COMPOUND MULTIPLICA TION 155. Is the method of finding the amount of a compound number by repeating it a proposed number of times (43). RULE. 157. Write the multiplier under the lowest denomination of the multiplicand. Reserve from each product as many units as may be had of the next higher denomination, and write down the excess, adding the number reserved to the next product. NOTE. This rule is susceptible of the same contractions as Simple Multiplication. COMPOUND DIVISION 156. Is the method of separating a compound number into any proposed number of equal parts (44). RULE. 158. Write the numbers as in Simple Division, and divide the several terms of the dividend successively by the divisor. Should the first term of the dividend be less than the divisor, reduce it to the next lower denomination, adding the number of the lower denomination. Do the same with the several remainders. NOTE. This rule is susceptible of the same contractions as Simple Division. QUESTIONS FOR PRACTICE. 3. What will 6 cows cost at £4 6s. 8d. apiece? 4. What will 9cwt. of cheese cost. at £1 11s. 5d. per cwt.? 5. What will 28 yards of broadcloth cost at 19s. 4d. per yard? 6. What will 96 quarters of rye cost at £1 3s. 4d. a qr.? 7. What will 47 yards of cloth cost at 17s. 9d. a yard? 8. How many yards in 17 pieces, each containing 29yds. 3qrs.? 9. What will 94 pair of stockings cost at 12s. 2d. a pair? 10. What will 512 bushels of wheat cost at 5s. 10d. a bushel? 11. If a span of horses eat 2 bu. 3 pks. of oats in one week, how many will they eat in 25 weeks? 3. If 6 cows cost £26, how much is that apiece? 4. If 9cwt. of cheese cost £14 2s. 9d. how much is that per cwt.? 5. If 28yds. of broadcloth cost £27 1s. 4d. what is that a yard? 6. If 96qrs of rye cost £112, how much is nat a qr.? 7. If 47yds. of cloth cost £41 14s. 3d. what is that a yard? 8. In505 yd. 3qr. how many pieces of 29yd. 3qr. each? 9. If 94 pair of stockings cost £57 3s. 8d. what is that a pair? 10. If 512 bushels of wheat cost £149 6s. 8d. what is that a bushel ? 11. If a span of horses eat 68bu. 3pk. of oats in 25 weeks, how much is that a week? MISCELLANEOUS. n 28 years of 365d. 6h. each? Ans. 883612800. 159. 1. How many seconds | ed to the same denomination, and add them together for a divisor the quotient will be the number of times required. 2. How many seconds from the birth of Christ to the end of the year 1824, allowing 365d. 5h. 48m. 57s. to a year? Ans. 57559853088. 3. How many seconds in 8s. 12° 14' 26" ? Ans. 908066. 4. How many inches from Montpelier to Burlington, it being 38 miles ? 6. In £33, how many guineas, pounds, dollars and shillings, of each an equal number? Ans. 12. 7. A person wishes to draw off a hogshead of wine into gallon bottles, two quart, quart and pint bottles, of each an equal number; how many must he have? Ans. 33 bottles of each kind, and 9pts. over. 8. If 4 men spend each 14s. 1d. at a tavern, what is the whole bill? Ans. £2 16s. 4d. 9. What will be the weight of 12 silver cups, each weighing 1lb. 1oz. 1pwt. 20 grains? 10. What will 700 bushels of potatoes cost, at 1s. 3d. a bushel? Ans. £43 15s. 11. How much wood in 27 loads, each containing 1 cord 18ft.? Ans. 30cor. 102ft. 12. If 4 men spend at a tavern £2 16s. 4d., what must each pay? 13. If 12 silver cups weigh 13lb. 1oz. 10pwt., what is the weight of each cup? 14. If 700bu. of potatoes cost £43 15s. what is that a bush el? 15. If 27 loads contain 30 cor. 102ft. of wood, how much in each load? 16. If a person travel 32rd. 12ft. 33in. in a minute, how far would he go, at that rate, in 2 hours? 17. If a man drink a pint of rum a day, how much will he drink in a year? Ans. 45gal. 2qt. 1pt. 18. How many barley corns will reach round the world, supposing it to be 25020 miles? Ans. 4755801600. 19. Divide $120 among 4 men, so that the shares shall be to one another as 1, 2, 3, 4. Ans. 12, 24, 36, 48. 20. How many steps of 2 feet 6 inches, must a man take in going from Burlington to Boston, it being 190 miles? Ans. 401280 steps. 21. If a person travel 12mi. 28rd. in 2 hours, how far does he go in a minute? 22. How many lots, each containing three quarters of an acre, are there in a square mile? Ans. 853 lots, and 40 rods over. 23. If a vintner be desirous to draw off a pipe of wine into bottles containing pints, quarts, and 2 quarts, of each an equal number, how many must he have? Ans. 144 of each. 24. There are three fields, one containing 7 acres, another 10 acres, and the other 12 acres and 1 rood; how many shares of 76 rods each are contained in the whole? Ans. 61 shares and 44 rods over. 25. In 172 moidores at 36s. each, how many eagles, dollars and nine-pences, of each an equal number? Ans: 92 of each, and 68 nine-pences over. 26. In 470 boxes of sugar, each 261b., how many cwt.? Ans. 109cwt. Oqrs. 121b. 27. If cigars cost one and a half cent each, and a person smoke 3 cigars per day, how much will it cost him for cigars during the months of January, February and March, in a common year? Ans. 405 cents, or $4 5 cts. 28. What is the difference between six dozen dozen and half a dozen dozen? Ans. 792. 29. What is the difference between half a solid foot and a solid half foot? Ans. 648 inches. 30. A note was on interest from March 20, 1819, till Jan. 26, 1824; what was the length of time? Ans. 4yr. 10mo. 6d. 31. Divide £7 among 8 men -give A. 8d. more than B., and B. 8d. more than C. &c.; what does H. receive? Ans. 15s. 2d. H's share. 32. A horse is valued by A at $60, by B at $69 50, and by Cat $72 25; what is the average judgment? 56 REVIEW. 160. 34. In 5529600 cubic inches, | should pay D $100; and Q how many cords of wood? said C. should pay D 855; but R said D should-pay C $25; how was the matter settled? Ans. 25 cords. 35. A and B wishing to swap horses, and disagreeing as to the conditions, referred the matter to three disinterested | persons, X, Y, and Z, whose judgments were as follows, viz., X said A should pay B $8, and Y said A should pay B $6; but Z said B should pay A $5; what is the average judgment? Ans. A must pay B $3.. A B In the exchange of X 180 88 articles, where the judgment of the referees is partly on one side of the equal5 14 ity, between them, and partly on the other, subtract one Y 1 0 Ref. 3 -- 6 0 3)9(3 Ans. side from the other, and divide the remainder by the number of referees for the average judg ment. 36. C and D, wishing to swap farms, referred the subject to O, P, Q and R, and agreed to abide their judgment, which was as follows, viz. O said C should pay D $70; P said C Ans. C pays D $50. 4hhd. of sugar, each weighing 37. What is the weight of 7cwt. 3qrs. 191b. Ans. 31 cwt. 2qrs. 20lb. 38. Three men and 2 boys hoed 30000 hills of corn, and each man hoed two hills while a boy hoed one; how many hills were hoed by each man, and how many by each boy? Ans. Each man hoed 7500, and each boy 3750 hills. 3x2+2 8 Divisor. 39. If $911.555 be divided among 5 men and 4 women, what is each man and woman's share, a man's share being double that of a woman? $65.111 wom's share. Ans. {$130.222 man's share. gitude 31° 37' 3"; what is their 40. Two places differ in londifference in reckoning time, allowing 15° to make an hour? Ans. 2h. 6′ 28′′. REVIEW. 1. When are numbers called compound, or complex ? 2. By what are the operations performed by compound numbers regulated? 3. Repeat the table of Federal money,of English money. 4. What are the names and values of the coins of the United States? 5. What are the most common foreign coins? what their several values? 6. What is the table of time? 7. How is the year commonly diin each month. vided? Repeat the number of days 8. What is meant by leap year? How may we know whether a year is leap year or not? What is meant by old and new style? Let the pupil be questioned in like 9. What is Reduction? 10. What is the rule for Reduction Descending? Ascending? 11. What is the method of proof in each ? 12. How would you proceed to multiply by 5? to divide by 5? 13. What is meant by Reduction of Decimals? 14. How would you proceed to find the value of a decimal in integers of a lower denomination? how to reduce compound numbers to decimals of a higher denomination? 15. How many days are commonly reckoned to a month, in computing interest? (145) How are days and months reduced to a decimal of a year? 16. What is Compound Addition ? -the Rule ?-Proof? 17. What is compound Subtraction ?-the Rule ?-Proof? 18. If you wish to subtract one date from another, how would you proceed? (152) 19. What is Compound Multiplication ?-the Rule? What is Compound Division ?-the Rule? What relation have these two rules to each other? Of what contractions are these rules susceptible? 20. What are the several contractions of Simple Multiplication? (90, 91, 92, 93,) of Division? (108, 109, 110, 111.) 21. What is meant by a simple number? What is the distinction between a simple and a compound? 22. How would you proceed to take quantities of several denominations, each an equal number of times, from a given quantity? SECTION V. PER CENT. 161. Per Cent. is a contraction of per centum, Latin, signifying by the hundred, and implies that calculations are made by the hundred. Per Annum signifies by the year. Interest. ANALYSIS. 162. If I lend a neighbor 25 dollars for one year, and he allow me 6 cents for the use of each dollar, or 100 cents, how much must he pay me in the whole at the end of the year? 25 .06 1.50 25. 26.50 If he pay 6 cents.06 of a dollar (132) for the use of 100 cts. or 1 dollar, he must evidently pay 25 times .06, or (86) .06 times 25-$1.50 for the use of 25 dollars. Hence, 25+1.50 26.50 is the sum due me at the end of the year. The $25 is called the principal, the .06 is called the rate per cent., the $1.50 is called the interest, and the $26.50 is called the amount. Hence the following DEFINITIONS. 163. Interest is a premium allowed for the use of money. The sum of money upon interest is called the principal. The rate is the per cent. per annum agreed on, or the interest of one dollar for one year, expressed decimally. |