Application of the two preceding Rules.

1. If a man purchase a yoke of oxen for £15 5. 8d. four cows for £20 10s. 6d. and a horse for £26, what did they all cost?

Ans. 61 16s. 2d.

QUESTIONS.

4. Reduction.

REDUCTION is the method of bringing numbers of one name or denomination into another, retaining the same value.

Reduction is of two kinds, Descending and Ascending.

Reduction Descending is when a higher denomination is to be brought into a lower, as pounds into shillings, pence and farthings, and is performed by Multiplication.

Reduction Ascending is when a lower denomination is to be brought into a higher, as farthings into pence, shillings and pounds, and is performed by Division.

1. REDUCTION DESCENDING.

Rule.

Multiply the highest denomination by the number which it takes of the next less to make one of that, adding the number of the second name; and so continue till you have brought it as low as the question requires.

Examples.

1. In 65 4s. 6d. 2qrs. how many farthings?

£. s.
d. qrs.
65 4 6 2
20

1304
12

156 54 4

62618

Here 65 pounds is the highest denomination. Then because 20 shillings make one pound, I multiply 65 by 20, adding at the same time, the 4s. to the product, and the sum is 1304 shillings; then because 12 pence make one shilling, I multiply the shillings by 12, adding the 6d. and the sum is 15654 pence; lastly, because 4 farthings make one penny, I multiply the pence by 4, adding the 2 farthings, and the work is done. In this way I find that in £65 4s. 6d. 2qrs. there are 62618 farthings.

2. In £1465 14s. 5d. how many farthings? Ans. 1407092.qrs. 3. In 22lb. 6 oz. 10 pwt. 15 grs. how many grains?

Ans. 129855. 4. In 4E. $8 4d. 6cts. 2m. how many mills?

3

Ans. 48462 mills.*

5. In 250 Eagles how many cents? Ans. 250000 cents. 6. In 37 pistoles, at 22s. how many pence and farthings?

Ans. 9768d. 39072 qrs. 6. In 29 guineas, at 28s. how many farthings? Ans. 38976 qrs.

* To reduce eagles to dollars add one cipher; to dimes add 2; to cents add ; to mills add 4. To reduce dollars to dimes add one cipher; to cents add 2; to mills add 3. To reduce dimes to cents add one cipher; to mills add 2. To reduce cents to mills add one cipher.

2. REDUCTION ASCENDING.

Rule.

Divide the lowest denomination by the number which it takes of that to make one of the next higher, and so continue to do till you have brought it into the denomination required.

Examples..

1. In 62618 farthings how many pounds?

4) 6 26 18

By comparing the examples in Reduction De12) 1 5 6 5 4 2qrs. scending with those in Reduction Ascending, it will be seen that they reciprocally prove each other.

210) 1 3 014 6d.

£6 5

4s.

Ans. £65 4s. 6d. 2qrs.

2. In 1407092 farthings how many pounds ?

Ans. £1465 14s. 5d.

3. In 20465 mills how many eagles, dollars, &c.

Ans. 2E. 80 4d. 6cts. 5 mills. 4. In 8642 mills how many dollars ?

Ans. 88 6d. 4cts. 2m.

5. In 39072 farthings how many pistoles? Ans. 37. 6. In 129855 grains how many pounds?

Ans. 22lb. 6oz. 10pwt. 15grs. 7. In 25684 cents how many eagles?

Ans. 25E. $6 8d. 4cts.

3. REDUCTION ASCENDING AND DESCENDING. It is thought to be unnecessary to give examples of all the weights and measures. The following will be sufficient to enable the attentive scholar to make a general application of the rules. His judgment will direct him to the tables by which the several examples are reduced.

1. In £151 10s. how many dollars ? Ans. $505. 2. In 75 pistoles, at 22 shillings, how many pounds?

Ans. £82 10s.

3. In 78lb. 5oz. 18pwt. how many pennyweights?

Ans. 18838pwt.

4. In 7cwt. Sqr: 10lb. how many drams ? Ans. 224768dr. 5. In 2349 pints how many bushels ?

Ans. 36bu. 2pk. 6qt. 1pt. 6. In 4 pieces of cloth, each 14 yards, how many nails? Ans. 896.

When it is required to take quantities of several denominations, each an equal number of times from a given quantity. RULE.-Reduce each of the quantities to the lowest denomination mentioned, and add them together for a divisor; reduce the given quantity to the same denomination for a dividend; and the quotient will be the number sought.

10. A man is desirous of drawing off a hogshead of wine into bottles containing gallons, two quarts, quarts and pints of each an equal number, how many must he have? Ans. 33 of each and 9 pints over.

11. How many spoons, each weighing 3oz. can be made from 5lb. of silver? Ans. 20. 12. In 1 ton how many drams? Ans. 573440dr.

13 In 425060 seconds how many hours? Ans. 118h. 4m. 20s. 14. In 63360 feet how many miles ?

3) 63360

54 † 11) 21120 yards.

1920
2

8 furlongs.

40

320 rods.
5*

1600

160

1760 yards.

3

5280 feet.
12

63360 inches.
3'

410) 3840 rods.

8) 96 furlongs.

Ans. 12 miles.

15. In £231 16s. how many ducats, at 4s. 9d. each? Ans.976.

16. How many seconds from the birth of Christ to the year 1824,allowing 365d. 5h. 48m.578. to a year? Ans. 57559853088.

17. How many inches from Montpelier to Burlington, it being 38 miles? Ans. 2407680.

18. How many seconds are there in 8 signs, 12° 14′ 26′′ ? Ans. 908066.

19. In 240,000rds. how many Ans. 1500 acres.

Ans. 190080 barley corns.

acres ?

*To multiply by take half the multiplicand. The several steps in this example present at one view the number of furlongs, rods, yards, feet, inches and barley corns in a mile.

For 5 divide by 11 and multiply the product by 2 because 5-11 halves, and 11 being twice as great as 54, the true divisor, the quotient will be only half as great as it ought to be; it must therefore be doubled.

1. If a man drink a pint of rum a day, how much will he drink in a year?

Ans. 45gal. 2qt. pt.

2. How many barley corns will reach round the world, supposing it to be 25020 miles? Ans. 4755801600.

3. Divide 8 20 among 4 men so that the shares shall be to one another as 1, 2, 3, 4. Ans. 12, 24, 36, 48. 4. How many steps of 2 feet 6 inches, must a man take in going from Burlington to Boston, it being 190 miles ? Ans. 401280.steps. 5. How many lots, each containing three quarters of an acre, are there in one square mile? Ans. 853 lots, and 40 rods over. 6. How many cubic inches in a cord of wood? Ans. 221184. 7. In £500 how many eagles, moidores, pistoles, crowns and dollars of each an equal number?

Ans. 76 of each, and 908 pence over. 8. If a vinter be desirous to draw off a pipe of wine into bottles containing piuts, quarts and 2 quarts, of each an equal number, how many must he have? Ans. 144 of each.

9. There are three fields, one containing 7 acres, another 10 acres and the other 12 acres and 1 rood; how many shares of 76 rods each are contained in the whole ?

Ans. 61 shares, and 44 rods over.

10. In 172 moidores at 36s. each, how many eagles, dollars and nine-pences, of each an equal number?

Ans. 92 of each, and 68 nine-pences over. 11. In 470 boxes of sugar, each 26lb. how many cwt.?

Ans. 109cwt. Oqrs. 12lb. 12. If cigars cost one and a half cent each, and a person smoke 3 cigars per day, how much will it cost him for cigars during the months of January, February and March in a common year?

Ans. 405 cents, or $4 5cts.

13. In 5529600 cubic inches, how many cords of wood ?

1. What is Reduction?

QUESTIONS.

2. Of how many kinds is Reduction? 3. What is Reduction Descending? 4. What is Reduction Ascending?

Ans. 25 cords.

wish to take quantities of several denominations, each an equal number of times from a given. quantity?

5. What is the rule for Reduction 9. How many shillings in a guinea?

Descending?

6. What is the rule for Reduction

Ascending?

7. How is Reduction proved?

8. How do you proceed when you

in a moidore? in a crown? in a ducat? in a pistole?

10. Which of the fundamental rules

are employed in Reduction?