Note 8.-A general rule to change the currency of each of the States to Federal Money. Reduce the given sum to shillings, or to sixpences, or to pence, and to these annex two cyphers; then divide by the number of shillings, sixpences, or pence in a dollar, as it passes in each State: the quotient will be cents. (For the value of a dollar, see the table at page 65.) 46. Reduce 63L. 15s. New-England or Virginia currency to Federal Money, a dollar being 6s. Facit $212.50. 47. Reduce 112L. 16s. New-York or North-Carolina Result $282.00 48. Reduce 161L. 14s. South-Carolina or Georgia currency, to Federal Money. currency, to Federal Money. Result $693.00 WEIGHTS AND MEASURES. 1. Reduce 47 pounds, 10 ounces, 15 pennyweights, to penny weights. Facit 11495dwt. 2. Reduce 5lb. 6oz. 4dwt. 20gr. to grains. Result 31796gr. 3. Bring 2 tons, 15cwt. 2 quarters, to quarters. Result 222qrs. 4. Bring 3 tons, 25lb. to pounds. Facit 14048oz. 6. Bring 27 73 23 19 2grs. to grains. Result 159022grs. 7. Bring 3 leagues, 2 miles, 7 furlongs, to furlongs. Result 95fur. 8. Bring 57 miles, 2 furlongs, to poles. Result 18320P. 9. Reduce 15 yards, 2 feet, to inches. Result 564in. 10. Bring 42 English ells, 3 quarters, to quarters. Result 213qrs. 11. Bring 17 yards, 2 quarters, 2 nails, to nails. Result 282na. 12. Reduce 11 acres, 2 roods, 19 perches, to perches. Result 1859P. 13. Bring 17 acres, 3 roods to perches. Result 2840P. 14. Reduce 14 tuns, 3 hogsheads, to hogsheads. Result 59hhd. Result 544qt. 15. Reduce 2 hogsheads, 10 gallons, to quarts. 16. Bring 40 gallons, 3 quarts, 1 pint, to pints. Result 327pt. 17. Bring 16 bushels, 1 peck, to pecks. Result 65pe. 18. Bring 15 bushels, 6 quarts, to quarts. Facit 486qt. 19. Reduce 18 years, 6 months, to months. Result 222mo. 20. Bring 3 weeks, 4 days, to days. Result 25D. 21. Bring 2 weeks, 20 hours, to minutes. Result 21360min. PROMISCUOUS QUESTIONS. 1. How many shillings are there in 45 pounds, 10 Ans. 910s. shillings? 2. How many cents are there in 630 pence, Penn sylvania currency? Ans. 700cts. Ans. 888far. 3. What number of farthings do 18s. 6d. make? 4. How many pence are there in 4L. 5s. 4d.? Ans. 1024d. 5. How many dollars are there in 37L. 10s. PennAns. $100. sylvania currency? 6. In 1400 cents, how many pence, Pennsylvania currency? Ans. 1260 pence. 7. In 64130 cents, how many pounds, Pennsylvania Ans. 240L. 9s. 9d. currency? 8. How many pounds, Pennsylvania currency, are there in 560 dollars? Ans. 210L. 9. How many dollars are there in 600 pounds, New York currency? Ans. $1500. 10. In 38L. 9s. 3d. sterling, how many dollars? Ans. $170.944+ 11. In 845 French crowns, how many pounds, Penn sylvania currency? Ans. 348L. 11s. 3d. 12. How many spoons weighing each 5oz. 10dwt. will 10lb. loz. of silver make? Ans. 22. 13. A grocer has 34cwt. 2qrs. 12lb. of sugar, and intends to divide it into parcels, each of which to weigh 68 pounds: how many of these parcels will there be? Ans. 57. 14. In 28cwt. 3qrs. 241b. how many pounds? Ans. 3244lb. 15. In 560 poles, how many miles? Ans. 1M. 6fur. 16. In 327 English ells of cloth, how many yards? Ans. 408yds. 3qrs. 17. How many quarters of a yard are there in 18 yards, 2 quarters? Ans. 74qrs. 18. A tract of land containing 1299600 square perches, is to be divided into 25 plantations of equal size: how many acres will there be in each? cider? Ans. 324A. 3R. 24P. 19. How many casks which will contain 33 gallons each, may be filled out of 5 pipes and 1 hogshead of Ans. 21. 20. In 15 bushels, 6qts. how many quarts? Ans. 486. 21. In 10 weeks, 2 days, how many days? Ans. 72. 22. In 17 years, 9 months, how many months? Ans. 213. 23. How many seconds are there in a solar year, which consists of 365 days, 5 hours, 48 minutes, and 58 seconds? Ans. 31556938sec. 24. How many days from the 24th of the fifth month, (May) 1797, to the fifteenth of the twelfth month, (December) 1798 inclusive? Ans. 571 days. SIMPLE PROPORTION, OR THE SINGLE RULE OF THREE. Four numbers are said to be proportional, when the first contains the second, or some part of the second, as often as the third contains the fourth, or a like part of the fourth. In questions which are solved by Simple Proportion three terms of a proportion are given to find the fourth. RULE. Write down, for the third term, that number which is of the same name or kind with the answer. Consider, from the nature of the question, whether the answer should be greater or less than this third term. If it is to be greater, set the greater of the two remaining numbers on the left hand, for the second term, and the other for the first; but if less, set the less of those two numbers for the second, and the other for the first. When the question is thus stated, if the first and second terms be not of the same denomination, reduce one or both of them till they are; and if the third term consist of several denominations, reduce it to its lowest denomination; then, Multiply the second and third terms together, and divide the product by the first term: the quotient will be the answer. Note. The product of the second and third terms is of the same denomination as the third term; and the learner may be reminded, that the quotient and remainder are of the same denomination as the number divided. See examples 14, 15, and 16, under rule 1, and 7, 8, under rule 3, Compound Division. The rule which is given above, as it renders the distinctions of direct and inverse proportion unnecessary, and has several other advantages, is preferable to the one which was formerly used; and it is likely to be generally adopted: but for the convenience of those teachers who have not yet determined to employ it, the last mentioned rule is subjoined. RULE FOR STATING. Set that term of the supposition which is of the same name or kind with the term of demand, in the first place, set the other term of supposition in the second place, and the term of demand in the third place. When the question is thus stated, consider whether the proportion is direct or inverse. The proportion is direct, when the third term is greater than the first, and the nature of the question requires that the fourth term, or answer, should be greater than the second; or when the third term is less than the first, and it is required that the fourth term be less than the second. The proportion is inverse, when the third term is greater than the first, and the fourth is to be less than the second; or when the third PROOF. Invert the question, making the answer the third term, as in the following wrought examples. EXAMPLES. 1. If 2 yards of muslin cost 4 shillings, what will 6 yards cost? term is less than the first, and the fourth is to be greater than the second. RULE FOR DIRECT PROPORTION. If the first and third terms be not of the same denomination, reduce both to the lowest in either; and if the second term consist of several denominations, reduce it to its lowest denomination; then, multiply the second and third terms together, and divide the product by the first term; the quotient will be the fourth term, or answer in the same denomination as the second, or that to which the second was reduced. EXAMPLE. If 2 yards of muslin cost 4 shillings, what will 6 yards cost? yds. S. yds. RULE FOR INVERSE PROPORTION. Multiply the first and second terms together, and divide the product by the third; the quotient will be the answer in the same denomination as the second, or that to which the second was reduced. EXAMPLE. If 4 men can build a wall in 4 days, how many men can do it in 8 days. men. days. days. 4 6)16 2 Answer. |