Note 4th.-When the divisor is 10, 100, 1000, 10000, &c. point off as many figures from the right of the dividend, as there are cyphers in the divisor; the figures on the left of the point will be the quotient, and those on the right, the remainder. Ex. 1. Divide 19375468 by 10000. Quo. 1937, rem. 5468. 2. Divide 99885566 by 100000. Quo. 998, rem. 85566. 3. Divide 47429 by 10. Quo. 4742, rem. 9. 4. Divide 463581 by 100. 5. Divide 618293 by 1000. Quo. 4635, rem. 81. Note 5th.-When the divisor consists of a number of figures with cyphers annexed, the cyphers may be cut off from the divisor, and an equal number of figures from the right of the dividend, and the remainder of the dividend divided by the significant figures of the divisor. After the division, the figures cut off from the dividend are to be placed at the right of the remainder. Ex. 1. Divide 36418235700 by 98700. Quo. 368979, rem. 8400. 2. Divide 11579112 by 890000. 3. Divide 8317642500 by 814600. APPLICATION. Quo. 13, rem. 9112. 1. If 246 men incur an expense of $175152, what is each man's share? Ans. $712. 2. A gentleman left an estate of $65468 to 6 sons; what was each one's share? Ans. $109113. 3. Twelve men own a bridge, for which they annually receive $2352, in toll; what is each man's share? Ans. $196. 4. Suppose 7776 peach trees to be planted in 108 rows; how many trees are there in a row? Ans. 72. 5. If light comes from the sun to the earth in 8 minutes, how far does it travel in one minute, the distance being 95000000 miles? Ans. 11875000 miles. 6. If a man travel 9125 miles in a year, what is his average daily progress? Ans. 25 miles. 7. If a horse run 288 miles in 36 hours, how far does he run in one hour? Ans. 8 miles. 8. In 437850 yards of cloth, how many rolls of 75 yards each? Ans. 5838.1 APPLICATION OF THE PRECEDING RULES. 1. A farmer sold 3 yoke of oxen at $96 each; 12 cows at $24 each; 83 sheep at $3 a head; 239 bushels of wheat at $2 per bushel, and distributed the avails equally among his 7 sons. What was each one's share? Ans. $1864. 2. A man to whom was entrusted the settlement of an estate, found that the whole value of the estate was $95688. There were five claims against the estate; viz. one of $8672; another of $3421; a third of $10637; a fourth of $356; and a fifth of $1673. After the payment of these several claims, the balance was to be divided equally among 9 heirs. What was the share of each? Ans. $7881. 3. A farmer had 16 calves worth 5 dollars per head; 45 sheep worth $3 per head; and 75 bushels of grain worth $2 per bushel; he gave the whole for a horse worth $136; a carriage worth $195, and a harness worth $63. Did he gain or lose, and how much? Ans. Gained $29. 4. A merchant received by boat, 9696 bushels of salt, and hired it carted 16 miles, at a dollar a load of 24 bushels. How much did the cartage cost? Ans. $404. 5. When the dividend is 290864196 and the quotient 9382716, what is the divisor? Ans. 31. 6. A man purchased a farm for which he paid $18000. He sold 60 acres for 50 dollars an acre, and then the remainder stood him at $75 per acre. How much land did he purchase? Ans. 260 acres. QUESTIONS.-How does division differ from multiplication? How may multiplication be performed? How may division be performed? How many numbers are given in division ? What are they, and what are they called? What is the number obtained by the operation called? What does it signify? What is the remainder? How does it always compare with the divisor? How is division proved? What is short division? What is the rule for it? What is the rule when the divisor is more than 12 and a composite number? How is the true remainder obtained, when we divide by the component parts of the divisor? What is long division? What is the rule? How do you divide by 10, 100, 1000, &c.? When the divisor consists of a figure greater than 1, with cyphers annexed, how do you divide? FEDERAL MONEY. Federal Money is the currency of the United States. Its denominations are Mills, Cents, Dimes, Dollars, and Eagles, increasing like simple numbers in a ten-fold ratio, as represented in the following table: TABLE OF FEDERAL MONEY. 10 Mills (marked m.) make one cent, marked c. or ct. The 64 cent and 12 cent pieces, &c. are not American coinage. The copper coins are, the cent and the half-cent. Halfcents are seldom used. The gold and silver coins are not composed of pure metal; but are alloys, that is, compounds of these metals with the baser metals. The purity of a metal is expressed by the word, carat; which word is used to express a twenty-fourth part of a given quantity. If, for example, a quantity of gold be said to be 18 carats fine, the meaning is, that 18 equal portions of the whole are gold, and 6 equal portions are of a less valuable metal. By recurring to the preceding table, it will be seen that the denominations of federal money may be added, subtracted, multiplied, and divided by the same rules as the simple numbers, as they increase in the same ratio. The scholar should however remember that the dollar is the unit money; and that dimes, cents, and mills are decimals; or tenths, hundredths, and thousandths of the dollar, or unit denomination. It is therefore always important to know which of a number of figures is the dollar, or unit figure. This is shown by the decimal point (.) or period, which always stands between the dollars and dimes; thus, 63.78, read, sixty-three dollars and seventy-eight cents. The first figure on the left of the point is dollars, and the second eagles. They are however called dollars indiscriminately; as in the above number, the 6 is eagles, and the 3, dollars; but usually read, 63 dollars. Likewise, the 78 is usually read, 78 cents, instead of 7 dimes and 8 cents. Both methods express the same value. To reduce the higher denominations to the lower, it is necessary to bear in mind, 1st. That cents are converted into mills by annexing one cypher; thus, 8 cents 80 mills. 2d. That dollars may be changed into cents by annexing two cyphers; thus, 3 dollars 300 cents; and into mills by annexing three cyphers; thus, $3 3000 mills. 3d. The reverse operation will convert mills into cents and cents into dollars. Ex. 1. How many mills in 47 cents? 2. How many mills in 69 cents? 3. How many mills in 156 cents? Ans. 470. Ans. 690. Ans. 1560. How many 4. In 78 dollars, how many cents? Ans. 7800. mills? Ans. 78000. 5. In $637, how many cents? Ans. 63700. mills? Ans. 637000. How many 6. In 450 mills, how many cents? 7. In 470 mills, how many cents? 8. In 6700 mills, how many cents? 9. In 6700 mills, how many dollars? 10. Change $6 into cents. 11. 12. Change $95 dollars into mills. cents. 14. 28000 mills into dollars. 16. 9876 mills into dollars. Ans. 45. Ans. 67. Change 42 cents into mills. 13. Change 460 mills into 15. 439 mills into cents. ADDITION OF FEDERAL MONEY. RULE.-Set the numbers one under another, so that dollars shall stand under dollars, dimes under dimes, cents under cents, and mills under mills. Then add up the several columns as in Simple Addition, and place the decimal point, in the amount, directly under those in the numbers added. If the above rule be followed in writing down the several numbers, the separating points will stand directly under each other. Ex. 1. What is the sum of 136 dollars 21 cents; 75 dollars 13 cents; 7 dollars 78 cents; 66 dollars 19 cents; and 196 dollars 72 cents? Ans. 482.03. PERFORMED. 1 3 6.2 1 7.78 6 6.1 9 1 9 6.7 2 $48 2.0 3 Amount. 2. Add together $432.73; $297.38; $172.66; and $333.62. Amount, $1236.39. 3. What is the sum of $1.55; $0.72; $340.89; $0.01; $1460.99? Ans. $1804.16. 4. What is the sum of $72.01; $1; $0.01; $0.10; $40.70; $560.88? Ans. $674.70. 5. What is the sum of $101.01; $20.15; $42.89; $79.81; $41.41; $51.51; $38.41? Ans. $375.19. 6. What is the sum of $16.64; $20.84; $462.573; $29.922; $56.32; $84.48? Ans. $670.775. 7. A farmer bought a cow for $23.75; a yoke of oxen for |