sums of money, in the preceding question, we deduce the following rule.

RULE. Write down the given sums or quantities, placing numbers of the same denomination under one another, in separate columns.

Add the numbers of the lowest denomination, and change the amount to the next higher denomination, by dividing it by so many of the same denomination as are equal to a unit of the next higher; write the remainder under the column, and add the quotient with the numbers of the next higher denomination.

Add the numbers of each succeeding higher denomination in the same manner, and write down the whole amount of the highest denomination.

30. What is the amount of £47. 14s. 71d.; £52. 5s. 41d. ; £60. Os. 11d.; £39. 19s. 1d.; and £40. 4s. 61d.? Ans. £240. 4s. 61d.

31. A man's real estate is worth £4750. 14s. 6d.; his personal property amounts to £2600. 13s. 4d.; and he has debts due him amounting to £500. 15s. 10d. What is the whole amount of his property? Ans. £7852. 3s. 8d.

32. A gentleman's farm is valued at £2958. 16s. 10d.; he has a ship which is worth £2309. 6s. 8d.; he has notes amounting to £812. 8s. 91d.; and he has cash to the amount of £408. 12s. 13d. What is the whole amount of his property? Ans. £6489. 4s. 51d.

33. Purchased a silver tea-pot, weighing 23 oz. 17 pwts. 11 grs.; a sugar-bowl, weighing 8 oz. 13 pwts. 19 grs.; a cream-pitcher, weighing 5 oz. 11 grs.; six cups, weighing 18 oz. 18 grs.; twelve table-spoons, weighing 27 oz. 9 pwts.; and twelve tea-spoons, weighing 9 oz. 15 pwts. 14 grs. What was the weight of the whole ?

Ans. 92 oz. 17 pwts. 1 gr.

34. Purchased 4 hogsheads of sugar, weighing as follows: No. 1, 12 cwt. 3 qrs. 17 lbs.; No. 2, 12 cwt. 1 qr. 14 lbs.; No. 3, 11 cwt. 2. qrs. 21 lbs.; No. 4, 10 cwt. 3 qrs. 24 lbs. What was the whole weight of the 4 hogsheads?

Ans. 47 cwt. 3 qrs. 20 lbs. 35. Bought 4 pieces of cloth; No. 1 measured 38 yds. 2 3 na.; No. 2, 37 yds. 3 qrs. 2 na.; No. 3, 36 yds. 1 qr. 2 na.; No. 4, 35 yds. 3 qrs. 3 na. What was the whole number of yards purchased? Ans. 148 yds. 3 qrs. 2 na.

qrs.

chased?

36. A lady purchased 32 yds. 3 qrs. of sheeting; 31 yds. 1 qr. of shirting; 14 yds. 2 qrs. of linen; and 6 yds. 2 qrs. of cambric. What was the total number of yards purAns. 85 yards. 37. An ironmonger sold 94 tons 15 cwt. 3 qrs. of iron to one man; 75 tons 12 cwt. 2 qrs. to another; 64 tons 10 cwt. 2 qrs. 7 lbs. to another; and 45 tons 1 qr. 21 lbs. to another. What number of tons did he sell?

Ans. 279 t. 19 cwt. 1 qr. 38. What is the sum of 145 m. 3 fur. 25 rds.; 96 m. 4 fur. 15 rds.; 88 m. 5 fur. 30 rds.; 54 m. 2 fur. 10 rds.; and 106 miles? Ans. 491 miles. 39. A man has 4 farms; the first contains 420 a. 2 r. 25 rds.; the second, 375 a. 1 r. 15 rds.; the third, 280 a. 3 r. 35 rds.; and the fourth, 123 a. 0 r. 5 rds. What is the whole number of acres in the 4 farms? Ans. 1200 acres.

40. Purchased 4 sticks of timber; No. 1 contained 37 ft. 432 in.; No. 2, 35 ft. 864 in.; No. 3, 33 ft. 1296 in.; No. 4, 32 ft. 864 in. What was the whole number of feet purchased? Ans. 139 cubic feet.

41. Sold 4 hogsheads of molasses; the first contained 108 gals. 2 qts.; the second, 110 gals. 3 qts.; the third, 112 gals. 1 qt.; and the fourth, 118 gals. 2 qts. What was the whole quantity sold? Ans. 450 gallons.

42. Purchased 74 hhds. 37 gals. 2 qts. of beer at one time; 45 hhds. 41 gals. 3 qts. at another; 34 hhds. 15 gals. 1 qt. at a third; and 17 hhds. 15 gals. at a fourth. What was the whole quantity purchased?

Ans. 172 hhds. 1 gal. 2 qts. 43. A farmer raised 200 bu. 2 pks. of wheat; 175 bu. 3 pks. of rye; 320 bu. 1 pk. of corn; and 225 bu. 2 pks. of oats. What was the whole quantity of grain raised? Ans. 922 bushels.

44. From the first discovery of America by Columbus to the settlement of Plymouth, in Massachusetts, was 128 yrs. 1 mo. 30 da.; from the settlement of Plymouth to the declaration of independence, 155 yrs. 6 m. 13 da.; from the declaration of independence to July 4th, 1847, 71 yrs. How long was it from the discovery of America to July 4th, 1847? Ans. 354 yrs. 8 mo. 12 da.

45. What is the breadth of the torrid zone, which extends from the tropic of Cancer, in 23° 28′ north latitude, to the tropic of Capricorn, in 23° 28′ south latitude?

Ans. 46° 56'.

SUBTRACTION OF COMPOUND NUMBERS.

Art. 61. SUBTRACTION OF COMPOUND NUMBERS is the method of finding the difference between any two sums or quantities, each of which is composed of several denomina

tions.

The subtraction of compound numbers is performed in the same manner as the subtraction of simple numbers, with the exception of the number which it is necessary to add to the upper number of any denomination, whenever the lower number exceeds the upper.

2. Mary has 15s. 6d.; Jane has 12s. 8d. How much more money has Mary than Jane?

4. Subtract 4 lbs. 5 oz. 10 pwts. from 10 lbs.

6. Subtract 29, 15 grs. from 5 3, 10 grs.

8. Subtract 17 cwt. 3 qrs. from 5 tons.

10. Subtract 18 yds. 3 qrs. from 36 yds. 1 qr.

12. Subtract 9 ft. 6 in. from 5 rds.

14. Subtract 74 a. 1 r. 20 rds. from 150 a.

16. Subtract 29 gals. 2 qts. from 2 hhds.

18. Subtract 45 gals. 2 qts. from 5 hhds.

20. Subtract 3 pks. 5 qts. from 5 bu.

22. Subtract 3 w. 5 d. from 6 mo.

24. Subtract 44° 25′ from 90°.

Art. 62. If £41. 15s. 4d. 1qr. be taken from £75. 12s. 6d. 2 qrs., what will be the remainder or difference?

£. s. d. qrs. 75 12 6 2 41 15 4 1

We first write down the greater sum, £75. 12s. 6d. 2qrs.; we then write the less sum, £41. 15s. 4d. 1qr., under the greater, placing those numbers which are of the same denomination under each other. We then begin with the lowest denomination, and take 1 farthing from 2 farthings, the remainder is 1 farthing,

Ans. 33 17 2 1

which we write under the farthings. We then take 4 pence from 6 pence, the remainder is 2 pence, which we write under the pence. As we cannot take 15 shillings from 12 shillings, we add 20 shillings, which are equal to 1 pound, to the 12 shillings, the amount is 32 shillings; we then take the 15 shillings from 32 shillings, the remainder is 17 shillings, which we write under the shillings. We next add 1 pound to 41 pounds, the amount is 42 pounds, which we subtract from 75 pounds, the remainder is 33 pounds, which we write under the pounds. The whole remainder or difference is £33. 17s. 2d. 1qr.

By adding 20s. to the 12s. of the greater sum, and £1 to the £41 of the less sum, we have added the same amount to each; consequently, their difference is not altered. From the above illustration we deduce the following rule for subtraction of compound numbers.

RULE. Write down the greater sum or quantity; then write the less sum or quantity under the greater, placing those numbers which are of the same denomination directly under each other.

Begin with the lowest denomination, and take the lower number of each denomination, in succession, from the upper, and write each remainder under its respective denomination.

Whenever the lower number of any denomination is greater than the upper, add so many units of the same denomination to the upper number as are equal to a unit of the next higher, subtract the lower number from the amount, write the remainder underneath, then add a unit to the lower number of the next higher denomination before it is subtracted.

25. A man borrowed £50. 10s. 6d., and has paid £25. 18s. 9d.; how much remains unpaid? Ans. £24. 11s. 9d. 26. A merchant sold goods to the amount of £136. 15s. 6d. 2qrs., and has received in payment £50. 18s. 9d. 3qrs.; how much remains due? Ans. £85. 16s. 8d. 3qrs. 27. A man purchased a farm for £1250; he has paid at one time £750. 10s., at another, £250. 15s. How much remains unpaid? Ans. £248. 15s. 28. From 46 lbs. 2 oz. 3 pwts. 8 grs. take 19 lbs. 8 oz. 15 pwts. 12 grs. Ans. 26 lbs. 5 oz. 7 pwts. 20 grs.

29. From 15 lbs. 5 3,3 3,1 9, 13 grs. take 10 lbs. 11 3, 6 3, 2, 18 grs. Ans. 4 lbs. 53, 4 3, 1 9, 15 grs.

30. Bought a hogshead of sugar weighing 12 cwt. 1 qr. 14 lbs., and sold 7 cwt. 2 qrs. of it; what quantity remains unsold? Ans. 4 cwt. 3 qrs. 14 lbs.

31. A merchant purchased 151 yds. 2 qrs. of broadcloth, and has sold 53 yds. 3 qrs. of it; how many yards has he remaining unsold? Ans. 97 yds. 3 qrs.

32. The distance from Boston to Albany by railroad is 200 miles, from Boston to Worcester it is 44 miles; what is the distance from Worcester to Albany? Ans. 156 miles. 33. A man, who owned a farm containing 325 a. 2 roods, gave his son 150 a. 1 r. 25 rds.; how many acres had he remaining? Ans. 175 a. 0 r. 15 rds.

34. A man purchased 275 cords of wood, and has sold 115 cords and 64 cubic feet of it; what quantity remains unsold? Ans. 159 cords, 64 feet. 35. From a pipe of wine containing 126 gallons, 31 gal. 2 qts. 1 pt. have leaked out; how much remains in the pipe? Ans. 94 gals. 1 qt. 1 pt. 36. A merchant purchased 1500 bushels of Indian corn, and has sold 750 bu. 3 pks. of it; what number of bushels has he left? Ans. 749 bu. 1 pk. 37. William is 15 yrs. 9 mo. and 15 d. old, Henry is 12 yrs. 10 mo. and 25 d. old; what is the difference of their ages ? Ans. 2 yrs. 10 mo. 20 days.

When time is expressed in years, calendar months, and days, the difference of time between any two dates may be found by subtracting the former date from the latter, observing to number the months in their order.

38. A gave B his note, dated August 21st, 1844; the note was paid May 4th, 1845. How long was the note on interest?

yrs. mo. d. Latter date, 1845 4 4 Former date, 1844 7 21

8 14 Ans.

39. The United States declared war against Great Britain, June 18th, 1812, a treaty of peace was signed December 24th, 1814; how long did the war continue? Ans. 2 yrs. 6 mo. 6 days. 40. The latitude of London is 51° 32′ north, the latitude of Boston is 42° 23′ north; what is the difference of latitude between the two places? Ans. 9° 9'.

41. The longitude of Washington is 77° 43′ west from Greenwich, the longitude of Boston is 71° 3′ west; what is the difference of longitude between the two cities?

Ans. 6° 40'.