terms, produces the fraction ;I. ; this reduced to its proper quantity is the answer. 3. If my friend lends me 10 guineas for 10 weeks and 3 days, how long ought I to lend him 5l. 4s. 6d. to acquit myself of the obligation ? Explanation. I find that the answer will be greater than the second term, consequently I mark the less extreme, and proceed as before. 4. If by walking 23 miles an hour I can perform a journey in 84 days, how many days will another who can walk 3+ miles an hour require to go the same distance, allowing 12 hours to the day 2 3 5. If # of a cwt. of iron cost lo of a pound, what is the value 3 6. If # of a yard of cambric cost To of a pound, what cost 6 10. If * of a calf be worth 7 of a pound, what is the whole calf worth Ans. 21. Is. 1d.}. 11. If 7 men can mow a hay-field in 4; days, how long would 4 men require to mow the same 2 Ans, 843 days. 12. Paid 11 shillings for # of a gallon of brandy; what must be given for 4% gallons at the same rate 2 Ans, 7 l.2s. 5d3. 13. If # of a block of mahogany cost 2; L. what sum will 9 purchase the remaining ii’ Ans. 1 ll. 16s. 3d. 14. Suppose 15 feet of plank 9 inches wide sufficient to make a side-board, how many feet of plank 14 foot wide will be required to make another of equal dimensions? Ans. 7 feet 6 inches. 15. If 9 English ells of linen cost ll. 17s.6d. what cost 10 Flemish ells 2 Ans. ll. 5s. 16. What is the value of 53 fother of lead, at 16s. 4d. per cwt. 2 Ans. 4l. 11s. 6d. 3 #. 17. A corn-chandler charges 91.5s. 6d. for a load of barley; what must be given for 33 bushels at that price? Ans. 15s. 2d.;3. 18. Suppose 120 men can build a ship in 153 weeks, how long will it be building if 87 men only are employed Ans. 21 w. 5d.o.or. o 19. If 5l. 6s. 8d. be paid for the use of 1731. 2s. 6d. what sum must be paid for the use of 310, , L. for the same time Ans. 8l. 19s. 6d.or. 2 2 20. After using To of a Cheshire cheese, T3 of the remainder sold for 13s. 5d.; ; what was the whole cheese worth 2 Arts. ll. 2s. 5d.o. 21. If 33 yards of cloth 13 yard wide will make a suit of clothes, what quantity of cloth # yard wide will be necessary 22. If # of 3 guineas will purchase; of a lottery-ticket, how many tickets can be had for a thousand pounds? Ans. 514's tickets. 23. Bought # of a privateer, # of which part I presented to my brother, and afterward sold . of my remaining share for 225l. 10s.; what is the privateer worth 2 24. How many yards of carpet 14 yard wide will be required to cover a floor $3 yards long, and 63 yards wide 2 211. COMPOUND PROPORTION IN VULGAR ExAMPLEs. 1. If #. will pay the interest of 2: L. for * of a year, what sum will pay the interest of 10L. for # of a year. * This rule depends on the same reasons as Compound Proportion in whole numbers, and its operations are performed in the same manner, as far as relates to the general principle, differing only as a fractional differs from an integral process. ° It will be found more convenient to place the fractions all in one line, with the divisors inverted; thus, i. o X + x i x * (which by cancelling, Art. 203, becomes) = Earplanation. Having stated the question, and marked the divisors, &c. the complex fraction which arises from the operation is reduced to a simple one, by multiplying 5 by 60, and 14 by 7; the result is next reduced to its lowest terms, and then to its proper quantity, which is the answer. 2. If 12 men earn 2; L. in 44 days, what sum will 20 men earn in 124 days 2 Reduction. 3 3. If 34 yards of cloth T yard wide cost # L. what sum will 4 43 yards of To yard wide, and equal in quality, cost? 6. A trench is required to be dug 100 feet in length, and 10 men have been employed 63 days in digging 493 feet of it; how long will 12 men require to finish the remainder Ans. 5d. 8++sh. at 12 hours to the day. 212. If unity be supposed to be divided into 10, 100, 1000, &c. equal parts indefinitely, that is, into ten parts, or any multiple of ten, that which expresses any number of such parts less than that the unit is divided into, is called a Decimal Fraction. NOTATION OF DECIMALS. 213. It is well known, that the value of any figure is increased tenfold by removing it one place to the left hand of the place it occupies; thus 1 removed one place to the left (by placing a cipher to the right of it) becomes 10, or ten times l; remove it one place farther, and it becomes 100, or ten times 10; remove it one place farther, and it becomes 1000, or ten times 100; and so on without end. Hence likewise it follows, that if any figure be removed in a contrary direction from the left hand towards the right, its value will be decreased tenfold at every step of such removal; thus, by removing 1 one place to the right, 1000 becomes 100, or one tenth of 1000; 100 becomes 10, or one tenth of 100; 10 becomes 1, or one tenth of 10; and, since 1 is the least whole number, this is as far as we can go in whole numbers. 214. But it is plain, that 1 may be removed step by step indefinitely towards the right; if therefore we put a point to the right hand of the place of units to distinguish it, and then place the 1 to the right hand of the point, thus .1, it is evident from what has been said that it will express one tenth of an unit, or # if we remove the 1 a place farther to the right, by interposing a cipher between the point and the 1, thus 01, this will l - express one tenth of In or one hundredth part of unity; if two ciphers be interposed, thus .001, it will express one tenth of WO L. I. P |