32. John runs 32 rods in a minute, and Henry pursues him at the rate of 44 rods in a minute; how long will it take Henry to overtake John, if John have 8 minutes the start? Ans. 21 minutes. 33. If 4 barrels of flour cost $32.3, what will 7 barrels cost? Ans. $51. 34. If .875 of a ton of coal cost $5.635, what will 94 tong cost? Ans. $59.57. 35. For the first three years of business, a trader gained $1200.25 a year; for the next three, he gained $1800.62 a year, and for the next two he lost $950.87 a year; supposing his capital at the beginning of trade to have been $5000, what was he worth at the end of the eighth year? Ans. $12100.87. 36. What will be the cost of 18640 feet of timber, at $4.50 per 100? Ans. $838.80. 21 37. Reduce to a decimal fraction. 31 Ans. .78125. 38. What will 1375 pounds of potash cost, at $96.40 per ton? Ans. $66.275. 39. Reduce .5625 to a common fraction. 40. Reduce, .621, .37, 8, to decimals, and find their sum. Ans. 1.464375. 41. A man's account at a store stands thus: 42. A gardener sold, from his garden, 120 bunches of onions at $.12 a bunch, 18 bushels of potatoes at $.62 per bushel, 47 heads of cabbage at $.07 a head, 6 dozen cucumbers at $.18 a dozen; he expended $1.50 in spading, $1.27 for fertilizers, $1.87 for seeds, $2.30 in planting and hoeing; what were the profits of his garden? Ans. $23.68. REDUCTION. 175. A Compound Number is a concrete number whose value is expressed in two or more different denominations. 176. Reduction is the process of changing a number from one denomination to another without altering its value. Reduction is of two kinds, Descending and Ascending. 177. Reduction Descending is changing a number of one denomination to another denomination of less unit value; thus, $110 dimes 100 cents 1000 mills. 178. Reduction Ascending is changing a number of one denomination to another denomination of greater unit value; thes, 1000 mills 100 cents 10 dimes $1. 179. A Scale is a series of numbers, descending or ascending, used in operations upon compound numbers. The currency of Canada is decimal, and the table and denominations are the same as those of the United States money. NOTE. The decimal currency was adopted by the Canadian Parliament in 1858, and the Act took effect in 1859. Previously the money of Canada was reckoned in pounds, shillings, and pence, the same as in England. COINS. The silver coins are the shilling, or 20-cent piece, the dime, and half dime. The copper coin is the cent. NOTE. The 20-cent piece represents the value of the shilling of the old Canada Currency, II. ENGLISH MONEY. 181. English Currency is the currency of Great Britain. SCALE ascending, 4, 12, 20; descending, 20, 12, 4. NOTE. 1. Farthings are generally expressed as fractions of a penny; thus, 1 far., sometimes called 1 quarter, (qr.), —4d, 3 far. —‡d. 2. The gold coins are the sovereign (= £1), and the half sovereign, (-10s.) 3. The silver coins are the crown (=5s.), the half-crown (-2s. 6d.), the shilling, and the six-penny piece. 4. The copper coins are the penny, halfpenny, and farthing. 5. The guinea (-21s.) and the half-guinea (-10s. 6d. sterling), are old gold coins, that are still in circulation, but are no longer coined. 6. In France accounts are kept in francs and decimes. A franc is equal to 18.6 cents U. S. money. CASE I 182. To perform reduction descending. 1. Reduce 21£ 18 s. 10 d. 2 far. to farthings, OPERATION. 21 £ 18 s. 10 d. 2 far. 438 s 5266 d. 4 21066 far. Ans. × 5266 21064 far., and 2 far. 21066 far. in the given number. = ANALYSIS. Since in £1 there are 20 s., in 21 £ there are 20 s. x 21 = 420 s., and 18 s. in the given number added, makes 438 s. in 21£ 18 s. Since in 1 s. there are 12 d., in 438 s. there are 12 d. x 438 = 5256 d., and 10 d. in the given number added, makes 5266 d. in 21£ 18 s. 10 d. Since in 1 d. there are 4 far., in 5266 d. there are 4 far. in the given number added, makes Hence, RULE. I. MULTIPLY the highest denomination of the given number by that number of the scale which will reduce it to the next lower denomination, and add to the product the given number, if any, of that lower denomination. II. Proceed in the same manner with the results obtained in each lower denomination, until the reduction is brought to the denomination required. CASE II. 183. To perform reduction ascending. 1. Reduce 21066 farthings to pounds. OPERATION. 4) 21066 far. 12) 5266 d. 2 far. 20) 438 s. +10 d. = ANALYSIS. We first divide the 21066 far. by 4, because there are as many pence as farthings, and we find that 21066 far. = 5266 d. + a remainder of 2 far We next divide 5266 d. by 12, because there are as many shillings as pence, and we find that 5266 d. 438 ş. + 10 d. divide the 438 s. by 20, because there are 21 £+18 3. Ans. 21£ 18 s. 10 d. 2 far. = Lastly we as many pounds as shillings, and we find that 438 s. = 21 £ + 18 s. The last quotient with the several remainders annexed in the order of the succeeding denominations, gives the answer 21 £ 18 s. 10 d. 2 far. Hence, RULE. I. DIVIDE the given number by that number of the scale which will reduce it to the next higher denomination. II. Divide the quotient by the next higher number in the scale; and so proceed to the highest denomination required. The last quotient, with the several remainders annexed in a reversed order, will be the answer. NOTE. Reduction descending and reduction ascending mutually prove each other. EXAMPLES FOR PRACTICE. 1. In 14194 farthings how many pounds? 2. In 14 £ 15 s. 8 d. 2 far. how many farthings? WEIGHTS. 184. Weight is a measure of the quantity of matter a body contains, determined according to some fixed standard. Three scales of weight are used in the United States and Great Britain, namely, Troy, Apothecaries', and Avoirdupois. I. TROY WEIGHT. 185. Troy Weight is used in weighing gold, silver, and jewels; in philosophical experiments, &c. TABLE. 24 grains (gr.) make 1 pennyweight,..pwt. or dwt. 20 pennyweights 12 ounces 66 1 ounce, oz. lb. SCALE-ascending, 24, 20, 12.; descending, 12, 20, 24. 3. In 5 lb. 7 oz. 12 pwt. 9 gr., how many grains? 4. In 32457 grains how many pounds? Define weight. Troy weight. Repeat the table. Give the scale. |