. 2. Add together the following numbers, viz: 597, 236, 53 and 439. Hunds. σ w Tens. Units. 236 We add up the units, thus, 9 and 3 are 12 and 6 are 18 and 7 are 25 units. (=2 tens and 5 units.) We set down the right hand figure 5, units under the units, and carry or add the left hand figure, 2 tens, in with the other tens. Thus, we carry 2 to 3 are 5 and 5 are 10 and 3 are 13 and 9 are 22 tens, setting down the right hand figure 2 under the tens, and carrying the left hand figure 2 hundreds to the hundreds; thus, carry 2 to 4 are 6 and 2 are 8 and 5 are 13, setting down the whole amount. 5 3 4 39 1 3 2 5 (10) 2 4 4 6 5 0 8 7 3 6 4 5 0 3 2 60 9 7 5 58 1 6 9 5 304 9 89097 6 7 0 8 5 9 0 7 38 4 3 098 7 6 5 7 9 8 2 4 3 3 (11) 9706 4 4 3 9 6 2 8 5 3 0 8 5 6 27 4 9 5 0 6 4 39 90 7680 46 3 509 208 914091 12. Add together the following numbers, 152, 143, 56, 25 and 8. Ans. 384. 13. Find the sum total of 536, 213, 118, 95, 25 and 13. Ans. One thousand. 3482, 783645; 318, Ans. 10473020. 14. What is the whole amount of 7530 and 9678045 added together? 15. Add together the following numbers, 1118, 1469, 784645 and 956684. Ans. 1743916. 16. What is the sum total of 1650 dollars, 1975 dollars, 146 dollars, 3125 dollars, 918 dollars and 560 dollars? Ans. $8374. 17. Find the sum of 8301, 9461, 12648, 1275 and 8315. Ans. Forty thousand. 18. What is the whole sum of 10356, 204560, 126432, 84031, 978402 and 8596218 ? Ans. 9999999. 19. Find the amount of the following sums of money, viz: 78 dollars, 48 dollars; 68 dollars, 58 dollars, 35 dollars, 85 dollars, 94 dollars and 34 dollars. Ans. $500. 20. Add 784645, 97632, 548301, 750562 and 318860 into one sum. Ans. Two millions five hundred thousand. 21. What is the sum total of the following numbers, viz : Four hundred and eighty-six, Five thousand five hundred and eight, Answer, 8901530. 22. Write down and add together the following nume bers, viz: Nine hundred and twenty-seven, Two thousand three hundred and forty-eight, Fifty-two thousand six hundred, |