7. Planted 420 apple-trees in 7 rows; how many in each row? Ans. 60. 8. Paid for the above apple-trees, 37 dollars 80 cents; what is that for each apple-tree? Ans. 9 cents. 9. Paid a man for working for me 24 days, the sum of 15 dollars; what is that per day? Ans. 62 cents. 10. Á man travelled from New-York to this town, (Washington, G. C. Ohio,) in 23 days. How much did he travel each day, allowing the distance to be 460 miles? Ans. 20 miles. Division of divers denominations. RULE. In dividing into the left hand, or greater division of the given sum to be divided, divide as in whole numbers, and reduce the remainder, (if any,) to the next lowest denomination, adding to it the number of the same denomination in the given sum, and divide this in like manner; and so proceed till all are divided. If any remain after the last division is obtained, that remainder is of the same name as the dividend or denomination that was last divided. 03. dwt. grs. how 4)5 18 12 1 9 15 EXAMPLES. Here I give one to shew more clearly you are to proceed with the following. First, I say, how often is 4 contained in 5, which is 1, and 1 over. The t that is over is 1 ounce, which you must reduce to the next lowest denomination, which is pennyweights. By having the table of Troy weight committed to memory, ere you come this far, you will find 1 ounce contains 20 pennyweights, to which you add the 18 dwts. in the given sum, making 38; and divided by 4, the quotient is 9, which I set down in the place of pennyweights, and there is 2 over, which 2 is penny. weights. By the table, each pennyweight contains 24 grs. making 48 grains in the 2 dwts. and the 12 grs. in the given sum, will make 60 grains. Then I seek how often 4 will go into 6, (the first figure of the grains,) and find the quotient is 1, which I set in grains, and 2 over, which 2, with the cipher annexed to 6, make 20. Then I say, how often will 4 go into 20, and find the quotient 5, which I set down on the right hand of the last 1, making the quotient in all, 1 oz. 9 dwt. 15 grs. Teaches to bring or change numbers of a higher denomination to that of a lower, yet retaining the same value. RULE. Multiply the highest denomination given, by so many of the next less, as make one of that greater; and this continue, till you have brought it down as low as your question requires. But if there be smaller denominations attached to the greater, as 3 cwt. 2 qrs. 14 lbs. you must, in your multiplying, add in the denomination that is of the same name of that which you are reducing the higher one to, and so on, as for example: Reduction ascending, (improperly called,) is the bringing a lower denomination to a greater, yet retaining the same value. RULE. Divide the lowest denomination given, by as many of the same name as make one of the next greater or higher, and so on through all the denominations, as far as your question requires. But if there happens to be a remainder, after your first divisor is divided, that remainder is of the same name as the dividend, before it was divided; and all the remainders, throughout the operation of the question, will be of the same name as the dividend, before it was divided. For example, bring 406 lbs. to cut. qrs. lbs. Here, 28 lbs. make a quarter, which I divide, because a quarter is the next highest denomination, and the quotient is 14, and 14 remains, which 14 is pounds, as the dividend was pounds, before it was divided by 28. Now, the quotient 14 is quarters, therefore the remainder, after that is divided, will be quarters. Here again I divide by 4, the next greatest denomination, as 4 qrs. make 1 cwt. and there remains 2, which 2 is quarters, and the quotient 3 cwt, See the operation. 1. Reduce 24 eagles 8 dollars 6 dimes 8 cents 7 mills, to Ans. 248687 mills. mills. Ans. 24 eag. 8 dolls. 6 dim. 8 cts, 7 m, 3. Reduce 764 dollars 75 cents to cents. 4. Bring 76475 cents to dollars. Ans. 76475 cents, Ans. 764 dollars 75 cents. Ans. 800000 mills. 5. Reduce 800 dolls. to mills. 8. Bring 64125 mills to cents. Ans. 80 eagles. Ans. 64125 mills. Ans. 6412 cents. Ans. 64 dollars 12 cents. 10. Reduce 380 dollars 12 cents to mills. 11. Bring 6543794 mills to dollars. Ans. 380125 mills. Ans. 6543 dolls. 79 cts. 4 m. 12. Reduce 719 dollars 62 cents to mills. 13. Bring 719625 mills to dollars. Ans. 719625 mills. Ans. 719 dolls. 62 cts. NOTE.cent is 5 mills. See table of money, where 10 mills make 1 cent; consequently, 5 mills make cent. TROY WEIGHT. 1. Reduce 47 lbs. 10 oz. to grains. 2. Bring 275520 grs. to pounds. Ans. 275520 grs. Ans. 47lbs. 10 oz. 3. In 10 pounds of silver, how many spoons, each 5 oz. 10 dwts.? Ans. 21 spoons, and 90 dwts. over. 4. Reduce 20 pounds of silver to grains. Ans. 115200 grains. Ans. 20 lbs. 5. Bring 115200 grs. to pounds. 6. In 4560 grains, how many teaspoons, each half an Ans. 19 teaspoons. ounce ? 7. In 19 teaspoons, each half an ounce, how many grains? Ans. 4560 grains, 8. In 17 ingots of silver, each 27 oz. 10 dwts. how many grains? Ans. 224400 grains. AVOIRDUPOIS WEIGHT. 1. Reduce 7 cwt. 2 qrs. 17 lbs. to pounds. Ans. 857 lbs. Ans. 7 cwt. 2qrs. 17 lbs. 2. Bring 857 lbs. to cwt. Ans. 878 lbs. 4. In 14048 ounces, how many hundred weight? 5. Bring 3 tons to pounds. 6. Bring 6720 lbs. to cwt. Ans. 7 cwt. 3 qrs. 10 lbs. 7. Reduce 60 cwt. to quarters. Ans. 6720 lbs. Ans. 60 cwt. Ans. 240 qrs. 8. In 3 lbs. of cloves, how many parcels, each 12 oz. ? Ans. 4 parcels. 9. In 400 lbs. of soap, how many parcels, each 5 lbs.? Ans. 80 parcels. 10. In 4 loads of hay, each 5 cwt. 1 qr. 10 lbs. how many pounds? 11. Bring 2392 pounds to tons. Ans. 2392 lbs. Ans. 1 ton 1 cwt. 1 qr. 12 lbs. APOTHECARIES' WEIGHT. 1. Reduce 14 lbs. 8 oz. 4 drs. 2 scr. 16 grs. to grains. 2. Bring 84776 grains to pounds. Ans. 84776 grains. Ans. 14 lbs. 8 oz. 4 drs. 2 scr. 16 grs. 3. Reduce 5 pounds of medicine to grains. CLOTH MEASURE. Ans. 28800 grains. 1. Reduce 26 yds. 2 qrs, to quarters. 2. Bring 106 quarters to yards. Ans. 106 qrs. Ans. 26 yds. 2 qrs |