16. 350 tons at 70s. per ton. [£350× £34=£1225.] Ans. £1225. 17. 400 tons at 85s. per ton. Ans. £1700.

REDUCTION

TEACHES how to reduce numbers of one denomination into other numbers of another denomination, retaining the same value, and is performed by Multiplication and Division.

FIRST.-All great names are brought into small, by multiplying with so many of the less as make one of the greater.

SECONDLY.-All small names are brought into great, by dividing with so many of the less as make one of the greater.

REDUCTION DESCENDING.

1. In £8, how many shillings and pence?

20

The pounds are multiplied by 20 to reduce them

160 shillings. to shillings, because there are 20 shillings in each pound. The shillings are multiplied by 12, to reduce them to pence, because there are 12 pence in each shilling.

12

1920 pence.

2. In £12, how many shillings, pence, and farthings?

Ans. 240s., 2880d., 11520 far. 3. How many shillings, pence, and farthings are there in £18? Ans. 360s., 4320d., 17280 far. 4. Reduce £7 and 1 crown into shillings and pence.

Ans. 145s., 1740d.

5. How many farthings are there in 21 guineas ?*

Ans. 21168 far. 6. In £17 5s. 34d., how many farthings? Ans. 16573. 7. In £25 14s. 1d., how many shillings and pence?

Ans. 514s., 6169d.

8. In 15 crowns, how many shillings and sixpences? Ans. 75s., 150 sixpences.

9. How many crowns and shillings in £25 ?

Ans. 100 crowns, 500s.

*21s. equal 1 Guinea.

10. In 57 half-crowns, how many pence and farthings? Ans. 1710d., 6840 far.

11. In 52 crowns, as many half-crowns, shillings, and pence, how many farthings? Ans. 21424. 12. How many half-crowns, sixpences, and threepences are there in £75?

Ans. 600 half-crowns, 3000 sixpences, 6000 threepences.

REDUCTION ASCENDING.

13. In 1920 pence, how many shillings and pounds? 12)1920 2|0)16|0 shillings. pence make 1 shilling; then the shillings are

8 pounds.

The pence are divided by 12, because 12 divided by 20, because 20 shillings make one pound.

14. In 11520 farthings,

and pounds?

how many pence, shillings, Ans. 2880d., 240s., £12.

15. How many pence, shillings, and pounds are there in 17280 farthings?

Ans. 4320d., 360s., £18.

16. Reduce 1740 pence into shillings and pounds.

Ans. 145s., £7 58.

17. How many guineas in 21168 farthings? Ans. 21. 18. In 16573 farthings, how many pounds?

Ans. £17 5s. 34d.

19. In 6169 pence, how many shillings and pounds?

Ans. 514s., £25 14s. 1d.

20. In 900 pence, how many shillings and crowns?

Ans. 75s., 15 crowns.

21. How many crowns and pounds in 500 shillings? Ans. 100 crowns, £25.

crowns ?

22. In 6840 farthings, how many pence and halfAns. 1710d., 57 half-crowns. 23. In 21424 farthings, how many crowns, half-crowns, shillings, and pence, and of each an equal number? Ans. 52. 24. How many sixpences, half-crowns, and pounds, in 6000 threepences?

Ans. 3000 sixpences, 600 half-crowns, £75.

ASCENDING AND DESCENDING.

25. In 1560 pence, how many crowns and shillings? Ans. 26 crowns, 130s.

26. Reduce 130 shillings into crowns and pence. Ans. 26 crowns, 1560d. 27. How many shillings, crowns, and pounds, in 60 guineas? Ans. 1260s., 252 crowns, £63. 28. In £63, how many crowns, shillings, and guineas? Ans. 252 crowns, 1260s., 60 guineas.

29. In 96 sovereigns, how many crowns, half-crowns, and shillings? Ans. 384 crowns, 768 half-crowns, 1920s. 30. How many shillings, half-crowns, and crowns, are there in £556, and of each an equal number?

Ans. 1308 each, and 2s. over.

31. In 1308 half-crowns, as many crowns and shillings, how many pounds? Ans. £555 18s. 32. Seven men brought £15 10s. each into the mint, to be changed into guineas; how many must they have in all ? Ans. 103 guineas, 7s. over. 33. If 103 guineas and 7 shillings are to be divided among seven men, how many pounds sterling is that to each ? Ans. £15 10s.

34. A gentleman left £50 to the poor, and ordered that should be given to aged men, each 5s.; to poor women, each 2s. 6d. ; to poor boys, each 1s.; to poor girls, each 9d.; and the remainder to the person who distributed it: how many of each sort were there, and what had the distributor for his pains?

Ans. 66 men, 100 women, 200 boys, 222 girls, and £2 13s. 6d. to the person.

TROY WEIGHT.

35. In 2 lb. 4 oz. 7 dwt. 9 gr., how many grains?

12

28

20

567

24

2277

1134

Ans. 13617 grs.

The multipliers are 12, 20, and 24, because in each pound there are 12 ounces, in each ounce 20 pennyweights, in each pennyweight 24 grains; and the 4 oz. 7 dwt. 9 grs. in the multiplicand are added in.

36. In 12960 grains of gold, how

many

?

ounces
Ans. 27 ozs.

37. In 3 lb. 10 oz. 7 dwt. 5

gr., how many grains? Ans. 22253 grs.

38. In 8 ingots of silver, each weighing 7 lb. 4 oz. 17 dwts. 15 grs.; how many ounces, pennyweights, and grains? Ans. 711 oz. 14221 dwts. 341304 grs. 39. How many ingots of 7 lb. 4 oz. 17 dwts. 15 grs.. each are there in 341304 grains? Ans. 8 ingots.

40. Bought 7 ingots of silver, each containing 23 lb. 5 oz. 7 dwts.; how many grains? Ans. 945336 grs.

41. A gentleman sent a tankard to his goldsmith that weighed 50 oz. 8 dwt. to make into spoons, each to weigh 2 oz. 16 dwt.; how many had he? Ans. 18.

9

42. A gentleman gave to a goldsmith 137 oz. 6 dwt. gr. of silver, to make into tankards of 17 oz. 15 dwt. 6 gr. each; spoons of 21 oz. 11 dwt. 13 gr. per dozen; salts at 3 oz. 10 dwt. each; and forks at 21 oz. 11 dwt. 13 gr. per dozen; every tankard to have one salt, 12 spoons, and 12 forks: what number must each have?

Ans. 2 of each sort: 8 oz. 9 dwt. 17 gr. over. APOTHECARIES' WEIGHT.-See Table, p. 30. 43. In 27 lb. 7 3. 2 3. 19. 2 gr., how many grains?

Ans. 159022 grs.

44. How many b. 3. 3. 9. gr. are there in 159022 Ans. 27 b. 7 3. 2 3. 19. 2 gr.

grains?

AVOIRDUPOISE WEIGHT.-See Table, p. 31.

45. In 8 cwt. 2 qr. 10 lb., how many lbs. ?

1 roll.

4

34

28

282

68

Ans. 962 lbs.

The cwts. multiplied by 4 produce qrs., because 4 qrs. make 1 cwt.; and the qrs. multiplied by 28 produce lbs., because 28 lbs. make 1 qr.

46. Bought 32 bags of hops, each 2 cwt. 1 qr. 14 lb. and another of 150 lb.; how many cwt. in the whole ? Ans. 77 cwt. 1 qr. 10 lb. 47. In 34 tons. 17 cwt. 1 qr. 19 lb., how many pounds? Ans. 78111.

48. In 27 cwt. of raisins, how many parcels of 18 lb. each?

Ans. 168. 49. In 9 cwt. 2 qr. 14 lb. of indigo, how many pounds? Ans. 1078.

50. Bought 27 bags of hops, each 2 cwt. 1 qr. 15 lb., and 1 bag of 137 lb.; how many cwts. in the whole ? Ans. 65 cwt. 2 qr. 10 lb.

51. How many pounds in 27 hogsheads of tobacco, each weighing neat 83 cwt. ? Ans. 26460 lbs. 52. How many parcels of sugar of 16 lb. 2 oz. are there in 16 cwt. 1 qr. 15 lb. ?

Ans. 113 parcels; 12 lb. 14 oz. over.

Cwts. may be readily reduced by this method:-Multiply the cwts. by 12 mentally, adding in the qrs. and lbs. ; put the product below the cwts. two places to the right hand, then add the two lines together. Thus,

The allowance usually made in this weight are TARE, TRET, and

CLOFF.

TARE is an allowance made to the buyer of any commodity for the weight of the box, cask, &c., containing the same.

TRET is an allowance of 4 lb. in every 104 lb., or 1 lb. in 26 lb., on account of waste, dust, &c.

CLOFF is an allowance of 2 lb. on every 3 cwt., or 1 lb. in every 168 lb. to make the weight hold out when retailed.

GROSS WEIGHT is the whole weight of any sort of goods, and that which contains it.

SUTTLE WEIGHT is when part of the allowance is deducted from the gross.

NEAT WEIGHT is the pure weight, all allowances deducted. RULE 1.-When the tare is at so much per bag, barrel, &c., multiply the number of bags, barrels, &c., by the tare, and subtract the product from the gross, the remainder is neat.