Ans. ab. 3. What part of an ounce is io of a scruple ? 4. What part of a ton is of an ounce ? Ans. totoo Ans. to 5. What part of a mile is g of a rod ? 6. What part of an acre is of a square foot ? Ans. ਚਤ ਹੈ ਕo Ans. godio 7. What part of a day is ff of a second ? 8. What part of 3 acres is of a square foot ? Ans. 294030 9. What part of 3hhd. is 4 of a quart ? Ans. 1323 10. What part of t of a solid foot is a cube whose sides are each of a yard square ? Ans. 171. To find the value of a fraction in whole numbers of a lower denomination. Ex. 1. What is the value of To of 1 £ ? Ans. 78. 9d. 1ffar. OPERATION. 7 18) 140 ( 7s. 1 2 6 14 1 2 18) 168 (9d. 1 6 2 Since 1£ 208., is of a £ is of 20s. 714s.; and since 1s. 12d., 1 of a shilling is 1 of 12d. 1980. =9&d.; and since id. Afar., i of 4far. iffar. 1ffar. Therefore 1] = 7s. Id. iffar. 6 4 18) 24 (1 ffar. 18 ffar. RULE. Multiply the numerator of the given fraction by the number required to reduce it to the next lower denomination, and divide the product by the denominator. Then, if there is a remainder, proceed as before, until it is reduced to the denomination required. 171. What is the rule for finding the value of a fraction in whole numbers of a lower denomination ? EXAMPLES FOR PRACTICE. 2. What is the value of } of a cwt. ? Ans. 3qr. 2lb. 12oz. 7fdr. 3. What is the value of of a yard ? Ans. 3qr. Ofna. 4. What is the value of f of an acre ? Ans. 1R. 28p. 155ft. 824 in. 5. What is the value of g of a mile ? Ans. lfur. 31rd. 1ft. 10in. 6. What is the value of of an ell English ? Ans. lqr. 11'inas 7. What is the value of of a hogshead of wine ? Ans. 18gal. 8. What is the value of it of a year ? Ans. 232da. 10h. 21m. 494 sec. 172. To reduce one denominate number to the fractional part of another. Ex. 1. What part of 1£ is 3s. 6d. 2ffar. Ans. .£. Since numbers compared 3s. 6d. 23 far. 512 must be of the same unit, we reduce the 3s. 6d. 2[tar. 1£ · 2880 to thirds of far., the lowest denomination in the question, for the numerator of the required fraction, and 1£ to the same denomination for the denominator. We then reduce this fraction to its lowest terms, and obtain a£ for the OPERATION. =85£. answer. RULE. Reduce the given numbers to the lowest denomination mentioned in either of them. Then, write the number which is to become the fractional part for the numerator, and the other number for the denominator, of the required fraction. Note. — The part that one abstract number is of another may be found in like manner. EXAMPLES FOR PRACTICE. 2. Reduce 4s. 8d. to the fraction of 1£. 3. What part of a ton is 4cwt. 3qr. 121b. ? · Ans. Jo 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? 5. What part of 2A. 2R. 32p. is 3R. 24p. ? 6. What part of a hogshead of wine is 18gal. 2qt. ? Ans. 30 Ans. + Ans. 176 172. What is the rule for reducing a denominate number to the fractional part of any other denominate number of the same kind ? 7. What part of 30 days are 8 days 17h. 20m.? Ans. 13. 8. From a piece of cloth containing 13yd. Oqr. 2na. there were taken 5yd. 2qr. 2na. What part of the whole piece was taken ? 9. What part of 3 yards square are 3 square yards ? Ans. 4. Ans. 1. ADDITION OF FRACTIONS OF DENOMINATE NUMBERS. 173. To add fractions of denominate numbers. Ex. 1. Add of a pound to šof a shilling. Ans. 17s. 11d. 024 far. We find the value of each fraction separately, and add the Value of $£ 1 29 two values, according to the Value of gs. 9 1} rule for adding compound num bers. (Art. 101.) 17 11 04 FIRST OPERATION. 8. d. 17 far. SECOND OPERATION. We first reduce = the fraction of a 9 x 20 shilling to the frac$£tigo£= 14%!£= 17s. 11d. 04far. tion of a pound, then add the two fractions and find the value of their sum. (Art. 171.) EXAMPLES FOR PRACTICE. 2. Add At of a pound to of a shilling. Ans. 7s. 11d. 34 far. 3. Add together if of a ton, s of a ton, and of a cwt. Ans. 1T. 14cwt. lqr. 565%. 4. Add together of a yard, f of a yard, it of a quarter. Ans. lyd. 2qr. 2na. 0}{in. 5. Add together tf of a mile, $ of a mile, it of a furlong. and It of a yard. Ans. 6fur. 29rd. 3yd. 1ft. 0:{fin. 6. Add together I of an acre, # of a rood, and of a square rod. Ans. 1A. OR. 3p. 169ft. 102$ in. 7. Sold 4 house-lots; the first of an acre, the second 4 of an acre, the third of an acre, and the fourth of an acre; what was the quantity of land in the four lots ? Ans. 3R. 38p. 45,9 ft. 173. What is the first method of adding fractions of denominate numbers 1 What is the second ? SUBTRACTION OF FRACTIONS OF DENOMINATE NUMBERS. FIRST OPERATION. 8. d far. SECOND OPERATION. 174. To subtract fractional parts of denominate numbers. Ex. 1. From of a pound take 1 of a pound. Ans. 93. 10d. 149 far. We find the value of each fraction separately, and subValue of £ 17 1 2qfar. tract one from the other, acValue of 11 € 7 cording to the rule for sub9 10 144 tracting compound numbers. (Art. 102.) We first subtract the less fraction from 8£ -*£= the greater, and then find the value of their difference. (Art. 171.) 9s. 10d. 144far. EXAMPLES FOR PRACTICE. 2. From # of a ton take it of a cwt. Ang. 11cwt. Oqr. 787, lb. 3. From f of a mile take ts of a furlong. Ans. 5fur. 33rd. 5ft. 6in. 4. From if of an acre take of a rood. Ans. 3R. 16p. 154ft. 5. From a hogshead of molasses containing 100 gallons, i of it leaked out ; of the remainder I kept for my family ; what quantity remained for sale ? Ans. 24gal. Oqt. 1}}p. 6. The distance from Boston to Worcester is about 41 miles. A sets out from Worcester, and travels t of this distance towards Boston; B then starts from Boston to meet A, and, having travelled of the remaining distance, it is required to find the distance between A and B. Ans. 12m. 6fur. 9rd. 5ft. 9 in. 7. A agrees to labor for B 365 days; but he was absent on account of sickness + part of the time; he was also obliged to be employed in his own business of the remaining time ; required the time lost. Ans. 137da. 11h. 13m. 1494 sec. 8. From 11 acres, 33 poles, 10116 feet of land, I sold to A, of the remainder to B, and four house-lots, each 144 feet square, to C; what is the value of the remainder, at 84 cents per square foot ? Ans. $3937.8973. 174. What is the first method of subtracting fractions of denominate numbers? The second ? QUESTIONS TO BE PERFORMED BY ANALYSIS. 1. If one yard of cloth cost $ 4.40, what will of a yard cost? ILLUSTRATION. - If 1 yard cost $ 4.40, † of a yard will cost of $ 4.40, or $ 0.88; and will cost 4 times $ 0.88, or $ 3.52, Ans. 2. If a barrel of flour cost $ 7.80, what will of a barrel cost? Ans. $ 2.34. 3. If a load of hay cost $ 17.84, what will z.of a load cost? Ans. $ 15.61. 4. If $ 786.63 are paid for a cargo of wheat, what is the cost of 1} of the cargo? Ans. $ 665.61. 5. What is it of $ 87.50 ? Ans. $ 80.20%. 6. What is as of 17£ 18s. 9d. ? Ans. 13£ 9s. O d. 7. What is 4 of 3T. 16cwt. 3qr. 231b. ? Ans. 2T. 3cwt. 3qr. 2341b. 8. What is of 27A. 3R. 33p. ? Ans. 12A. 1R- 28p. 9. If $ 3.52 are paid for of a yard of cloth, what is the price of 1 yard ? Ans. $ 4.40. ILLUSTRATION. — If of a yard cost $ 3.52, } will cost of $3.52, or $ 0.88; and, or a whole yard, will cost 5 times $0.88, or $4.40, Ans. 10. If ix of a barrel of flour cost $ 2.34, what will be the cost of a whole barrel ? Ans. $ 7.80. 11. When $ 15.571, are paid for f of a ton of hay, what will 1 ton cost? Ans. $ 17.80. 12. When 1} of a cargo of flour cost $ 665.50, what sum will pay for the whole cargo ? Ans. $ 786.50. 13. If $ 73.605 are paid for 11 of a ton of potash, what sum must be paid for a ton ? Ans. $ 80.30. 14. Boughts of a bale of broadcloth for 13£ 9s. Ojd. ; what would have been the cost of the whole bale ? Ans. 17£ 18s. 9d. 15. If t of an acre produce 18cwt. Oqr. 12lb. of hay, what quantity will a whole acre produce ? Ans. 77cwt. Oqr. llb. 16. Bought of a lot of land containing 12A. 1R. 303p.; what were the contents of the whole lot? Ans. 27A. 3R. 391p. 17. If it of a ton of potash cost $ 80.204, what is the value of a ton ? Ans. $ 87.50, |