11. A man's wages are 45 shillings per week, and his expences average 41s. 94d. How much can he save yearly?

12. According to astronomical calculation, the Earth is ninetyfive millions; and Sirius, the brightest of the stars, thirty-two billions of miles distant from the Sun. Express their distances in figures?

13. Borrowed £600.- and have returned £149. 17s. 21d.— £78. 16s. 93d. - 50 guineas-£48. 9s. 101d. — £86. 3s. 7d. £104. 14s. 8d.—£35. 2s. 14d. What remains due?

14. Multiply fifty-seven millions, three hundred and ninety-two thousand, and seventy-eight, by forty-seven thousand, nine hundred, and six.

15. A silversmith bought 47 lb. 8 oz. of silver: he made 5 lb. 10 oz. 3 dwts. into tea-pots-3 lb. 4 oz. 15 dwts. 17 grs. into table-spoons4 lb. 11 oz. 7 dwts. 19 grs. into tea-spoons-6 lb. 3 oz. 5 dwts. 9 grs. into dish-covers-and 5 lb. 8 oz. 13 dwts. 22 grs. into mugs. What quantity had he remaining?

16. Add together 547218, 13097, 28216, 917380, 28163, 47182, and 573; and from the total subtract nine hundred and seventy thousand, two hundred, and eighty-five.

17. Bought tea at £26. 16s. 8d. per Cwt. What is the price per lb. ?

18. Required the whole value of 12 yards of silk at 15s. 2d.25 yds. of cloth, at 1s. 8d.-15 yds. of satin, at 3s. 7d.-414 yds. of linen, at 2s. 74d.-and 48 yds. of ribbon, at 9 d.

19. Multiply two millions, eight hundred and seven thousand, six hundred, and thirty-nine, by fifty thousand, four hundred, and seventy-two; and divide the product by twelve thousand, six hundred, and eighteen.

20. What is the weight of 43 hogsheads of sugar, each 3 cwt. 2 qr. 17 lb.?

21. Divide five billions, seven hundred and eight thousand, and four millions, two hundred and eighty-six thousand, and seventy-one, by seven hundred and forty-nine thousand, and sixty-three.

22. Multiply eighty-seven millions, two hundred and ninety-six thousand, four hundred and five, by five hundred and eighty-four thousand, and ninety-seven.

REDUCTION

Teaches to change numbers of one name into others of another name, without altering their value.

RULE I.-Great names are brought into small, by multiplying by as many of the small as make one of the great.

RULE 2.-Small names are brought into great, by dividing by as many of the small as make one of the great.

Example.

£ S. d. 3246 18 7 20

Reduce £3246. 18s. 7d. into shillings and pence.

64938 shillings.*

12

779263 pence.*

Example.

lb. oz. dwts. grs.
17 5 13 17
12

209 ozs.

20

4193 dwts.* 24

16789

8386

100649 grains.*

To reduce pounds into shillings and pence, is to change great names (pounds) into small (shillings and pence).

By Rule 1. Multiply the pounds by 20, because 20 shillings=1 pound, taking in 18 shillings. Next, multiply the shillings by 12, because 12 pence=1 shilling, taking in 7 pence.

Answer, 64938 shillings, and 779263 pence.

In 17 lb. 5 oz. 13 dwts. 17 grs. of silver, how many grains?

To reduce pounds into grains, is to bring great names (lb.) into small (grs.)

Multiply by 12, because 12 ozs. = 1 lb.; next by 20, because 20 dwts.1 oz.; lastly, by 24, because 24 grs.1 dwt.

EXERCISES.

Answer, 100649 grains.

1. Reduce £62. 13s. 9d. into shillings and pence.

Answer, 1253 sgs. 15045 pence.

2. In £2735 how many crowns and shillings?

Answer, 10940 crowns. 54700 sgs.

3. Reduce 427 guineas into shillings, pence, and farthings. Answer, 8967 sgs. 107604 pence. 430416 farthings

* Always affix the names to the several products.

D

4. In £5027 how many crowns and half-crowns?

Answer, 20108 crowns. 40216 half-crowns.

5. Reduce £265. 17s. 10 d. into farthings.

Answer, 255257 farthings.

6. In £372. 18s. 6d. how many sixpences?*

Answer, 14917 sixpences.

Example. In 12214 farthings how many pence, shillings, and pounds?

To reduce farthings into pence, shillings, and pounds, is to change small names (farthings) into great (pence, shillings, and pounds).

By Rule 2. Divide by 4, because 4 farthings =1 penny. Divide the pence by 12, because 12 pence 1 shilling. Divide the shillings by 20, because 20 shillings=1 pound.

pence, 254 shillings 54d., and £12. 14s. 5 d.

Reduce 12843499 drams into tons.

8) 802718+2=11 drs.

2) 100339+6

7)50169+1=14 ozs.

28

4)7167

4) 1791+3=21 lb.

20) 44.7+3 qrs.

Tons. 22. 7 cwt. 3 qrs. 21 lb. 14oz. 11 drs.

To reduce drams into tons, is to change small names (drams) into great (tons).

Divide by 16, because 16 drs.=1 oz. Again, by 16, because 16 oz.=1 lb. Next, by 28, because 28 lb. 1 qr. Next, by 4, because 4 qrs. 1 cwt. Lastly, by 20, because 20 cwt. 1 ton.

Answer, 22 tons. 7 cwt. 3 qrs. 21 lb. 14 ozs. 11 drs.

EXERCISES.

7. In 71854 pence how many shillings and pounds?

Answer, 5987 sgs.+10d.

£299. 7s. 10d. 8. Reduce 207563 farthings into pence, shillings, and pounds. Answer, 51890 pence, 4324 sgs. 2 d. £216. 4s. 2 d. 9. Reduce 29560 sixpences into half-crowns and pounds.

Answer, 5912 half-crowns, 739 pounds.

* Multiply by the number of sixpences in a pound.

10. In 25643 twopences how many shillings and pounds?

Answer, 4273 sgs. 10d. £213. 13s. 10d.

11. Reduce 38716 half-crowns into crowns and pounds.

Answer, 19358 crowns. £4839. 10s.

12. In 283526 farthings how many pounds?

Answer, £295. 6s. 91⁄2d.

Examples, combining Rule 1st and Rule 2d. Reduce 5178 guineas into shillings and pounds.

Guineas.
5178
21*

2,0)10873,8 shillings.

£5436,18

To reduce guineas into shillings, is to change great names into small. By Rule 1st, multiply by 21, because 21 shillings= 1 guinea. Again, to reduce shillings into pounds, is to change small names into great. By Rule 2d, divide by 20, because 20 shillings = 1 pound.

Answer, 108738 sgs. and £5436. 18s.

In £8205. 14s. how many pieces, each £3. 12s.?

13. Reduce £8701. 15s. into shillings and guineas.

Answer, 174035 shillings, 8287 guineas, 8s. 14. In 7254 moidores, each 27 shillings, how many shillings and pounds? Answer, 195858 shillings. £9792. 18s. 15. Reduce 1874 pieces, each 5s. 6d., into sixpences and pounds.

Answer, 20614 sixpences. £515. 7s.

16. In 21587 guineas how many shillings and moidores ?

Answer, 453327 shillings. 16789 moid. 24 sgs.

17. In £6285. 15s. how many sixpences, and pieces each 4s. 6d. ? Answer, 251430 sixpences. 27936 pieces, 3s.

18. How many pounds are in 25070 dollars, each 4s. 2d.?

Answer, £5222. 18s. 4d.

Multiplied in one line, as taught in the Contractions of Simple Multipli

EXERCISES IN MONEY, WEIGHTS, AND MEASURES. 19. Reduce 8739 half-guineas into pence and farthings. Answer, 1101114 pence, 4404456 farthings. 20. In £213. 14s. how many ducats, each 4s. 9d.?

Answer, 899 ducats, 3s. 9d.

21. Reduce 59 lb. 9 oz. 13 dwts. of silver into grains.

Answer, 344472 grains.

22. In 37 cwt. 2 qrs. 17 lb. how many pounds?

Answer, 4217 pounds.

23. In 26173 crowns how many shillings and guineas?

Answer, 130865 shillings. 6231 guineas, 14s.

24. Reduce 20571500 drams into tons.

Answer, 35 tons. 17 Cwt. 1 qr. 25 lb. 6 oz. 12 drs. 25. Reduce 37 miles. 3 fur. 28 poles. 2 yds. 2 ft. 9 in. into inches.

Answer, 2373729. 26. In 17 pieces of Cloth, each containing 24 Flemish ells, how many yards? Answer, 306 yards. 27. In 26 Cwt. 2 qr. 17 lb. of Tobacco, how many parcels, each 15 lb. ? Answer, 199 parcels.

28. How many spoons can be made, each to weigh 3 ounces, from 215 lb. 8 oz. of Silver? Answer, 739 spoons, 1 oz.

29. In 75 hogsheads of Wine how many gallons and pints? Answer, 4725 gallons, 37800 pints. 30. From the 7th of May, 1843, to the 19th February, 1844, both days inclusive, how many days? Answer, 289 days. 31. Reduce 41729 farthings into pence and dollars, each 4s. 5d. Answer, 104324 pence. 196 dollars, 3s. 8d.

32. Reduce 97 yards, 3 qrs. into ells English.

Answer. 78 ells, 1 qr. 33. How many seconds are in a solar year, or 365 days, 5 hours. Answer, 31556935 seconds.

48 min. 55 sec.? 34. Reduce £4079 into shillings, and pieces each £3. 12s. Answer, 81580 sgs. 1133 pieces. 4s. 35. In 13 hogsheads of Sugar, each 18 Cwt. 2 qrs. 17 lb., how many pounds? Answer, 27157 lb. 36. If a person step at an average 23 feet, how many steps will he take in walking 15 miles? Answer, 31680 steps.

37. In 17 hogsheads of Tobacco, each weighing 15 Cwt. 2 qrs. 14 lb. how many parcels, each 171⁄2 lb. ?

38. How many hours have elapsed since the birth of Christ to the present day inclusive, allowing the year to consist of 365 days?

39. Bought 23 pockets of Hops, each weighing 1 Cwt. 2 qr. 17 lb., how many pounds?

40. Required the number of days and hours from the 17th of October, 1831, to the 8th of April, 1844, both days exclusive.