ART. 70. SUBTRACTION of denominate numbers is finding the difference between two denominate numbers. 1. From £38 8s. 10d. 1 far., take £12 15s. 4d. 3 far. OPERATION. 20 12 14 £. S. Min. 38 8 Sub. 12 15 Rem. 25 13 5 2 EXPLANATION.-Write the subtrahend under the minuend, observing to place the numbers of the same denomination one under another; and begin at the right to subtract. We cannot take 3 farthings from 1 far., therefore, from the 10d. (of the minuend) we take 1 penny, which equals 4 far., and add it to 1 far., which makes it 5 farthings; 3 far. from 5 far. leave 2 far, which place under the column of farthings. We now take the 4d. from the 9d., or add 1 penny to the 4d., and take this sum from 10d., which in either case gives the same remainder, 5d. As we cannot take 15s. from 8s., we borrow £1, 20s., from the £38, and add it to the 8s.; from this sum, we take the 15s., and obtain 13s. for a rema nder. We now take £12 from £37, = or add £1 to the £12, and take the sum from the £38, which in either case, gives the same remainder, £25. Hence the difference of the two quantities is £25 13s. 5d. 2 far. PRACTICAL QUESTIONS IN ADDITION AND SUBTRACTION OF DENOMINATE NUMBERS. 1. From a piece of cloth containing 27 yards 3 qrs. 1 na., there were taken three garments; the first contained 3 yds. 3 qrs. 2 nas.; the second 4 yds. 1 qr. 3 nas.; and the third 2 yds. 3 qrs. 3 nas.;-how much remained? 2. Bought a hogshead of sugar wieghing 9 cwt. 3 qrs. 21 lbs.; sold to A 1 cwt. 2 qrs. 15 lbs.; to B 2 cwt. 3 qrs. 24 lbs.; and to C 3 cwt. 1 qr. 15 lbs.;-how much remained unsold? 3. A man agrees to build 136 rods and 15 feet of stone fence; at one time he built 36 rds. 2 feet; at another time 56 rds. 3 feet; and at another time 10 rds. 1 foot. How much still remains to be built. 4. I agreed to let a person have 24 T. 9 cwt. 2 qrs. 15 lbs. of hay. He took away four loads, the weight of which were as follows: the first weighed 16 cwt. 2 qrs. 18 lbs.; the second, 19 cwt. 3 qrs. 12 lbs.; the third, 1 T. 2 cwt. 1 qr. 21 lbs.; and the fourth, 1 T. 5 cwt. 2 qrs. 14 lbs. ;-to how much hay is he still entitled? 5. How many yard of cloth in three pieces: the first containing 12 yds. 3 qrs. 2 nas.; the second 6 E. English 2 qrs. 1 na.; the third 9 E. French, 1 qr. 3 nas.? 6. Bought three pieces of cloth: the first containing 25 yds. 3 qrs. 1 na.; the second 47 yds. 1 qr. 3 nas; and the third 35 yds. 3 qrs. 2 nas.;-I sold 73 yds. 3 qrs. 2 nas. of it. How much remained unsold? 7. A merchant bought, at one time 956 bushels and 3 pecks of Indian corn; at another time 759 bushels, 2 pks. and 7 quarts; and sold 325 bush. 3 pks. and 6 qts. of it. How much had he remaining? 8. John is 23 years, 9 month, and 18 days old; James is 18 years, 10 months, and 25 days old. What is the difference of their ages ? 9. Suppose a person was born February 29, 1788; how many birth-days will he have seen on February 29, 1840, not counting the day on which he was born? 10. A merchant sold goods to the amount of £397 18s. 6d. 2 qrs.; and received in payment £199 19s. 10d. 3 qrs.; how much remains due ? 11. From a pile of wood containing 423 cords, I sold at one time, 56 C. 112 cu. ft.; at another time, 97 C. 113 cu. ft.; at another time, 126 C. 96 cu. ft. How many cords remain unsold? 12. How long from the birth of William Shakspeare, April 23, 1564, to the birth of Milton, Dec. 9, 1608? 13. A farmer raises 125 bush. 2 pks. 6 qts. of wheat on one field; 197 bush. 1 pk. 7 qts. on another field: he sells to one person 97 bush. 3 pks. 7 qts.; and to another person 112 bush. 2 pks. 6 qts. How many bushels has he remaining? 14. A gentleman owned three tracts of land: the first of which contained 127 acres, 3 R. 15 rods; the second, 496 A. 1 R. 25 rods; the third, 525 A. 0 R. 35 rods; how much remained after he sold 1008 A. 2 R. 25 rods? 15. Suppose a note given Sept. 10, 1796, to be paid March 5, 1808. How long was the note on interest, if we count 30 days to the month? How long if the time is accurately computed? MULTIPLICATION OF DENOMINATE NUMBERS. ART. 71. MULTIPLICATION of denominate numbers is taking a quantity of different denominations as many times as there are units in another number. Multiply £5 12s. 6d. by 5. OPERATION. £ s. d. 5 12 6 5 EXPLANATION.—The numbers being properly written down, we begin at the right to multiply. 5 times 6d. are 30d., in 30d. how many shillings? There are 12d. in 1s., therefore, one-twelfth of the number of pence equals the number of shillings. 12 is contained in 30, 2 times, and 6d. remaining;—write the 6d. under pence, and reserve the 2s. 5 times 12s. are 60s., and 2s. added, are 62s., which equals £3 2s. ;write the 2s. under shillings, and reserve the £3. 5 times £5 are £25, and £3 added are £28. Hence, &c. 28 26 11. How much cloth will it take for 9 suits of clothes, if each suit require 8 yds. 2 qrs. 2 nas. ? 12. How long will it take a man to chop 14 cords of wood, if it take him 7 hours, 40 minutes, and 50 seconds to chop 1 cord ? 13. What is the weight of 12 hogsheads of sugar, each weighing 8 cwt. 3 qrs. 23 lb. ? 14. If a span of horses, at 1 load, can draw 1 cord 212 cubic feet of wood, how many cords can they draw in 14 loads? 15. If a family of 6 persons, consume 10 gallons, 3 quarts, and 1 pint of molasses in 1 week; what quantity will a family of double the number of persons consume in 1 year ? |