13 In 2046 ft. how many yards and rods?

Ans. {

682 yd. 124 r.

14. How many seconds in a lunar month; or, 29 days, 12 hours, 44 minutes, 3 seconds?

Ans. 2551443.

15. What will a bushel of clover seed come to, at the rate of 12 cents a pint ? Ans. $8. 16. Suppose a hogshead of molasses, which cost $23, to be retailed at 12 cents a quart, what is the profit on it? Ans. $8.50. 17. How many times will a wheel, 16 feet 6 inches in circumference, turn round in going 100 miles?

Ans. 32000. 18. How many bottles, containing a pint, a quart, and 2 quarts, an equal number of each, can be filled from half a pipe of wine? Ans. 72 of each. 19. If a barrel of beer be retailed at 3 cents the half pint, how much will it amount to?

20. In 20571005 drams, how many tons?

Ans. $17.28.

Ans. 35 T., 17 cwt., 1 qr., 23 lb., 7 oz., 13 dr. 21. In 469 dollars, how many cents and mills?

Ans. 46900 cts., 469000 m.

NOTE. AS 100 cents and 1000 mills, each make 1 dollar, the reduction of dollars to cents, is performed by simply annexing 2 ciphers, and to mills by annexing 3 ciphers.

If the number be dollars and cents, it is reduced to cents by erasing or disregarding the decimal point. So, likewise, if it contain mills, the whole may be considered as mills.

Mills are reduced to dollars by cutting off three, and cents by cutting off two, of the right hand figures by a separatrix; in other words, dividing by 1000, and by 100.

22. How many cents in $ 65?

23. How many mills in $17?

Ans. 6500.

Ans. 17000.

Ans. 1205.

24. Reduce 12 dollars 5 cents to cents.
25. Reduce 9 dollars, 6 cents, 5 mills, to mills.

26. Reduce 15 cents, to mills.
27. How many dollars in 1246 cents?
28. How many dollars in 1246 mills?

Ans. 9065.

Ans. 150.

Ans. $12.46. Ans. $1 24 6

29. How many mills in 5 pieces of the gold coin denominated eagles? Ans. 50000. 30. If you purchase 75 bunches of quills, each containing 25 quills, at the rate of 6 mills a piece, how many dolars will they cost? Ans. $11.25.

QUESTIONS.

Is the value of any given number changed by reduction to another denomination?

How do you know when to employ multiplication, and when division, in performing numbers?

One of these methods has sometimes been denominated "Reduction Ascending," and the other, "Reduction Descending;" you can probably designate both of them.

If you wished to prove the accuracy of your work, what method would you take?

When in Reduction Ascending you have a remainder, after any division, of what denomination is it!

Of what denomination is the quotient in relation to the dividend?

ADDITION OF COMPOUND NUMBERS.

RULE. Place the numbers so that the same denominations may stand under each other; add the several columns containing the different denominations, separately, beginning with the lowest; and divide the sum of each by the number of that denomination, which makes one of the next higher; set down the remainder, and carry the quotient to the next column.

The propriety of a distinct rule for the addition of compound numbers will be evident, if we reflect that pounds, shillings, pence, &c., cannot be put into one common aggregate, which would express the amount in any one of the denominations.

3. What is the sum of £16 8s. 4d., £19 12s. 7d. 3qr. £104 15s. 11d. 1qr., £20. 11d. 1qr.?

4. Add together, 4 lb. 10 oz. 17 dwt. 13 gr., 1 lb. 9 oz. 8 dwt. 7 gr., 11 oz. 15 dwt. 10 gr., 1 lb. 6 dwt., Troy. 5. What is the sum of 2 oz. 15 dwt. 11 gr., 1 lb. 9 oz. 15 dwt., and 19 dwt. 14 gr. of silver?

6. Add together 16 cwt. 2 qr. 11 lb. 14 oz., 18 cwt. 3 qr. 22 lb. 8 oz., 3 qr. 9 lb. 11 oz., and 17 cwt. 1 qr. 13 oz.

7. What is the weight of 4 loads of hay, weighing severally, 1 T. 3 cwt. 20 lb., 19 cwt. 3 qr. 16 lb., 1 T. 5 cwt., and 18 cwt. 2 qr. 14 lb. ?

8. How much is 16 yd. 3 qr. 3 n., 12 yd. 1 qr. 2 n., 9 yd. 3 n., and 6 yd. 2 qr. 1 n. of cloth?

9. What is the sum of 4 E. e. 3 qr. 2 n., 7 E. e. 4 qr. 3 n., 5 E. e. 3 qr., and 4 qr. 3 n. of cloth ?

10. How much corn in 3 bags, containing severally 3 bu. 2 pk. 7 qt., 2 bu. 1 pk. 5 qt., and 2 bu. 6 qt.

11. Add together 2 hhd. 51 gal. 2 qt. 1 pt., 3 hhd. 10 gal 1 pt., 60 gal. 3 qt., and 1 hhd. 3 qt. 1 pt.

12. How much wine in 4 p. 125 gal. 3 qt., 68 gal. 2 qt. 1 pt., 34 p. 59 gal., 43 gal. 3 qt. 1 pt. ?

13. Add 58 m. 5 fur. 23 r., 17 m. 4 fur. 18 r., 23 m. 39 r., 16 m. 7 fur. 1 r., 6 fur. 30 r., and 20 m. 1 fur. 12 r.

14. Add 46 m. 6 fur. 29 r. 15 ft. 10 in., 39 m. 1 fur. 36 r. 14 ft. 6 in., 53 m. 7 fur. 24 r. 9 ft. 8 in., 7m. 39 r. 11 ft. 9 in.

15. How much land in 4 lots, containing severally 36 A. 2 R. 18 r., 59 A. 3 R. 12 r., 75 A. 39 r., and 19 A. 11 R. 39 r.?

16. Add 4 yd. 5 ft. 68 in., 3 yd. 8 ft. 114 in., 11 yd. 2 ft. 58 in., and 6 yd. 7 ft. 108 in. square measure.

SUBTRACTION OF COMPOUND NUMBERS.

RULE. Place the numbers as in Compound Addition. Begin with the lowest denomination in the subtrahend, and take it from the number above it; but if that above be the least, add as many to it as make one of the next higher denomination; then subtract, and carry 1 to the next denomination in the subtrahend.

The method of proof is the same as in simple subtraction

4. Subtract 2 oz. 14 dwt. 23 gr., from 4 oz. 19 dwt. 21 gr. 5. From 4 lb. 9 oz. 16 gr., take 3 lb. 10 oz. 16 dwt. 15 gr. 6. A merchant having received 7 cwt. 2 qr. 14 lb. of sugar, sells 5 cwt. 3 qr. 25 lb.; how much remains on hand? 7. Subtract 10 T. 11 cwt. 20 lb. 10 oz. 11 dr., from 13 T. 9 cwt. 1 qr. 12 oz.

8. From 35 . 7 3. 3 3. 19. 14 gr., take 17. 10 3. 6 3. 19. 18 gr.

9. If from a piece of cloth containing 20 yd., two garments be taken, each 3 yd. 3 qr.; how much remains of the piece?

10. Subtract 15 m. 6 fur. 26 r. 12 ft., from 28 m. 5 fur. 16 r.

11. From a pipe of wine, a merchant sold to one man, 31 gal. 2 qt., to another, 5 gal., and to a third, 3 gal. 1 qt. 1 pt.; how much remains of the pipe?

12. From 1 bl. take 16 gal. 3 qt.

13. From 13 bu. 7 qt. 1 pt., take 7 bu. 3 qt. 1 pt.

14. Subtract 75 d. 12 h. 35 m., from 114 d. 9 h. 26 m. 15. From 7 d. 21 h. 59 m. 16 s., take 4 d. 23 h. 41 m. 50 s.

16. From a pile of wood, containing 19 cords 96 ft. were sold at different times, 3 cords 26 ft., 4 cords 19 ft., and 7 cords 28 ft.; how much remains of the pile?

17. What is the difference in longitude between two places, one of which is 75° 15' 36" west from an assumed meridian; and the other 46° 20' 32" west?

18. From 112 A. 3 R. 25 r. of land, take 19 A. 2 R. 37 r.

MULTIPLICATION OF COMPOUND NUMBERS.

I. When the multiplicand consists of different denominations.

RULE. Place the multiplier under the least denomination of the multiplicand; multiply each denomination separately, beginning with the lowest, and observe the same rules for carrying, &c., as in addition of compound numbers.

1. What is the cost of 8 lb. of tea at 5s. 8d. per lb. ?

3. 9cwt. of cheese, at £1 11s. 5d. per cwt.

Ans. £14 2s. 9d.

4. 12 cwt. of sugar, at £3 78. 4d. per cwt.

Ans. £40 8s.

5. The weight of 3 chests of tea, each weighing 3 cwt. Ans. 10 cwt. 2 qr. 27 lb.

2 qr. 9 lb.