EXERCISES IN FRACTIONS.

1. A man bought 3 pieces of cloth, one of which contained 453 yards, another 63ğ yards, and the other 564 yards: how many yards did he buy?

2. If you travel 857 miles in one day, 9511 miles the second, and 115,5 miles the third day, how far will you travel in all?

3. What is the sum of 7 of of 6, 753, 16339, and 185,7% ? 4. What is the sum of 693, § of 360, of 2 of 461, and 761 ? 5. A man having 1783 acres of land, sold 873 acres: how many acres had he left?

6. A young man having 6857 dollars, lost 263 dollars by gambling: how much did he have left?

7. If I buy of a ship, and sell of what I buy, how much shall I then own?

8. A miller having 675 barrels of flour, sold 17 barrels more than of it: how much did he have left?

9. What will 175 gallons of oil cost, at 13 dollar per gallon? 10. What cost 783 boxes of sugar, at 243 dollars per box? 11. What is 29 times 3 of 14641?

12. What is the product of 1⁄2 of

of 13. If you pay 1253 dollars for 89 how much is that per basket?

of 23 into of 453?

baskets of peaches,

14. If 2133 barrels of beef cost 18357 dollars, how much is that per barrel?

15. How many times is 2 of 3 of 32 contained in 5631? 16. How often is 27 contained in 3 of 7 of 842?

17. What is the sum of 1563 and 833? What is their dif ference?

18. What is the product of of of 156, and 113? What is the quotient?

19. What is the sum, difference, product, and quotient of 2635, and 75% ?

20. What cost 353 cords of wood, at 32 dollars a cord? 21. What cost 68, tons of coal, at 65 dollars a ton?

22. At 173 dollars per week, how much will it cost a family to board 43 weeks?

23. A drover bought 45 cows, at 19 dollars apiece, and 68 oxen, at 395 dollars: how much did he pay for both?

24. If from of 10 of 781 miles, you subtract of of 163 miles, how many miles will be left?

25. If you divide 871⁄2 by 163, and multiply the quotient by 273, what will the product be?

26. If the sum of 8711 and 11719 is divided by their difference, what will be the quotient?

27. If the difference between 914 and 653 is multiplied by of the former, what will be the product?

28. If you pay 1883 pounds sterling for 168 tons of Liverpool coal, how much is that per ton?

29. A merchant paid 1468 pounds sterling for 1731 packages of goods: what was that a package?

30. If you pay of 7 of 43 cents apiece for pears, how many can you buy for of of 183 cents?

31. What number must be taken from 1851, that the difference may be 63 ?

32. What number must be taken from 2561, that the remainder may be 116?

33. By what number must 123 be multiplied, that the product may be 56 ?

34. What number must be multiplied by 153, that the product may be 561?

35. What number must be divided by 283, that the quotient may be 35?

36. What number must be divided by 371, that the quotient may be of of 8?

37. What number must be added to 26%, and the sum multiplied by 72, that the product may be 496 ?

38. Bought a piece of silk containing 963 yards, and having used of it, sold of the remainder, at 11 dollar a yard; the remnant was put at dollar a yard: how much did the parts sold come to?

39. A man having 561 tons of hay, sold of it at 10ğ dollars per ton, and the remainder at 93 dollars: how much did he receive for his hay?

40. A grocer bought 843 barrels of flour, at 53 dollars per barrel, and sold it at 61 dollars per barrel: how much did he gain?

41. What number must be multiplied by 453, that the product may be 171⁄2 times 123?

SECTION VII.

COMPOUND OR DENOMINATE NUMBERS.

ART. 145. SIMPLE Numbers are those which express units of the same kind or denomination; as one, two, three; 3 pears, 5 feet, 7 roses, &c.

COMPOUND Numbers are those which express units of different kinds or denominations; as the divisions of money, weight, and measure. Thus, 6 shillings and 7 pence; 7 feet and 3 inches, &c., are compound numbers.

Note.-Compound Numbers are frequently called Denominate Numbers.

FEDERAL MONEY.

146. Federal Money is the currency of the United States. Its denominations are Eagles, dollars, dimes, cents, and mills.

OBS. Federal Money was established by Congress, Aug. 8th, 1786. Previous to this, English or sterling money was the principal currency of the country.

146.a. The national coins of the United States are of three kinds, viz: gold, silver, and copper.

1. The gold coins are the eagle, the double eagle*, half eagle, quarter eagle, and gold dollar.*

The eagle contains 258 grains of standard gold; the double eagle, half eagle, and quarter eagle, like proportions.

2. The silver coins are the dollar, half dollar, quarter dollar, the dime, half dime, and three-cent-piece.t

The dollar contains 4121 grs.; the half dollar 192 grs.; the quarter dollar 96 grs.; the dime 38.4 grs.; the half dime 19.2 grs.

QUEST.-145. What are simple numbers? What are compound numbers? 146. What is Federal Money? What are its denominations? Recite the Table. Obs, When and by whom was it established? 146.a. Of how many kinds are the coins of the United States? What are they? What are the gold coins? The silver coins? By Act of Congress, Feb. 20th, 1949. † March 3d, 1851. Feb. 1859,

3. The copper coins are the cent, and half cent.

The cent contains 168 grains of pure copper; the half cent, a like proportion. Mills are not coined.

OBS. 1. The fineness of gold used for coin, jewelry, and other purposes, also the gold of commerce, is estimated by the number of parts of gold which it contains. Pure gold is commonly supposed to be divided into 24 equal parts, called carats. Hence, if it contains 10 parts of alloy, or some baser metal, it is said to be 14 carats fine; if 5 parts of alloy, 19 carats fine; and when absolutely pure, it is 24 carats fine.

2. The present standard for both gold and silver coins of the United States, by Act of Congress, 1837, is 900 parts of pure metal by weight to 100 parts of alloy. The alloy of gold coin is composed of silver and copper, the silver not to exceed the copper in weight. The alloy of silver coin is pure copper.

STERLING MONEY.

147. English or Sterling Money is the national currency of Great Britain. Its denominations are pounds, shillings, pence, and farthings.

4 farthings (gr. or far.) make 1 penny, marked

12 pence

20 shillings

21 shillings

d.

8.

1 pound, or sovereign, £.

66

1 shilling,

OBS. 1. It is customary to express farthings in fractions of a penny. Thus 1 qr. is written 4d.; 2 qrs, td.; 3 qrs., d.

2. The Pound Sterling is represented by a gold coin, called a Sovereign. According to Act of Congress, 1842, the value of a pound sterling is 4 Dollars and 84 cents. Its intrinsic value, according to assays at the United States Mint, is 4 dollars, 86 cents, and 1 mill. The legal value of an English shilling is 24 cents.

Note.-Most children have very erroneous and indistinct ideas of the weights and measures in common use. It is, therefore, strongly recommended for teachers to illustrate them practically, by referring to some visible object of equal magnitude, or by exhibiting the ounce; the pound; the linear inch, foot, yurd, and rod; also a square and cubic inch, foot, and yard; the pint, quart, &c.

QUEST.-The copper? Obs. How is the fineness of gold estimated? Into how many carats is pure gold supposed to be divided? When it contains 10 parts of alloy, how fine is it said to be? 5 parts of alloy? 2 parts? 4 parts? What is the present standard for the gold and silver coins of the United States? What is the alloy of gold coins? What of silver coins? 147. What is Sterling Money? What are its denominations? Repeat the Table. Obs. How are farthings usually expressed? How is a pound sterling represented? What is its value in dollars and cents? What is the legal value of an English shilling? How many farthings in 5 pence? How many farthings in 8d.? Ia 10d.? In 12d.? How many pence in 3 shillings? In 5s.? In 78.? In 11s.?

Note. It will be found profitable to drill the class in mental exercises like the preceding, upon each of the subsequent Tables.

TROY WEIGHT.

148. Troy Weight is used in weighing gold, silver, jewels, liquors, &c., and is generally adopted in philosophical experiments. Its denominations are pounds, ounces, pennyweights, and grains.

24 grains (gr.) make 1 pennyweight, marked put.

The carat, by which the weight and value of diamonds are estimated, is equal to 4 grains.

OBS. 1. The standard of Weights and Measures is different in different countries and in different States of the Union. In 1834, the Government of the United States adopted a uniform standard, for the use of the several custom houses and other purposes. Since that, many of the States have adopted the same.

1000

2. The standard unit of Weight adopted by the United States, is the Troy Pound of the United States Mint, which is equal to 22,794 cubic inches of distilled water, at its maximum density, the barometer standing at 30 inches, and is identical with the Imperial Troy pound of England, established by Act of Parliament, A. D. 1826.* The maximum density of water is at the temperature of about 40° Fahrenheit.-Olmsted's Philosophy.

3. Troy Weight was formerly used in weighing articles of every kind. It was introduced into Europe from Cairo in Egypt, about the time of the Crusades, in the 12th century. Some suppose its name was derived from Troyes, a city in France, which first adopted it; others think it was derived from Troy-novant, the former name of London.t

AVOIRDUPOIS WEIGHT.

149. Avoirdupois Weight is used in weighing groceries and coarse articles; as sugar, tea, coffee, butter, cheese, flour, hay, &c., and all metals, except gold and silver. Its denominations are tons, hundreds, quarters, pounds, ounces, and drams.

QUEST. 148. To what is Troy Weight applied? What are its denominations? Repeat the Table. Obs. When was Troy Weight introduced into Europe? From what was its name derived? Do all the States have the same standard of weights and measures? What is the standard unit of weight adopted by the Government of the United States? 149. In what is Avoirdupois Weight ised? What are its denominations? Repeat the Table.

* Hassler on Weights and Measures, p. 10. Also, Reports of the Secretary of he Treasury, March 3d, 1831; and June 20th, 1832.

† Hind's Arithmetic, Art. 224. Also, North American Review, Vol. XLV.