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and the longitude of Jupiter is 11S. 25°. 30'. 50".; how far will Jupiter have to move in his orbit to be in the same longitude of the star?

Ans. 3S. 22°. 43'. 45′′.

Section 12.

REDUCTION.

MENTAL OPERATIONS.

1. In 2 pence how many farthings? In 4 pence? In 5 pence? In 7 pence? In 8 pence? In 10 pence ? 2. How many pence in 8 farthings? In 12 farthings? In 16 farthings? In 24 farthings? In 36 farthings? 3. In 2 shillings how many pence? In 4 shillings? In 5 shillings? In 6 shillings? In 7 shillings?

4. In 4 yards how many quarters? In 5 yards? In 6 yards? In 7 yards? In 8 yards? In 9 yards?

5. In 8 quarters how many yards? In 12 quarters? In 16 quarters? In 24 quarters ? In 32 quarters ? 6. In 3 feet how many inches? In 5 feet? In 7 feet? In 8 feet? In 9 feet? In 10 feet? In 12 feet? 7. In 36 inches how many feet? In 48 inches? In 60 inches? In 72 inches? In 96 inches? In 144 inches ? 8. In 6 feet how many yards? In 9 feet? In 12 feet? In 21 feet? In 24 feet? In 30 feet? In 36 feet? 9. In 4 yards how many feet? In 3 yards? In 7 yards? In 9 yards? In 10 yards? In 11 yards? In 12 yards? 10. In 2 acres how many roods? In 3 acres? In 4 acres? In 6 acres? In 7 acres? In 10 acres ? 11. In 12 roods how many acres? In 8 roods? In 16 roods? In 20 roods? In 32 roods? In 36 roods ? 12. How many furlongs in 2 miles? In 3 miles? In 6 miles? In 7 miles? In 8 miles? In 10 miles ? 13. In 12 furlongs how many miles? In 16 furlongs? In 40 furlongs? In 44 furlongs? In 96 furlongs? 14. In 5 dimes how many cents? In 6 dimes? In 8 dimes? In 9 dimes? In 10 dimes? In 12 dimes?

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 29 days? In 35 days? In 42 days? In 56 days? 22. How many pecks in 1 bushel? In 3 bushels? In 4. 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.

1. In 16cwt. 3qr. 18lb. how many pounds?

OPERATION.

Cwt. qr. lb.
16 3 18

4

64

3

67

28

536

134

1876

18 1894

Ans. 1894lb. In this question, we multiply the 16cwt. by 4, because it takes 4 quarters to make one hundred weight; and to this product we add the 3qr. in the question. Then we multiply by 28, because it takes 28 pounds to make one quarter, and to the product we add the 18 pounds in the question, and our work is done.

From the above illustration, we deduce the following

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 37lb.
5. In 171b. of calomel how many grains?
6. In 15 tons how many ounces?
7. In 17cwt. 3qr. 19lb. how many pounds?
8. How many quarters in 144 yards?
9. How many nails in 57 Ells English?

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?

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cause 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.

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NOTE 1. To divide by 5, or 16, reduce both divisors and dividends to halves by multiplying by 2. To divide by 2724, reduce the number to fourths by multiplying 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?

5. 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?

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