EXERCISES IN COMPOUND ADDITION AND SUBTRACTION.

1. What is the sum of 16£. 5s. 8d. 2qr.-31£. 16s. 11d. 3qr.—21£. 11s. 1qr.—19£. Os. 10d. Sqr.—13£. 13s. 7d. Sqr. and 28£. 17s. 5d. Îqr.? Ans. 131£. 5s. 81d.

2. Bought of a London tailor a vest for 1£. 13s. 4d., a coat for 7. 12s. 9d., pantaloons for 2£. 3s. 9d., and surtout for 9£. 8s. Od.; what was the whole amount ?

Ans. 20£. 17s. 10d.

3. Bought a silver tankard, weighing 1lb. 8oz. 17dwt. 14gr., a silver can, weighing 1lb. 2oz. 12dwt., a porringer, weighing 11oz. 19dwt. 20gr. and three dozen of spoons, weighing 1lb. 9oz. 15dwt. 10gr.; what was the whole weight?

Ans. 5lb. 9oz. 4dwt. 20gr. 4. What is the weight of a mixture of 3lb. 43. 23. 29. 14gr. of aloe, 2lb. 73. 63. 19. 13gr. of picra, and 1lb. 103. 13. 29. 17gr. of saffron ? Ans. 7b. 103. 33. 19. 4gr. 5. Add 32b. 93. 13. 29. 14gr.; 13b. 73. 63. 19. 13gr.; and 16b. 113. 73. 19. 12 gr. together.

Ans. 63lb. 43. 73. 29. 19gr. 6. Sold 4 loads of hay; the first weighed 27cwt. 3qr. 18lb. ; second 31cwt. 1qr. 15lb.; third 19cwt. 1qr. 15lb.; and fourth 38cwt. 2qr. 27lb.; what is the weight of the whole ?

Ans. 117cwt. 1qr. 19lb.

7. Bought 5 pieces of broadcloth; the first contained 17yd. 3qr. 2na.; second, 13yd. 2qr. 1na.; the third 87yd. 1qr. Sna. ; the fourth 27yd. 1qr. 2na.; and the fifth 29yd. 1qr. 2na. ; what was the whole quantity purchased? Ans. 175yd. 2qr. 2na.

8. A pedestrian travelled, the first week, 371m. 3fur. 37rds. 5yd. 2ft. 10in.; the second week, 289m. 2fur. 18rds. 3yds. 1ft. 9in. ; and the third week he travelled 399m. 7 fur. 3ft. 11in. ; how many miles will he have travelled?

Ans. 1060m. 5fur. 16rds. 5yds. 1ft. 9. A man has 3 farms; the first contains 186A. 3R. 14p.; the second 286A. 17p.; and the third, 115A. 2R.; how much do they all contain? Ans. 588A. 1R. 31p.

10. The Moon is 5s. 18°. 14. 17". east of the Sun; Jupiter is 7s. 10°. 29. 28". east of the Moon; Mars is 11s. 12°. 11'. 56′′. east of Jupiter; and Herschell is 7s. 18°. 38'. 15". east of Mars; how far is Herschell from the Sun ? Ans. 7s. 29o. 33'. 56′′.

11. I have 4 piles of wood; the first contains 7 cords, 76ft. 1671in. ; the second 16c. 28ft. 56in.; the third 29c. 127ft. 1000in.; and the fourth 29c. 10ft. 1216in.; how much is there in all ? Ans. 82c. 115ft. 487in.

12. A vintner sold at one time 73hhd. 43gal. Sqt. 1pt. of wine; at another, 27hhd. 3gal.; at another, 15hhd. 3qts. 1pt.; and, at another, 161hhd. and 2qts. ; how much did he sell in all ? Ans. 276hhd. 48gal. 1qt.

13. A man has 3 sons; the first is 14y. 3m. 2w. 5d. old; the second is 9y. 10mo. 3w. 4d. 23h. 12m. 15sec.; and the third is 2y. 1mo. 3w. 2d. 7m. ; what is the sum of their ages? And how much older is the first than the second?

Ans. 26y. Smo. 1w. 4d. 23h. 19m. 15sec. 66 4y. 5mo. 3w. Od. Oh. 47m. 45sec.

4. I have 73A. of land; if I should sell 5A. 3R. 1p. 7ft., how much should I have left? Ans. 67A. OR. 38p. 2654ft. 15. A. owes B. £ 100; what will remain due after he has paid him 3s. 64d.? Ans. £99, 16s. 5d. 16. It is about 25000 miles round the globe; if a man shall have travelled 43m. 17rds. 9in. how much will remain to be travelled? Ans. 24956m. 7fur. 22rds. 15ft. 9in. 17. Bought 7 cords of wood; and 2 cords 78ft. having been stolen, how much remained? Ans. 4c. 50ft. 18. I have 15 yards of cloth; having sold Syds. 2qr. 1na., what remains? Ans. 11yds. 1qr. 3na. 19. If a wagon loaded with hay weighs 43cwt. 2qr. 18lbs., and the wagon is afterwards found to weigh 9cwt. 3qr. 23lbs., what is the weight of the hay? Ans. 33cwt. 2qr. 23lbs. 20. Bought a hogshead of wine, and by an accident 8gal. Sqts. 1pt. leaked out; what remains? Ans. 54gal. 1pt. 21. Í have 10A. 3R. 10p. of land; I have sold two house lots, one containing 1A. 2R. 13p., the other, 2A. 2R. 5p.; how much have I remaining? Ans. 6A. 2R. 32p.

22. The Moon moves 13°. 10. 35". in a solar day, and the Sun 59. 8". 20".; now supposing them both to start from the same point in the heavens, how far will the Moon have gained on the Sun in 24 hours? Ans. 12°. 11. 26". 40"".

23. A farmer raised 136bush. of wheat; if he sells 49bu. 2pk 7qt. 1pt., how much has he remaining? Ans. 86bu. 1pk. Oqt. 1pt. 24. If from a stick of round timber, containing 2T. 18ft. 1410in., there be taken 38ft. 1720in., how much will be left? Ans. 1T. 19ft. 1418in. 25. If from 1b. of ipecacuanna there be taken at one time 43. 23. 13gr. and at another, 33. 13. 29. 14gr., how much will be left? Ans. 43. 33. 29. 13gr. 26. A brewer has in one cellar 18bbls. 3gal. 2qt. of beer, and in another, 13bbls. 1p.; what is the whole quantity, and how much more is in one cellar than the other?

Ans. 31bbls. 3gal. 2qt. 1pt. 5bbls. 3gal. 1qt. 1pt.

27. If from $100.00 there be paid at one time $17.28.5, at another time, $10.00.5, and at another

nain?

$37.15, how much will Ans. $35.56.

SECTION VII.

MENTAL OPERATIONS IN REDUCTION.

In 60 ?

70 ?

In 6 ?

In 4? In 5?
In 15? In 20 ?

In 60?
In 95? In 130?

In 80 ? In

In 5s. 9d.?

In 500? In 1000 ?
In 4s. 2d.? In
In 6s. 3d.? In
In 9s. 10d. ?
In 4? In
In 11 ?

1. In 8 farthings how many pence? In 12? In 16? In 20? In 24? In 36 ? In 40? In 48? In 60? In 30? In 80 ? 2. How many farthings in 2 pence? In 3? In 4? In 6? In 8? In 9? In 12? In 14? In 15? In 16? In 18? 3. In 3 shillings how many pence? In 4? In 5? In 6? In 8? In 9? In 10? In 11? In 12? In 15? In 17? In 20 ? 4. In 24 pence how many shillings? In 36? In 48 ? In 72? In 84? In 30? In 40? In 50? In 60? In 5. In 2 pounds how many shillings? In 8? In 10? In 20? In 12? In 14? 6. In 40 shillings how many pounds? 120? In 160? In 200? In 70? In 90? 135? In 150? In 155? In 170? In 199? 7. In 3s. 6d. how many pence? In 3s. 2d.? 4s. 6d. ? In 4s. 9d.? In 5s. 7d.? 6s. 7d.? In 6s. 11d.? In 7s. 6d. ? In 8s. 3d.? 8. In 2 pence how many farthings? In 34? 5? In 6? In 7? In 9? In 10? In 114? 9. In 2£. 3s. how many shillings? In 2£. 6s.? In 5£. 8s.? In 6£. 8s.? In 10€. 12s.? In 7£. 8s. ? 10. In 2lbs. how many ounces? In 3lbs.? In 4lbs.? In 6? In 8? In 10? In 12? In 15? In 20? In 24 ? In 25 ? 11. In 32 ounces how many pounds? In 64? In 80? In 90 ? 12. In 3cwt. how many quarters? In 5? In 7? In 8? In 10? In 12? In 15? In 16? In 20? In 24? In 25? In 30? 13. In 13 quarters how many cwt.? In 16? In 20? In 32? In 36 In 60? In 66? In 68? In 70? In 72 ? In 80 ? 14. In 5 tons how many cwt.? In 6? In 7? In 9? In 12? In 15? In 24? In 26? In 28? In 30? In 32 ? In 36 ? 15. In 40cwt. how many tons? In 60? In 120? In 160?

In 5£. 5s.?

In 10?

In 72 ? In 120 ? In 10 ? 40 ?

In 200? In 220? In 230? In 240? In 250? In 260 ? 16. In 57cwt. how many tons? In 69? In 75 ? In 82? In 105? In 115? In 125? In 180? In 185? In 140 ? 17. In 5lbs troy how many ounces? In 6? In 8? In 12? In 15? In 20? In 24? In 25? In 28? In 30? 18. In 36 ounces how many pounds troy? In 60? In 84? In 90 ? In 95? In 98? In 100? In 110? 19. In 7 ounces how many pennyweights? In 8? In 12? In 14? In 16? In 28? In 30 In 35? In 20. In 40 grains how many pennyweights? In 70? In 90? In 120? In 130? In 140? In 150? 21. In 7 scruples how many grains? In 8? 22. In 40 grains how many scruples? In 50? In 80? In 100? In 110? In 120. In 180? In 140?

In 50?

In 60 ? In 160 ?

In 9? In 10? In 60? In 70 ?

23. In 2 yards how many quarters? In 3? In 5? In 10? In 12? In 15? In 16? In 20? In 24? In 26? In 30?

24. In 3 ells English how many quarters? In 7? In 12? 25. In 12 quarters how many yards? In 16? In 19? In 24? In 30? In 36? In 38? In 40? In 41? In 47?

26. In 6 quarters how many nails? In 6? In 7? In 8? In 12? In 14? In 16? In 20? In 22? In 30?

27. In 24 nails how many quarters? In 30? In 36? In 40 ? In 46? In 50? In 70? In 100? In 150? In 160? 28. In 100 pence how many shillings? In 144? In 160? 29. In 140 shillings how many pounds? In 150? In 160? 30. In 96 ounces how many lbs.? In 100? In 200? In 300? 31. In 56lbs. how many quarters? In 84? In 112? In 200? 32. In 8 quarters how many cwt.? In 12? In 16? In 28 ? In 44? In 48? In 50? In 60? In 66? In 70? In 80? 33. In 40cwt. how many tons? In 80? In 100? In 120 ? In 180? In 200? In 800? In 850? In 866? In 1000? 34. In 48qrs. how many dwt.? In 72? In 96? In 144? 35. In 9 scruples how many drams? In 12? In 18? 36. In 48 ounces, troy, how many lbs.? 87. In 12 quarters how many lbs.? In 16? In 48? In 56? In 60? In 100? In 120? In 130? 38. In 25 quarters how many ells English? In 70? In 100? In 110? In 120?

In 96?

In 144?

In 28?

In 40?

In 150 ?

In 30?

In 60 ?

In 125?

In 150?

In 48?

In 60?

In 144?

In 140?

In 150 ?

In 24?

In 30 ?

39. In 36 inches how many feet? In 180? In 190? In 100? In 120? In 130? 40. In 12 feet how many yards? In 15? In 48? In 60? In 66? In 90? In 100? In 120? In 140? 41. In 80 rods how many furlongs? In 120? In 720? 42. In 24 furlongs how many miles? In 32? In 48? In 72 ? In 80? In 90? In 96? In 100? In 200? In 300? In 400 ? 43. In 3 weeks how many days? In 4? In 5? In 6? In 7? In 8? In 9? In 12? In 14? In 20? In 25? In 30? In 50? 44. In 5 years how many months? In 3? In 4? In 8? In 9? In 10? In 12? In 24? In 30? In 32? In 36? 45. In 2 quarts how many pints? In 4? 10? In 20? In 50? In 60? In 190? 46. In 5 years how many months? In 3? 9? In 10? In 12? In 24? In 26? In 28? In 30? 47. In 2 quarts how many pints? In 4? In 6? 10?

In 6?

In 40? In 8? In In 150?

In 4?

In 8? In

In 120?

In 32?

In 8? In

In 20? In 50? In 60? In 70? In 75? In 80? In 90?

48. In 3 gallons how many quarts? In 4? In 5? In 6? In 8? In 9? In 10? In 20? In 40? In 50? In 100? In 200? 49. In 2 hogsheads how many gallons? In 3? In 4? In 5? In 6? In 7? In 8? In 10? In 12? In 14? In 20? In 24? 50. In 3 pipes how many hogsheads? In 10? In 12? In 20? In 24? In 26? 51. In 2 tuns how many hogsheads? In 5? In 9? In 10? In 12? In 14? In 16? In 20?

In 50 ?

In 60 ?

In 20?

In 80 ?

In 10?

In 20? In

In 150?

In 160?

In 50 ?

In 10?
In 3?

In 20?

In 4? In 5?

In 10?

In 4?

52. In 2 bushels how many pecks? In 3? In 5? In 6: In 8. In 10? In 15? In 20? In 60 ? In 70 ? In 80 ? 53. In 3 pecks how many quarts? In 4? In 5? In 10? In 12? In 15? In 20? In 25? In 30? In 40? In 50? In 60 ? 54. In 2 feet how many square inches? In 4? In 5? In 10? In 20? In 50? In 60? In 70? In 80? In 90? In 100? 55. In 3 square yards how many feet? In 4? In 6? In 7 ? In 8? In 10? In 20? In 30? In 40? 56. In 5 roods how many rods? In 10? 57. In 2 acres how many roods? In 5? 80? In 40? In 50? In 100? In 120? 58. In 3 acres how many rods? In 5? 59. In 5 minutes how many seconds? 60. In 2 hours how many minutes? In 8? In 12? In 15? In 20? In 30? In 35? In 40? 61. In 3 days how many hours? In 5 ? In 6? In 8? In 10? In 15? In 20? In 25? In 50? In 100? In 120 ? 62. In 2 cents how many mills? In 3? 8? In 9? In 12? In 16? In 18? In 25? In 35? 63. In 20 mills how many cents? In 30? In 40? In 70? In 80? In 90? In 100? In 120? In 150? In 160 ? 64. In 3 dimes how many cents? In 5? In 7? In 9 ? 65. In 30 cents how many dimes? In 80? In 100? In 200? 66. In 2 dollars how many cents? In 5? In 6? In 7? In 10? In 20? In 30? In 50? In 100? In 120? In 130? 67. In 300 cents how many dollars? In 400? In 500? In 600? In 800? In 900? In 1000? In 10000? In 100000 ? 68. In 5 eagles how many dollars? In 6? In 10? In 20? In 25? In 35? In 75? In 100? In 120? In 200? In 300 ? 69. In 20 dollars how many eagles? In 30? In 50? In 100? In 200? In 1000? In 1500? In 100000? 70. In 4 yards how many nails? In 8? In 10? In 12? 71. In 2 Ells English how many yards? In 3? In 4? In 5? 72. What is the difference between 3 square feet, and 3 feet square?

In

6? In In 45?

In 60 ?

In 70?

73. How many inches round one foot square? 2 feet? 3 feet?

The student will now perceive that the object of

REDUCTION is to change numbers of one denomination to another without losing their value.

It consists of two parts, Descending and Ascending. The former is performed by Multiplication, the latter by Division.

Reduction Descending teaches to bring numbers of a higher denomination to a lower; as, to bring pounds into shillings, or tons into hundred weights.

Reduction Ascending teaches to bring numbers of a lower denomination into a higher; as, to bring farthings into pence, or shillings into pounds.