of a cwt.? Ans. 5. What part of an ounce is 172 6. Reduce 1320 of a furlong to the fraction of a foot. Ans.. 7. What part of a square foot is 58090 of an acre? 8. What part of a second is goo of a day? 10. What part of a pound is of a bushel? of a cwt.? Ans. 3 Ans. 23 Ans. Ans. ART. 170. To reduce a fraction of a lower denomination to a fraction of a higher. Ex. 1. Reduce of a farthing to the fraction of a pound. Ans. 2160 there will be as many pence as farthings; therefore we divide theby 4, and obtain d. And, since 12d. make a shilling, there will be as many shillings as pence; hence we divide by 12, and obtain 28. Again, since 20s. make a pound, there will be go as many pounds as shillings; therefore we divide 2 by 20, and obtain 0£. = 2160£. for the answer. RULE. Divide the given fraction by the same numbers that would be employed in reduction of whole numbers to the higher denomination required. EXAMPLES FOR PRACTICE. 2. Reduce of a grain Troy to the fraction of a pound. Ans. 10080. QUESTIONS. Art. 170. Do you multiply or divide to reduce a fraction of a lower denomination to the fraction of a higher? What is the rule? of a quart ? Ans. 294030. 9. What part of 3hhd. is 10. What part of of a solid foot is of a yard solid? Ans. . ART. 171. To find the value of a fraction in whole numbers of a lower denomination. 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 reducea to the denomination required. QUESTION. Art. 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. 7дdr. 3. What is the value of 3 of a yard? 4. What is the value of of an acre? Ans. 1R. 28p. 155ft. 82 in. 5. What is the value of of a mile? 6. What is the value of 7. What is the value of 4 Ans. 1 fur. 31rd. 1ft. 10in. of an ell English? Ans. 1qr. 15na. of a hogshead of wine? 8. What is the value of of a year? Ans. 18gal. Ans. 232da. 10h. 21m. 49 sec. ART. 172. To reduce a simple or compound number to the fractional part of any other simple or compound number of the same kind. Ex. 1. What part of 1£. is 3s. 6d. 23far. OPERATION. 3s. 6d. 23far. = 512 1£. =2880 Ans. £. In performing this operation, we reduce the 3s. 6d. 2 far. to 5. 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 £. for the 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. 2. Reduce 4s. 8d. to the fraction of 1£. Ans. 1. Ans. 37 126. QUESTION. Art. 172. What is the rule for reducing a simple or compound number to the fractional part of any other simple or compound number of the same kind? 7. What part of 30 days are 8 days 17h. 20m.? Ans. 8. From a piece of cloth containing 13yd. Oqr. 2na. there were taken 5yd. 2qr. 2na. What part of the whole piece was taken ? Ans. 3. 9. What part of 3 yards square are 3 square yards? Ans.. ADDITION OF FRACTIONS OF COMPOUND NUMBERS. 9 X 20 Ans. 17s. 11d. 0far. We find the value of each fraction separately, and add the two values together, according to the rule for adding compound numbers. (Art. 101.) 9£. ++70£.=1188£. = 17s. 11d. 0far. the two fractions together and find the value of their sum. (Art. 171.) EXAMPLES FOR PRACTICE. 2. Add of a pound to of a shilling. Ans. 7s. 11d. 323far. 3. Add together 1 of a ton, 3 of a ton, and ‡ of a cwt. Ans. 1T. 14cwt. 1qr. 563. 4. Add together of a yard, § of a yard, of a quarter. Ans. 1yd. 2qr. 2na. 0 in. of a mile, of a furlong, Ans. 6fur. 29rd. 3yd. 1ft. 01fin. and 5. Add together of a yard. 6. Add together of a mile, of an acre, rod. of a rood, and of a square Ans. IA. OR. 3p. 169ft. 102gin. 7. Sold 4 house-lots; the first of an acre, the second 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. 45ft. QUESTIONS. Art. 173. What is the first method of adding fractions of compound numbers? What is the second? SUBTRACTION OF FRACTIONS OF COMPOUND NUMBERS. ART. 174. To subtract fractional parts of compound numbers. Ex. 1. From & of a pound take of a pound. FIRST OPERATION. 8. d. far. 7 1 29 31 £.= SECOND OPERATION. = #£. 9s. 10d. 19far. Ans. 9s. 10d. 159far. We find the value of each fraction separately, and subtract one from the other, according to the rule for subtracting compound numbers. (Art 102.) We first subtract the less fraction from the greater, and then find the value of their difference. (Art. 171.) EXAMPLES FOR PRACTICE. Ans. 3R. 16p. 154ft. containing 100 gallons, 5. From a hogshead of molasses of it leaked out; of the remainder I kept for my family; what quantity remained for sale? Ans. 24gal. Oqt. 13 pt. 6. The distance from Boston to Worcester is about 41 miles. A sets out from Worcester, and travels 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 Ans. 137da. 11h. 13m. 149 sec. the time lost. 8. From 11 acres, 33 poles, 101 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 81 cents per square foot? Ans. $3937.89. QUESTIONS. Art. 174. What is the first method of subtracting fractions of compound numbers? The second? |