2. Reduce EXAMPLES FOR PRACTICE. Ans.. 5. What part of an ounce is 1728 of a cwt.? Ans. 1. 6. Reduce 1320 of a furlong to the fraction of a foot. Ans.. 7. What part of a square foot is`555ʊ of an acre? Ans.. ART. 168. 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. RULE. Divide the given fraction by the numbers that would be employed in reduction of whole numbers to reduce the denomination of the fraction to the higher denomination required. EXAMPLES FOR PRACTICE. 2. Reduce of a grain Troy to the fraction of a pound. QUESTIONS. Ans. Too8o. Art. 168. Do you multiply or divide to reduce a fraction of a lower denomination to the fraction of a higher? What is the rule? 3. What part of an ounce 7. What part of a day is 9. What part of 3hhd. is of a quart? of Ans. 1323. 10. What part of of a solid foot is of a yard solid? Ans. . ART. 169. To find the value of a fraction in whole numbers of a lower denomination. Ex. 1. What is the value of g of 1£.? OPERATION. 7 Ans. 7s. 9d. 1qr. 18) 140 (7s. 126 14 12 18) 168 (9d. 162 6 4 The reason of this operation will be seen, if we analyze the question according to Art. 167. Thus, 7 X 20 18 14 X 12 == = 168d. = 6 X 4 18 18 =2qr.=1qr. Ans. 7s. 9d. 13qr. Multiply the numerator of the given fraction by the number required of the next lower denomination to make ONE of the denomination of the given fraction, and divide the product by the denominator. Then, if there is a remainder, proceed to multiply and divide in this manner, until it is reduced to the denomination required; and the several quotients will be the answer. QUESTION. Art. 169. What is the rule for finding the value of a fraction in whole numbers of a lower denomination? Ans. 1fur. 31rd. 1ft. 10in. 6. What is the value of of an ell English? Ans. 1qr. 1na. 7. What is the value of of a hogshead of wine? Ans. 18gal. Oqt. Opt. 8. What is the value of of a year ? Ans. 232da. 10h. 21m. 49sec. ART. 170. 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. 24qr.? Ans. £. In performing this operation, we reduce the 3s. 6d. 23qr. to thirds of qr., 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. EXAMPLES FOR PRACTICE. Ans.. Ans. +3. Ans. 44. Ans.. 2. Reduce 4s. 8d. to the fraction of 1£. ? Ans. 37 126 QUESTION. Art. 170. 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. 1. 8. From a piece of cloth containing 13yd. Oqr. 2na. there What part of the whole piece was were taken 5yd. 2qr. 2na. taken ? Ans.. Ans.. 9. What part of 3 yards square are 3 square yards? ADDITION OF FRACTIONS OF COMPOUND NUMBERS. ART. 171. To add fractions of compound numbers. Ex. 1. Add & of a pound to 7 of a shilling. Ans. 17s. 11d. Oqr. We find the value of each fraction separately, and add the two values together according to the rule for adding compound numbers. (Art. 101.) of a shilling=0x20=170£. 9 $£. +180£. = 11.17s. 11d. Oqr. We first reduce the fraction of a tion of a pound, shilling to the frac then add the two fractions together, and find the value of their sum. (Art. 169.) EXAMPLES FOR PRACTICE. 2. Add of a pound to of a shilling. Ans. 7s. 11d. 349qr. 3. Add together 1 of a ton, 3 of a ton, and of a cwt. Ans. 1T. 14cwt. 1qr. 683lb. 4. Add together of a yard, & of a yard, of a quarter. and Ans. lyd. 2qr. 2na. 0 in. of a mile, of a furlong, Ans. 6fur. 29rd. 3yd. 1ft. Offin. of a mile, 5. Add together of a yard. 6. Add together of an acre, rod. of a rood, and of a square Ans. IA. OR. 3p. 169ft. 102 in. of an acre, 7. Sold 4 house-lots, the first of an acre, the second of an acre, the third of an acre, and the fourth what was the quantity of land in the four lots? QUESTIONS. Art. 171. What is the first method of adding fractions of compound numbers ? What is the second? SUBTRACTION OF FRACTIONS OF COMPOUND NUMBERS. ART. 172. To subtract fractional parts of compound numbers. Ex. 1. From of a pound take of a pound. Ans. 9s. 10d. 159qr. 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. 169.) EXAMPLES FOR PRACTICE. 2. From of a ton take of a cwt. Ans. 11cwt. Oqr. 8 lb. 3. From of a mile take of a furlong. Ans. 5fur. 33rd. 5ft. 6in. 4. From 1 of an acre take of a rood. 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 the time lost. Ans. 137da. 11h. 13m. 149 sec. - QUESTIONS. Art. 172. What is the first method of subtracting fractions of compound numbers? The second? |