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15. How many dimes in 20 cents ? In 30 cents? In 40

cents ? In 80 cents ? In 90 cents ? In 100 cents ? 16. How many square feet in 1 yard ? In 2 yards ? In

3 yards? In 5 yards? In 7 yards? In 8 yards ? 17. In 9 square feet how many square yards? In 27

feet? In 36 feet? In 54 feet? In 63 feet? In 108 feet ? 18. In 1 gallon how many quarts? In 3 gallons ? In 5 gallons ? In 7 gallons ? In 8 gallons? In 9 gallons ? 19. How many gallons in 4 quarts ? In 8 quarts ? In 16 quarts? In 24 quarts? In 32 quarts ? In 40 quarts 20. How many days in 2 weeks ? In 4 weeks ? In 5

weeks? In 7 weeks? In 9 weeks ? In 10 weeks? 21. In 14 days how many weeks? In 21 days ? In 23

days? In 35 days ? In 42 days? In 56 days ? 22. How many pecks in 1 bushel ? In 3 bushels ? In 40

bushels ? In 6 bushels ? In 7 bushels ? In 9 bushels ? 23. In 8 pecks how many bushels ? In 12 pecks ? In 16

pecks? In 24 pecks? In 32 pecks? In 40 pecks? 24. If in 1 pound of gold there are 12 ounces, how many

ounces in 3 pounds ? In 4 pounds ? In 6 pounds ? 25. In 24 ounces how many pounds ? In 36 ounces?

In 40 ounces? In 60 ounces? In 84 ounces ? 26. In 24 pence how many shillings ? In 36 pence ? In 48 pence? In 60 pence? In 72 pence? In 144 pence ? The student will now perceive, that the object of

Reduction is the changing of numbers of one denomination to another without losing their value.

It consists of two parts, Descending and Ascending. The former is performed by Multiplication, and the latter by Division.

Reduction Descending teaches to bring numbers of a higher denomination to a lower; as, to bring pounds into shillings, or tons into hundred-weights.

Reduction Ascending teaches to bring numbers of a lower denomination into a higher ; as, to bring farthings into pence, or shillings into pounds.

Section 13.

REDUCTION DESCENDING.

OPERATION.

Cwt. qr.

Ib.

1. In 16cwt. 3qr. 181b. how many pounds?

Ans. 18941b.
In this question, we multiply the

16cwt. by 4, because it takes 4 quar-
16 3 18
4

ters to make one hundred weight ; and 64

to this product we add the 3qr. in the question.

Then we multiply by 28, 3

because it takes 28 pounds to make one 67

quarter, and to the product we add the 28

18 pounds in the question, and our 5 36

work is done. 134

From the above illustration, we de

duce the following 1876

18 1894

RULE.

Multiply the highest denomination given by so many of the next less, as will make one of that greater ; and so proceed until it is brought to the denomination required, observing to bring in the lower denominations to their respective places.

Note 1. To multiply by a }, we divide the multiplicand by 2; and to multiply by a 4, we divide by 4.

Note 2. The answers to Reduction Descending will be found in the questions of Reduction Ascending. 2. In £379 how many farthings ? 3. In £ 46. 18s. 5d. how many pence ? 4. How many grains Troy in 3ilb. 5. In 17lb. of calomel how many grains ? 6. In 15 tons how many ounces? 7. In 17cwt. 3qr. 191b. how many pounds ? 8. How many quarters in 144 yards ? 9. How many nails in 57 Ells English?

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10. How

many

rods in 97 miles ? 11. How many inches in 7 furlongs ? 12. In 95,000,000 miles how many inches ? 13. In 48deg. 18m. 7fur. 18r. how many feet? 14. How many square feet in 76 acres ? 15. How many square yards in 144 acres ? 16. How many square inches in 25 square miles ? 17. How many square feet in 7A. 3R. 16p. 218ft ? 18. In 15 tons of timber how many cubic inches ? 19. How many cubic inches in 19 cords, 116 feet? 20. In 7 hogsheads of wine how many pints ? 21. In 5hhd. 17gal. 3qt. how many quarts ? 22. In 17hhd. of beer how many pints ? 23. How many pints in 57 bushels ? 24. How many quarts in 15Ch. 16bu. 3pk. ? 25. In 57 days how many minutes ? 26. In 365da. 6h. how many seconds ? 27. In 1842 years (365da. 6h. each) how many hours ? 28. In 8S. 14°. 18'. 17". how many seconds ?

Section 14.

REDUCTION ASCENDING.

OPERATION.

1. In 18941b, how many hundred weight ?

Ans. 16cwt. 3qr. 181b.

We first divide by 28, 28 ) 18 9 4 lbs.

because it takes 281b. to 4) 6 7. 18lbs.

make a quarter of a 1 6cwt. 3qr. 181b. Ans. hundred weight. We

then divide by 4, because it takes 4 quarters to make one hundred weight. Hence the following

RULE.

Divide the lowest denomination given by that number, which it takes of that denomination to make one of the next higher; so proceed until it is brought to the denomination required.

Note 1. To divide by 51, or 161, reduce both divisors and divi. dends to halves by multiplying by 2. To divide by 2724, reduce the number to fourths by inultiplying by 4. If there be a remainder, it will be halves or fourths, like the dividend.

NOTE 2. The answers to Reduction Ascending are the questions in Reduction Descending. 2. In 363840 farthings how many pounds ? 3. In 11261 pence how many pounds ? 4. In 213120 grains Troy how many pounds? ö. In 97920 grains how many pounds, Apothecaries'

weight? 6. In 537600 ounces how many tons ? 7. How many hundred weight in 2007 pounds ? 8. How many yards in 576 quarters ? 9. How many ells English in 1140 nails ? 10. How many miles in 31040 rods ? 11. How many furlongs in 55440 inches ? 12. How many miles in 6,019,200,000,000 inches ? 13. How many degrees in 17714037 feet ? 14. In 3310560 feet how many acres ? 15. How many acres in 696960 square yards ? 16. How many square miles in 100362240000 sq. in. ? 17. How many acres in 342164 square feet? 18. How many tons of timber in 1036800 cubic inches ? 19. How many cords of wood in 4402944 cubic inches ? 20. In 3528 pints of wine how many hogsheads ? 21. In 1331 quarts of wine how many hogsheads ? 22. In 7344 pints of beer how many hogsheads ? 23. How many bushels in 3648 pints ? 24. How many chaldrons in 17816 quarts ? 25. How many days in 82080 minutes ? 26. How many days in 31557600 seconds ? 27. How many years in 16146972 hours ? 28. In 915497" how many signs ?

S

Section 15.

MISCELLANEOUS. QUESTIONS TO EXERCISE THE FOREGOING RULES. 1. At $5 per ream, how many reams can be bought for $ 175 ?

Ans. 35 reams. 2. At $ 7.50 per barrel, how many barrels of flour can be obtained for $ 217,50 ?

Ans. 29 barrels. 3. At $ 75 per ton, how many tons of iron can be purchased for $ 4875 ?

Ans. 65 tons. 4. At $4 per yard, how many yards of cloth can be bought for $ 1728 ?

Ans. 432 yards. 5. If a ton of coals cost $ 8.40, what cost one cwt. ?

Ans. 42 cents. 6. At $2.40 per bu., what cost 1 pk. ? What cost 17bu. 3pk.

Ans. $ 42.60. 17. At $ 3.50 per quintal, what cost 37 quintals ?

Ans. $ 129.50. 8. John Webster bought 5cwt. 3qr. 18lb. of sugar at 9 cents per lb., for which he paid 25 barrels of apples at $ 1.75 per barrel ; how much remains due ?

Ans. $ 15.83. 9. If 97lb. of beef cost $8.73, what cost llb. ? What cost 1471b. ?

Ans, $ 13.23. 10. If a man travel 45 miles in 9 hours, how far will he travel in 1 hour ? How far in 59 hours ?

Ans. 295 miles. 11. If a ton of hay can be purchased for $ 18.40, what will be the price of lcwt. ? What of 47cwt. ?

Ans. $ 43.24. 12. Bought 65 barrels of flour for $ 422.50, what cost

one barrel ? What cost 15 barrels ? Ans. $ 97.50. 13. For 45 acres of land, a farmer paid $ 2025; what

cost one acre ? What 180 acres ? Ans. $ 8100.00. 14. For 5 pairs of gloves, a lady paid $3.45 ; what cost 1 pair? What cost 11 pairs ?

Ans. $ 7.59. 15. When $ 1480 are paid for 25 acres of land, what cost 1 acre ? What cost 1 rod ? What cost 37A. 2R.

Ans. $ 2226.66.

18p

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