Operation.

£6 78. 8d. 2qrs.

20

127

12

1532

4

It is plain, that if in one pound there are 20s., in 6 pounds there are 6 times as many, or 120s. ; and in £6 7s. there are 127s. Again, if in one shilling there are 12d., in 127s. there are 127 times 12, which, with the 8d. added, equals 1532d. Lastly, it is evident that, if in 1 penny there are 4 farthings, in 1532d. there are 4 times the number of farthings, or 6130, the 2qrs. in the given question being added. Hence it appears, that in any given number of pounds there are 20 times as many shillings as pounds, 12 times as many pence as shillings, and 4 times as many farthings as pence. This process is called Reduction Descending, because higher denominations are brought into lower.

6130qrs. Ans.

2. In 6130 farthings, how many pounds? Operation. 4)6130

12)1532 2qrs. 2/0)12/7 8d.

It will be seen that this question is the reverse of the former; and as 4 farthings are equal to 1 penny, so the number of pence in 6130qrs. will equal the number of times it contains 4, or 1532d. and 2qrs.

£6 7s. 8d. 2qrs. Ans. over. Again, as 12d. are equal to 1 shilling, so in 1532d. the number of shillings will equal the number of times it contains 12, or 127s. and 8d. over. Lastly, since 20s. is equal to 1 pound, 127s. must equal 6 pounds and 7s., because 20 is contained in 127s. 6 times, and 7s. over. It is always to be remembered, that the remainder is of the same denomination as the dividend, whatever may be the divisor. This latter process is called Reduction Ascending, because lower denominations are brought into higher. By these examples, it appears that Reduction Ascending and Descending mutually prove each other. From the preceding operations we derive the following Rules:

Art. 118.

Reduction Descending.

RULE.

Multiply the highest denomina

Art. 119.
Reduction Ascending.

RULE.

Divide the denomination given

tion given by that number which by that number which expresses expresses how many it takes of the

how many of that denomination it

next lower to make one of the | takes to make one of the next highhigher, observing to add the next er. Divide farthings by as many lower denomination to the product.|farthings as it takes to make a Multiply pounds by what makes a penny; pence by as many pence pound; shillings by what makes as it takes to make a shilling, and a shilling, and so on, until you so on, until you have reduced it to have reduced it to the denomina- the denomination required. tion sought in the question.

15. In 5 tons, 16 cwt. 3 qrs. 16. Reduce 3350762 drs. to 12 lbs. 14 oz. 10 drs., how many tons.

drams?

17. What will be the cost of 40 tons of lead, at $0.12 per pound?

19. What must I pay for 20 tons, 18 cwt. of hay, at the rate of 5 cts. per pound?

18. Bought lead to the amount of $10752, at $0.12 per pound. What was the weight?

20. How much hay can be bought for $2340.80, at 5 cts. per pound?

Apothecaries' Weight.

21. Reduce 6b 103 73 20 16 grs. to grains.

23. Reduce 21tb 113 33 10 13 grs. to grains.

22. In 39836 grains, how many pounds?

24. In 126453 grains, how many pounds?

QUESTIONS.-3. What is the process called? 4. By what numbers do you divide In question 2? and why? 5. What is this process called? 6. What is the rule for Reduction Ascending? 7. For Reduction Descending?

27. How many barleycorns will reach across the Indian Ocean, it being 45 degrees?

29. A teamster, after travelling 20 miles, met a man who offered him as many 5 cent pieces for his load, as his larger wheel had turned round times since he commenced his journey, the wheel being 20 feet in circumference. How much did he get for his load?

31. How many barleycorns

28. How many degrees in 594475200 barleycorns?

30. If a teamster receive for his load $264.00, being paid 5 cents for each revolution of the larger wagon-wheel, the circumference being 20 feet, how far had he travelled?

32. In 4755801600 barley

will reach round the globe, it corns, how many degrees? being 360 degrees?

Land, or Square Measure.

33. If in a county there are

34. How many square miles

1200 square miles, how many in 122880000 square rods?
square rods are there in this
county?

35. How many square inches in 430 square acres?

36. In 2697235200 square inches, how many square acres?

Solid, or Cubic Measure.

37. How many solid inches in 10 cords of wood?

39. In 40 cords, how many cord feet?

41. How many solid inches in a pile of timber containing 54 tons ?

38. Reduce 2211840 solid inch-. es to cords.

40. In 320 cord feet, how many cords?

42. In 3732480 solid inches of round timber, how many tons ?

61. How many minutes in 10 yrs. 30 da. 18 hrs. 45 m. ?

63. How many seconds from May 1, 1830, to April 12, 1837, inclusive?

65. Alexander the Great as

62. In 5303925 minutes, how many years?

64. In 219326400 seconds, how many years?

66. In 1140807240 minutes,

cended the throne 332 years be- how many years?

fore the Christian era. How

many minutes from that period to

1837 ?

SUPPLEMENT TO REDUCTION OF WHOLE NUMBERS. Art. 120.-1. How many dollars in £480 18s. ?

2. In £332 16s. 8d. how many ninepences?

Ans. $1603.

Ans. 8875 and 5d.

3. How many times will a regular clock strike in 400 years? Ans. 22776000.

4. A man sold four trees standing in the forest, measuring as follows: 6 tons, 5 tons, 4 tons, 3 tons, at 121 cts. per foot. What was their value? Ans. $92.50.

5. A man buys 20 tons of hay, at 45 cts. per cwt. He pays a man 624 cts. a day for himself, and 50 cts. for his team. It takes him 6 days to cart it. How much does the hay cost him? Ans. $186.75. 6. How many plank one foot wide will it take to cover a bridge 60 rods in length, and 2 rods wide, and what will it cost, at 20 cts. per hundred feet ? (990 plank. Ans. {365.34 cost.

7. If a boy be paid for wheeling a bushel of apples over said bridge 1 mill for every revolution of the wheel, which is 5 feet in circumference, how much does he receive?

Ans. 19 cts. 8 m.

cents a Ans. $252.

8. What will 2 tons of molasses amount to, at 6 pint? 9. A Vermonter, being in Boston, 80 miles from home, sold his dog and returned. At 6 o'clock the following night, the dog left his new master, and at 6 o'clock the next morning stood at the door of his former master. How many steps did he take of 8 inches each?

10. What will the plastering of a room, 15 feet square, the walls 9 feet high, amount to at 23 cents a square yard, deducting for 2 doors, 7 feet by 3, and 2 windows, 5 feet by 3? Ans. $17.71. 11. How much time would a person lose in 20 years, by lying in bed half an hour later every day than he ought? Ans. 152 days, 4 hours, 30 minutes. 12. How many cords of wood would a man draw in 6 weeks, drawing 4 loads a day, and 6 cord feet at a load?

Ans. 117 cords.

13. A merchant failing in trade, owes A. £15 7s. 9d.; B. £69 11s. 6d.; C. £102 16s. 11d.; D. £41 19s. 10d.;