BXAMPLES-FROM A LESS TO A GREATER DENOMINATION. 1. In 171360 pence, how many pounds ? Ans. £714. 2. How much will 63lb. 70%. 10pwt. Ilgr. of gold cost at 20 cents per grạin ? Ans. $73298,20. 3. In 243648 farthings, how many dollars at 6s. each ? 4. How many pounds of gold can you buy for $55104, at 20 cents per grain ? Ans. 4776. 10oz. 5. How many tons of sugar can you buy for $146470, at 2 cents per dram ? Ans. 14T. 6cwt. Oqr. 77b. 6oz. 12dr. 6. Reduce 1720320 drams to tons. Ans. 7. What is the weight of 470 bags of sugar, each bag weighing 26 pounds ? Ans. 122cwt. 2016. 8. In 55799 grains of laudanum, how many pounds ? 9. At 6 cents a pint, how many barrels of beer can you buy for $820,80 ? Ans. 47bar. 18gal. 10. In 97397 grains, how many pounds Troy ? ' 11. How many degrees in 9511603200 barleycorns ? Ans. 720. 12. How long will it take to count 2000000 at the rate of 50 a minute ? Ans. 27da. 18hr. 40m. 13. In 1296000”, how many signs ? Ans. 12. 14. In 63360 inches, how many miles ? Ans. · 15. In 31557600 seconds, how many years ? Ans. 1. 16. In 2016 pints, how many tuns ? Ans. 1. 17. In 4014489600 square inches, how many miles ? Ans. 1. 18. In 11520 grains, how many pounds ? Ans. 2. 19. In 123456720 minutes, how many years ? Ans.. 234yr. 265da. Bhr. 20. In 811480“, how many signs ? Ans. 7s. 150 24' 40%. 21. In 2654208 solid inches, how many cords? Ans. 12. 22. If there is 15713280 inches in the distance from New York to Boston, how many miles ? Ans. 248. 23. If you have lived 399794890 seconds, how many years is that equal to ? Ans. 12yr. 244da. 6hr. 8m. 10sec. 24. In 4320 sheets of paper, how many reams ? 25. In 31556928 seconds, how many years of 365 days? Ans. lyr. 5hr. 48m. 48sec. 26. The surface of the earth contains 791300159907840000 square inches : how many square miles ? Ans. 197111025. 27. How many yards in 760 nails? Ans. 47yd. 29r. ADDITION OF DENOMINATE NUMBERS. 1. John buys a knife for 1s. 8d., and a bunch of quills for 1s. 2d. : what do they cost him ? Ans. 2s. 10d. 2. James gives 4s. 9d. for a pair of shoes, and 28. 4d. for a pair of stockings: how much do they cost him? Ans. 7s. Id. 3. How many hours in Bhr. +6hr.+7hr. +9hr. ? Ans. 30hr. 4. In Syd.+ 7yd. + 5yd.+6yd., how many yards? Ans. 2 yd. 5. How many pounds shillings and pence in £4 88. 9d., £27 14s. 11d., and £156 175. 10d. ? We write the denominations un. OPERATION. der each other, and draw a line £ d.. beneath them. We then add up 4 8 9 the column of pence, and find the 27 14 11 sum to be 30. But 30 pence are 156 17 10 equal to 2 shillings and 6 pence: £189 Is. 6d. we therefore write down the 6 and carry 2 to the shillings. We then find the sum of the shillings to be 41 ; that is, 2 pounds and 1 shilling over. Carrying the 2 to the column of pounds, we find the sum to be 189. 95. Addition of denominate numbers, like that of simple numbers, teaches how to express the value of several numbers by a single one, which is called their sum. 95. What is addition of denominate numbers? How do you set down the numbers for addition ? Where do you begin to add ? What you do with the first sum? What do you write down? What do you carry to the next column? What do you do at the last ? How do you prove addition ? do RULE. 1. Set down the numbers to be added so that all the denominations of the same kind shall stand in the same column. II. Begin with the column of the lowest denomination, and add it up as in whole numbers. III. Then consider how many units of this denomination make one unit of the next higher, and divide the sum by this number. Write down the remainder under the units of its kind, and carry the quotient to the next column, as in addition of simple numbers. IV. Proceed in the same way for all the columns to the last, and set down the entire sum of the last column. The proof is the same as in the addition of simple numbers. £ s. EXAMPLE ILLUSTRATING PRINCIPLES. What is the sum of £16 18s. 9d., £14 13s. 8d., and £15 17s. 6d.? Note.--In simple numbers 10 OPERATION. units of any one of the columns, d. make one unit of the next left 16 18 9 hand column, (Art. 8.) We 14 13 8 therefore carry one for every 10. 15 17 6 But in denominate numbers the Sum 47 9 11 higher denominations are formed differently. 30 11 For example, 12 2 pence make 1 shilling, the unit Proof 47 9 11 of the next higher denomination; and 20 shillings make 1 pound. In passing from pence to shillings, we must therefore carry 1 for every 12, and 1 for every 20 in passing from shillings to pounds. And, in general, we must carry 1 for so many units of the lower denomination as make one unit of the next higher. Ex. 1. In simple numbers, how many units of one order make one unit of the next higher order ? How do you carry in simple numbers ? How do you carry in passing frorn pence to shillings? In passing from shillings to pounds? Generally, how do you carry? 11 (1.) (3.) £ d. 173 13 5 705 17 31 104 18 91 87 17 7 354 17 23 404 17 83 75 18 73 · 175 17 33 467 11 104 25 17 87 87 19 71 597 14 41 10 10 101 52 12 73 22 18 5 373 18 3 1377 4 11 TROY WEIGHT. Adding up the grains, we OPERATION. find their sum to be 47; that Zb. oz. pwt. gr. is, lpwt. and 23gr.: setting 8 18 19 down 23, and carrying 1 to the 114 9 6 16 pennyweights, we find their 223 10 17 12 sum to be 42; that is, 20%. 350 5 2 23 and 2pwt. Carrying 2 to the ounces, we find their sum to be 29; that is, 21b. and 5oz.: carrying 2 to the pounds and adding, we find their sum to be 350. (1.) (2.) 7b. oz. pwt. gr. 16. oz. pwt. gr. Add 100 1019 20 171 6 13 14 432 6 0 5 391 11 9 12 80 3 2 1 230 6 6 13 7 0 0 9 94 7 3 18 0 11 10 23 42 10 15 20 0 0 8 9 31 0 0 21 Sum (1.) tb 3 24 7 2 1 17 11 7 2 36 6 5 0 15 9 7 1 9 3 4 1 APOTHECARIES WEIGHT. (2.) gr. 3 3 3 gr. 16 2 1 17 19 or vo co w 3 3 0 2 7 5 (3.) gr. 2 15 7 4 2 14 7 4 0 1 19 13 2 5 2 11 9 10 1 2 16 13 2 11 17 2 14 16 327 87 1 AVOIRDUPOIS WEIGHT. oz. dr. (1.) cwt. qr. ib. 14 1 25 14 9 13 2 20 1 15 9 3 6 7 3 10 0 18 12 11 7 2 27 3 2 6 1 19 8 1 4 3 0 15 5 12 2 0 0 (2.) T. cwt. qr. lb. oz. 15 12 1 10 10 71 8 2 6 0 83 19 3 15 5 36 7. 0 20 14 47 11 1 27 11 63 5 2 19. 7 12 13 1 14 9 9 7 0 5 10 13 3. A merchant bought 4 barrels of potash of the following weights, viz.: 1st, 3cwt. Igr. 251b. 12oz. 3dr.; 2d, 4cwt. lqr. 2116. 4oz. ; 3d, 4cut. ; 4th, 3cut. 3qr. 271b. 1502. 15dr.: what was the entire weight of the four barrels? Ans. 16cut. Xqr. 0lb. Doz. 2dr. LONG MEASURE. L. (1.) (2.) 90 2 11 2 155 1 9 1 327 0 7 0 50 2 1 2 CLOTH MEASURE. gr. na. gr. na. (1.) (2.) (3.) 1 4 15 3 1 |