6 47. Reduce to a simple fraction. Ans. 12. 31 48. Reduce 51 to a simple fraction. Ans. 11. 6 144. To multiply complex fractions together. First reduce the complex fractions to simple ones ; (Art. 143 ;) then arrange the terms, and cancel the common factors as in multiplication of simple fructions. (Art. 136.) Obs. 1. The terms of the complex fractions may be arranged for reducing them to simple ones and for multiplication at the same time. 2. To divide one complex fraction by another, reduce them to simple fractions, then proceed as in Art. 139. 21 44 51. Multiply by 27 13 Operation. The numerator 2}=ž. (Art. 122.) Place the 7 on the right hand and 3 3 18 94 on the left of the perpendicular line. %1 The denominator 2*=, which must g 4,2 be inverted; (Art. 143;) i. e. place 3 8=2]. Ans. the 4 on the right and the 9 on the left of the line. 44=;, and 14= 1, both of which must be arranged in the same manner as the terms of the multiplicand Now, canceling the common factors, we divide the product of those remaining on the right of the line by the product of those on the lest, and the quotient is 23. (Art. 136. Ex. 43.) Quest.–144. How are complex fractions multiplied together? Obs. How is one complex fraction divided by another ? bushels of pears 1. At i dollar per many can be bought for 5 dollars ? 2. At f of a penny apiece, how many apples can be bought for 18 pence? 3. At of a dollar a pound, how many pounds of tea will 7 dollars buy ? 4. How many bushels of pears, at 1$ dollar a bushel, can be purchased for 15 dollars ? 5. How many gallons of molasses, at 2} dimes per gallon, will 10 dimes buy? 6. How many yards of satinet, at 1} of a dollar per yard, can be purchased for 20 dollars ? 7. At 4f dollars per yard, how many yards of cloth can be obtained for 25$ dollars ? 8. At 64 cents a mile, how far can you ride for 62} cents ? 9. At 12} cents a pound, how many pounds of flax will 67 cents buy ? 10. At 164 cents per pound, how many pounds of figs can you buy for 874 cents ? 11. How many cords of wood, at 6} dollars per cord, will it take to pay a debt of 67} dollars ? 12. How many barrels of beer, at 11 dollars per barrel, can be obtained for 951 dollars ? 13. A man bought 154 barrels of beef for 124, dollars : how much did he give per barrel ? 14. A man bought 131 pounds of sugar for 945 cents : how much did his sugar cost him a pound? 15 A lady bouglit 158 yards of silk for 1451a shil. lings : how much did she pay per yard ? 16. Bought 15$ baskets of peaches for 24+ dollars : how much was the cost per basket ? 17. Bought 304 yards of broadcloth for 1814 dollars : what was the price per yard ? 18. Paid 375 dollars for 125} pounds of indigo : what was the cost per pound ? 19. How many tons of hay, at 161 dollars per ton, can be bought for 196į dollars ? 20. How many sacks of wool, at 17$ dollars per sack, can be purchased for 1500 dollars ? 21. How many bales of cotton, at 157 dollars per bale, can be bought for 2500 dollars ? 22. Divide 1451a by 16. 23. Divide 1675 by 25. 24. Divide 8526 by 4516: 25. Divide 12563 by 681}. 26. Divide 853 by 18%. 27. Divide 105 by 8225 28. Divideof is by 6. 29. Divide 4 of 16 by f off 30. Divide of30 by 19. 31. Divide i of by 21. 32. Divide 11 of by of 31. 33. Divide 1 of i bys off. SECTION VII. COMPOUND NUMBERS. Art. 146. Numbers which express things of the same kind or denomination, are called simple numbers. Numbers which express things of different kinds or denominations, are called compound numbers. Thus 6 oranges, 5 dollars, 7 roses, &c. are simple numbers ; 5 pounds and 2 ounces, 7 feet and 3 inches, &c. are compound numbers. Obs. Compound Numbers, by some late authors, are called Denominate Numbers. QUEST.–146. What are simple numbers ? What are compound numbers ? STERLING MONEY. 147. Sterling Money is the national currency of England. 4 farthings (gr. or far.) make 1 penny, marked d. 1 shilling, 20 shillings 1 pound, or sovereign, £. 21 shillings 1 guinea. 12 pence S. qrs., & d. Obs. 1. It is customary, at the present day, to express farthings in fractions of a penny. Thus, 1 qr. is written 1 d.; 2 qrs., 5 d.; 3 2. The Pound Sterling is represented by a gold coin, called a Sovereign. According to Act of Congress, 1842, it is equal to 4 Dollars and 84 cents. MENTAL EXERCISES. 1. In 5 pence, how many farthings? Solution. Since there are 4 sarthings in 1 penny, in 5 pence there are 5 times as many ; 5 times 4 are 20. Ans. 20 farthings. 2. In 8 pence, how many farthings? In 10d.? In 12d. 3. How many shillings are there in 3 pounds ? In £5? In £8? In £10 ? 4. How many pence are there in 8 farthings? Solution. Since 4 farthings make 1 penny, 8 farthings will make as many pence as 4 is contained times in 8. 4 is contained in 8, 2 times. 5. How many pence in 12 qrs. ? In 15 qrs. ? In 20 qrs. ? In 25 qrs. ? . In 33 qrs. ? In 36 qrs. ? 6. How inany shillings in 15 pence? In 24d. ? In 30d.? In 36d.? In 60d.? In 68d.? In 750. ? 7. How many pounds in 25 shillings? In 30s. ? In 40s.? In 65s.? In 80s. ? In 89s. ? Ans. 2 pence. Quest.–147. What is Sterling Money? Repeat the Table. Obs. How are farthings usually expressed? How is a pound sterling represented ? What is its value in dollars and cents ? TROY WEIGHT. Note.—Most children have very erroneous or 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, yard, and rod; also a square and cubic inch, foot, and yard ; the pint, quart, gallon, peck, bushel, &c. 148. Troy Weight is used in weighing gold, silver, jewels, liquors, &c., and is generally adopted in philosophical experiments. 24 grains (gr.) make 1 pennyweight, marked pwt. 20 pennyweights 1 ounce, 12 ounces 1 pound, OZ. 16. Obs. 1. Troy Weight was formerly used in weighing articles of every kind. It was introduced into Europe about the time of the Crusades frorn Cairo in Egypt, and was first adopted by the city Troyes, in France, from which some suppose its name was derived. Others think it was derived from Troy-novant, the former name of London.* 2. The standard of Weights and Measures is different 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. 3. The standard unit of Weight adopted by the Government is the Troy Pound of the United States Mint, which is identical with the Imperial Troy pound of England, established by Act of Parliament, A. D. 1826.7 8. How many grains in 2 pennyweights ? In 3 pwts. ? in 4 pwts.? 9. How many pennyweights in 2 ounces? In 3 oz. ? In 4 oz.? In 5 oz. ? 10. How many ounces in 2 pounds? In 3 lbs. ? In 4 lbs. ? In 5 lbs.? In 6 lbs. ? In 7 lbs. ? In 10 lbs. ? Quest.-148. What is Troy Weight ? Repeat the Table. Obs. When was Troy Weight introduced into Europe ? From what was its name derived? Do all of the States have the same standard weights and measures? What is the standard unit of weight adopted by the government of the United States ? * Hind's Arith., Art. 224. Also, North Amer. Rev., Vol. XLV. † Hasler on Weights and Measures, p. 10. Also, Reports of Sec. Treas., March 3, 1831; and June 20, 1832. |