Reduction teaches to change numbers of one denomination into those of other denominations, retaining the same value. Its operations are performed by Multiplication and Division. When performed by Multiplication, it is called Reduction Descending, when performed by Division, it is called Reduction Ascending.

QUESTIONS.

1. How many farthings will it take to make two pence? How many pence to make two shillings?-How many shillings to make two pounds?

2. How many gills to make three pints?-How many pints to make three quarts?-How many quarts to make three gallons?

3. How many quarts to make four pecks?-How many pecks to make four bushels?

4. How many pence are there in eight farthings?How many shillings in twenty-four pence?-How many pounds in forty shillings?

5. How many pints in twelve gills?-How many quarts in six pints?-How many gallons in twelve quarts?

6. How many pecks in thirty-two quarts?-How many bushels in sixteen pecks?

7. How many pounds and shillings in thirty shillings? How many shillings and pence in thirty pence?

REDUCTION DESCENDING.

RULE.

Multiply the numbers in the highest denomination given, by the number that it takes of the next less denomination to make one of that greater; and thus proceed until you shall have multiplied each higher denomination by the number that it takes to form the next lower, until you come to the lowest of all.

V.

Reduce 36 pounds to ounces. 36

16 ounces in a pound."

216

36

576 ounces.

6. Reduce 70 miles to furlongs
7. Bring 30 furlongs to rods.
8. Bring 20 rods to feet.

9. Bring 24 feet to inches. 10. Reduce 32 acres to roods.

Ans. 576 ounces.

Ans. 560 fur. Ans. 1200 rods.

Ans. 330 feet. Ans. 288 inches Ans. 128 roods.

11. Bring 24 square perches to square yards.

Ans. 726 square yards.

Ans. 630 gal. Ans. 200 pints. Ans. 92 pecks. Ans. 192 pints. Ans. 180 months. Ans. 1800 hours. Ans. 1440 minutes. Ans. 600 degrees.

12. Reduce 10 hogsheads to gallons.
13. Bring 25 gallons to pints.
14. Reduce 23 bushels to pecks.
15. Bring 12 pecks to pints.
16. Reduce 15 years to months.
17. Bring 75 days to hours.
18. Bring 24 hours to minutes.
19. Bring 10 signs to degrees.

Note.-In multiplying by 20, I added in the 17 shillings, by 12, the 11 pence; and by 4, the 3 farthings; and this must be observed in all similar cases.

To prove this sum, let the order of it be changed,

and it will stand thus: in 15263 farthings how many pounds?

4)15263

12)3815+3 quarters.

20)317+11 pence.

£15 17s. 11 d. 3 qrs. Ans.

In reducing Federal Money from a higher to a lower denomination, it is only necessary to annex as many cyphers as there are places from the denomination given to that required; or if the given sum be of different denominations, annex the figures of the several denominations in their order, and continue with cyphers, when the sum requires it, to the denomination intended.

2. Thus, in 7 eagles, 3 dollars, how many mills?

3. In 85 dollars, how many mills?
4. In 574 eagles, how many dollars?
5. In 469 dollars, how many cents?
6. In 844 dollars, 75 cents, how many

Ans. 73000.

Ans. 85000.
Ans. 5740.
Ans. 46900.

mills?

Ans. 844750.

7. In 1000 dollars, how many mills? Ans. 1000000. 8. In 25 dollars, 47 cents, 8 mills; how many mills? 9. In 29 guineas at 28s. each, how many pence?

1

Ans. 9744. 10. In 20 acres, 29 poles, or perches, how many square perches?

Ans. 3229.

11. How many solid feet in 30 cords of wood?

Ans. 3840.

12. How many grains in 100 lbs.-Troy Weight?

Ans. 576000.

13. How many lbs. in a ton:-Avoirdupois Weight?

Ans. 2240.

14. In 27 lbs.-Apothecaries Weight; now many grains?

Ans. 155520. Ans. 480. 16. In 360 degrees, being the distance round the world, how many inches, allowing 69 miles to a degree? Ans. 1,587,267,200. 17. How many pints are there in one tun of wine?

15. In 30 yards, how many nails?

Ans. 2016.

18. How many half pints in one hogshead of beer?

19

How many pints in 400 bushels?

Ans. 864. Ans. 25600.

20. How many seconds in 80 years of 365 days each? Ans. 2,522,880,000

21. How many yards in 4567 miles?

Ans. 8037920.

22. In £20 17s., how many pence and half pence? Ans. 5004 pence, and 10,008 half pence.

REDUCTION ASCENDING.

RULE.

Divide the figure or figures in the lowest denomination, by so many of that name as make one of the next higher; and continue the division until you have brought it into that denomination which your question requires.

In reducing Federal Money from a lower to a higher denomination, nothing more is necessary than to cut off so many places on the right hand side of the sum, as there are denominations lower than the one required. Thus, 98765 mills are reduced to dollars, cents, and mills, by cutting off one figure for mills, two more for cents, and the remaining figures being dollars, the amount is $98/7615—or ninety-eight dollars, seventy-six cents, five mills.

SIMPLE EXAMPLES.

1. How many dollars are there in 8000 mills?

810010 Ans. 8. 2. In 487525 cents, how many dollars and cents?

4875/25 Ans. $4875.25.