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4. A merchant has 3 pieces of cloth ; the first contains 37yd. 3qr. 3na., the second 18yd. Iqr. 3na., and the third 31yd. Iqr. 2na. ; what is the whole quantity ?

Ans. 87yd. 3qr. Ona. 5. Sold 3 loads of hay; the first weighed 2T. 13cwt. 1qr. 171b., the second 3T. 271b., and the third IT. 3qr. illb. ; what did they all weigh ?

Ans. 6T. 14cwt. Iqr. 271b. 6. What is the sum of the following distances ; 16m. 7fur. 18r. 14ft. llin., 19m. lfur. 13r. 16ft. 9in., 97m. 3fur. 27r. 13ft. 3in., and 47m. 5fur. 37r. 13ft. 10in ?

Ans. 181m. 2fur. 18r. Oft. 3in. 7. A gentleman has three farms, the first contains 169A. 3R. 15p. 227ft., the second 187A. IR. 15p. 165ft., and the third 217A. AR. 28p. 165ft. ; what is the whole quantity ?

Ans. 574A. 3R. 20p. 12 ft. 8. There are 3 piles of wood, the first contains 18cords, 116ft. 1000in., the second 17cords, 111ft. 1600in., and the third 21cords, 109ft. 1716in. ; how much in all ?

Ans. 58cords, 82ft. 860in. 9. John Thomson has four casks of molasses, the first contains 167gal. 3qt. lpt., the second 186gal. Iqt. Ipt., the third 108gal. 2qt. Ipt., and the fourth 123gal. 3qt. Opt. ; how much is the whole quantity ?

Ans. 586gal. 2qt. 1 pt. 10. Add together 17bu. 1pk. 7qt. Ipt., 18bu. 3pk. 2qt., 19bu. 1pk. 3qt. Ipt., and 5lbu. 3pk. Oqt. lpt.

Ans. 107bu. lpk. 5qt. lpt. 11. James is 13y. 4m. 13da. old, Samuel is 12y. 1lm. 23da., and Daniel is 18y. 9m. 29da. ; what is the sum of their united ages

?

Ans. 45y. 2mo. 5da. 12. Add together 18y. 345da. 13h. 37m. 15s., 87y. 169da. 12h. 16m. 28s., 316y. 144da. 20h. 53m. 18s., and 13y. 360da. 21h. 57m. 158.

Ans. 43hy. 290da. 20h. 44m. 16s. 13. Venus is 3S. 18o. 45'. 15'. east of the sun, Mars is 75. 15°. 36'. 18". east of Venus, and Jupiter is 5S. 21°. 38. 27". east of Mars ; how far is Jupiter east of the sun ?

Ans. 4S. 26°. 14. A merchant owes a debt in London amounting to £7671, what remains due after he has paid £1728. 175. 9d. ?

Ans. £ 5942, 2s. 3d.

15. From 731b. of silver there was made 26lb. lloz. 13dwt. 14gr. of plate ; what quantity remained ?

Ans. 46lb. Doz. 6dwt. 10gr. 16. From 71 lb. 83. 13. 17. 14gr. take 71b. 93. 13. 17. 17gr.

Ans. 63|b. 103. 73. 23. 17gr. 17. From 2T. 13cwt. take 10T. 17cwt. 191b. 14oz.

Ans. 17T. 15cwt. 3qr. 81b. 2oz. 18. From 76yd. take 18yd, 3qr. 2na.

Ans. 57yd. Oqr. 2na. 19. From 20m. take 3m. 4fur. 18r. 13ft. Sin.

Ans. 16m. 3fur. 21r. 2ft. 10in. 20. From 144A. 3R. take 18A. 1R. 17p. 200ft. 100in.

Ans. 126A. IR. 22p. 71ft. 80in. 21. From 18 cords take 3 cords 100ft. 1000in.

Ans. 14 cords. 27ft. 728in. 22. From 17T. take 5T. 18ft. 765in.

Ans. 11T. 21ft. 963in. 23. From 169gal. take 76gal. 3qt. 1pt.

Ans. 92gal. Oqt. 1pt. 24. From 17Ch. 18bu. take 5Ch. 20bu. lpk. 7qt.

Ans. 11Ch. 33bu. 2pk. Iqt. 25. From 33y. take 47y. 10mo. 27da. 18h. 50m. 14s.

Ans. 35y. Imo. 2da. 5h. 9m. 46s. 26. From 11S. 15°. 36'. 15“. take 5S. 18o. 50'. 18".

Ans. 5S. 26°. 45'. 57". 27. A carpenter sent two of his apprentices to ascertain the length of a certain fence. The first stated it was 17r. 16ft. llin., the second said it was 18r. 5in. The carpenter finding a discrepancy in their statements, and fearing they might both be wrong, ascertained the true length himself, which was 17r. 5yd. Ift. llin. ; how much did each differ from the other ? Ans. 28. From a mass of silver, weighing 1061b., a goldsmith made 36 spoons, weighing 5lb. lloz. 12dwt. 15gr., a tankard, 31b. Ooz. 13dwt. 14gr., a vase, 7lb. lloz. 14dwt. 23gr. ; how much unwrought silver remains ?

Ans. 881b. lloz. 18dwt. 20gr. 29. From a piece of cloth, containing 17yd. 3qr., there were taken two garments, the first measuring 3yd. 3qr. 2na., the second 4yd. lqr. 3na. ; how much remained ?

Ans. Syd. lqr. Zna. 30. The longitude of a certain star is 3S. 18o. 14. 35".,

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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. 38. 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 hy 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 3 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 23

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?

84 ounces? 26. In 24 pence how many shillings? In 36 pence? In 43 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.

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

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

16cwt. by 4, because it takes 4 quar16 3 18

ters to make one hundred weight ; and 4

to this product we add the 3qr. in the 64

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 536

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 d, we divide the multiplicand by 2; and to multiply by a }, 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 371b. 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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