34. A man sold 78 bushels of corn for $48.75. How much was it a bushel?

35. A farmer sold a load of potatoes, at $0.375 a bushel, for $9.1875. How many bushels were there?

36. How many bushels of beans, at $1.75 a bushel, will come to $43.75?

37. If the product of two factors is 4375, and one of the factors is 175, what is the other factor?

38. How many miles per hour must a steam-ship sail to cross the Atlantic in 12 days, the distance being 3000 miles? 39. How many miles per hour to cross it in 13 days=13.5 days?

40. In how many hours will she cross it if she sails 12 miles per hour? In how many days?

41. 9 times 987 is how many times 25?

42. 15 times 1040 is how many times 75?

43. How much is (171.84 × 10.17) ÷ .608? 87100).00075?

(9.105 X

44. The circumference of the earth is 360 degrees, and it revolves on its axis in 24 hours. How many degrees does it turn in 1 hour?

43. MISCELLANEOUS EXAMPLES IN REDUCTION.

After the exercises which the pupil has had in Reduction in the preceding articles, he will be able to understand the following definitions and rules, and to perform the miscellaneous exercises which follow them.*

Reduction is changing numbers from one denomination to another, without altering their value.

Reducing numbers to lower denominations, - that is, pounds to pence, miles to yards, &c., is sometimes called Reduction descending; reducing them to higher denominations is called Reduction asrending.

RULE FOR REDUCING A NUMBER FROM A HIGHER DENOMINATION TO A LOWER.

Multiply the highest denomination by that number which it takes of the next lower denomination to make a unit of the higher, and to the product add the number, if any, expressed in this lower denomination in the given example. Proceed in this manner through all the denomina

tions to the lowest.

*The exercises in this article, although in the smaller type, are intended for the slate.

RULE FOR REDUCING A NUMBER FROM A LOWER DENOMINATION TO

A HIGHER,

Divide the given number by so many as make one of the next higher; set aside the remainder, if any, and proceed in the same manner through all the denominations to the highest.

EXAMPLES.

1. In 24 tons 16 cwt. 2 qr. 15 lb. 9 oz. 14 dr. how many drams? 2. In 4865392 drams how many oz.? lb.? qr.? cwt.? tons? 3. In 2578 lb. 11 oz. 15 gr. Troy how many grains?

4. In 3801765 grains Troy how many pounds, &c.?

5. In 58 yd. 3 qr. 1 na. 2 in. how many inches? 6. In 384 165 nails how many English ells?

7. In £2516 8s. 31d. how many farthings?

8. In 81846758 farthings how many pounds?

9. In 8516 English quarters 3 bu. 2 pk. 5 qt. how many pints? 10. In 4579 gal. 3 qt. 1 gill how many gills?

11. In 817568419 gills how many gallons?

12. In 516 acres 2 R. 29 sq. rods how many sq. rods?

13. In 3 A. 35 sq. rods 25 sq. yd. 7 sq. feet how many sq. feet? 14. In 875164 sq. rods how many acres?

15. In 15 cu. yards 20 cu. ft. 1084 cu. in. how many cu. inches? 16. In 18476189 cu. inches how many cu. yards?

17. In 8416 cu. ft. 561 cu. in. how many cu. inches? How many wine gallons? How many beer gallons? How many dry gallons or half pecks?

18. În 857 bushels of wheat how many pounds? (Art. 62.) 19. How many pounds in 859 bushels of wheat? In 859 bushels of oats? Of Indian corn? Of rye? (62.)

20. How many pounds in 876 barrels of beef? In 849 barrels of pork?

21. How many barrels of beef in 8176 pounds of beef?

22. How many bushels in 3018 pounds of wheat? Of Indian corn? Of oats?

23. How many pounds in 875 barrels of flour?

24. How many barrels in 841675 pounds of flour?

MISCELLANEOUS EXAMPLES.

44. Review Art. 19. 1. Add 3556; 48+59; 317+ 125; 35875; 94+ 187.

2. Add 4.4+8.7. Say, 48 are 12, .4.7 are 11 tenths, or 1 and 1 tenth, which added to 12 makes 13.1; therefore, &c.

3. Add 3.45.2; 4.18+5.26; 6.007+8.145; 5.38.9; 25.8+38.9.

Review Art. 22. 4. How much is 317-208? Say, 200 from

300=100; 8 from 179, which added to 100 makes 109; therefore, 317 less 208 is 109.

6. What is the complement of 35? 47? 53? 32? 87? 46? 38? 58? 7. What is the complement of 127? Take 200 from 1000, and to the remainder add the complement of 27.

What is the complement of 573? Take 600 from 1000, and add to the remainder the complement of 73.

8. What is the complement of 643? 856? 359? 436? 729? 814? 538? 476?

9. How much is 549-387? Say, 400 from 549 = 149, and then add the complement of 87. How much is 644-173? 754-369? 835-275? 987-174? 694-397?

Review Art. 32, 35, and 36.

10. In 2 halves how many whole ones? In 3 halves? In 4 halves? 7 halves?

11. How much is 5 times 44? Say, 5 times 4 are 20, 5 times are 5 halves, or 2 and, which added to 20 makes 224; therefore, 5 times 4 are 224.

12. How much are 3 times 5? 8? 12? 13. In 3 thirds how many whole ones?

14. How much are 4 times 5}? 63? 7? 15. In 4 fourths how many whole ones? 16. How much are 5 times ? 5 times 1? 112 5 times 15?

35?

In ? ? ? £5?

15? 75? 116}?
In ? ? 15? 26?

5 times 34? 5 times

17. In 5 fifths how many whole ones? In ? ? 20? 28? 18. How much are 6 times ? 6 times 1? 6 times 32? 6 times 83 6 times 144? 6 times 35?

19. In 6 sixths how many whole ones? In 1? 15? 18? 40?

20. How much are 7 times ? 7 times ? 7 times ? 7 times 327 times 4? 7 times 8?

21. How much are 3 times 8? Say, 3 times 8 are 24, of 8 is 4, which added to 24, makes 28; therefore, 3 times 8 are 28.

45, or 34, which added to 20 makes 23; therefore, 4 times 5 are 231.

24. How much are 6 times 5? 4 times 9? 8 times 9? 63 times 15? 9 times 15? 83 times 36?

25. A man earns

3 days? In 6 days?

of a dollar per day. How much can he earn in In 3 weeks of 6 days each? In 8 weeks?

26. What will 6 lb. of beef cost, at 10 cents a lb.? 12 lb.? 9 lb.? 27. If 1 lb. of beef cost 8 cents, what will of lb. cost? 14 lb. ?

What will 3 lb. cost?

lb. ?

If 1 lb. costs 8 cents, of a lb. will cost of 8 cents, or 2 cents; will cost 3 times as much.

Therefore, &c.

28. If 1 yd. of cloth cost 12 cents, how much will of a yd. cost? yd.? 3 yd.? 5 yd.?

How much will yd. cost? yd.? } yd.?

Say, of a yd. will cost

cost 3 times 1 ct.; 3 times which added to 3 makes 4.

1

of 12 cents, which is 1 ct.;

will

are 3, and 3 times

are 12, or 1,

Ans. 4 cents.

29. What will 34 lb. of cheese cost, at 10 cts. a lb.? 54 lb.? 30. What will 5 yards of ribbon cost, at 84 cts. per yd.?

35. What part of 7 is 1? 6? 15? 27? 48? 21 35? 57? 36. If 5 lb. of beef cost 30 cts., what will 3 lb. cost? 7 lb.? 9 lb. ? 12 lb. ? 16 lb.?

Say, as 3 is of 5, 3 lb. will cost as much as 5 lb. cts. is cts., and are 3 times 6 cts., or 18 cts.

of 30

37. If 3 barrels of flour cost $15, what is the price of 2 barrels? 5 barrels? 8 barrels? 12 barrels?

38. If 8 yards of cloth cost $24, what will be the price of 3 yards?

9 yards? 12 yards?

39. What is

of 24?

43. If of a bushel of corn is worth 8 cents, what are worth? ?? 1 bushel? 5 bushels? 7 bushels?

44. If of a barrel of beef cost $10, what is worth? 1 barrel? 5 barrels?

45. Bought 2 cords of wood for $17; what was the price per cord?

NOTE. 23: =2; and or 1 cord will cost 3 times $2, 3 cords? 5 cords? 8 cords?

. If of a cord cost $17, will cost of $17,

$63. What cost 46. If 3 pounds of cheese cost 30 cents, what is 1 lb. worth? 3 lb. 54 lb.?

MISCELLANEOUS EXAMPLES IN ALL THE PRECEDIng Rules.

45. 1. Multiply one thousand seven hundred and one, and five hundredths, by thirty thousand and four, and add to the product six thousand and one.

2. A borrowed $85.00. He has paid $30.12 at one time, $15.125 at another, and $18.875 at another. How much remains unpaid? How many pounds of butter, at 18 cents a pound, will it take to pay the balance?

3. A grocer buys 15 firkins of butter, each weighing 45 pounds, at 15 cents a pound. How much molasses will it take to pay for it at 24 cents a gallon?

4. A farmer sold 575 pounds of pork, at 65 cents a pound; 3 tons of hay, at $.75 a cwt.; 1 ton of carrots, for $12.00. He received in pay 2 barrels of flour, at $6.50; 50 pounds of salt fish, at 4 cents a pound; 25 pounds of sugar, at 5 cents a pound; 15 pounds of rice, at 4 cents a pound, and 24 yards of cotton cloth, at 74 cents a yard. How much was the balance?

5. What will 5 bu. 3 pk. 6 qt. of meal come to, at 2 cents per qt.?

6. A farmer sold a fat ox. The fore quarters weighed 341 pounds each; the hind quarters, 312 pounds each; the hide weighed 75 pounds; the tallow, 63 pounds. He had 5 cents a pound for the fore quarters, 64 cents a pound for the hind quarters, 8 cents a pound for the tallow, and 6 cents a pound for the hide. What did the ox come to?

7. A publisher is about printing a new edition of a book. It will take 12 reams of paper, each ream weighing 29 lb., at 11 cts. per lb.; he is to pay $1.50 per ream for printing, and 121 cts. a book for the binding. What will an edition of 1000 copies cost? How much for each book?

In this and other questions in which the answer is in Federal Money, the pupil may get the answer to the nearest mill. 8. A merchant buys 50 barrels of flour for $257.00. At what price must he sell it per barrel to gain $55.50 on the whole?