LESSON III. 1. If 1 half of a yard of cloth cost 5 cents, what will 2 halves, or a whole yard, cost ? 2. If 1 third of a yard of cloth cost 4 cents, what will 2 thirds of a yard cost? What will 3 thirds, or a whole yard, cost ? 3. If 1 fourth of a gallon of milk is worth 5 cents, what are 2 fourths of a gallon worth? 3 fourths? What is a gallon worth? 4. If 1 fifth of a bushel of apples is worth 10 cents, what are 2 fifths of a bushel worth? 3 fifths ? 4 fifths ? What is a bushel worth? 5. If 1 sixth of a bushel of wheat is worth 12 cents, what are 2 sixths of a bushel worth? 3 sixths? 4 sixths? 5 sixths ? What is a bushel worth? 6. If 1 seventh of a yard of silk cost 10 cents, what will 2 sevenths of a yard cost ? 3 sevenths ? 4 sevenths ? 5 sevenths ? 6 sevenths ? What will a yard cost ? 7. If 1 eighth of a pound of tea cost 7 cents, what will 2 eighths of a pound cost? 3 eighths? 4 eighths ? 5 eighths ? 6 eighths ? 7 eighths ? What will a pound cost ? 8. If 1 ninth of an acre of land is worth 12 dollars, what are 2 ninths of an acre worth? 3 ninths ? 4 ninths ? 5 ninths ? 6 ninths ? 7 ninths ? 8 ninths ? What is an acre worth? 9. If 1 tenth of a bushel of apples cost 10 cents, what will 2 tenths of a bushel cost? tenths? 4 tenths? 5 tenths ? 6 tenths ? 7 tenths ? 8 tenths ? 9 tenths? What will a bushel cost? 10. If 1 twelfth of a pound of gold dust is worth 16 dol lars, what are 2 twelfths of a pound worth? 3 twelfths? 4 twelfths ? 5 twelfths ? 6 twelfths ? 7 twelfths? 8 twelfths ? 9 twelfths ? 10 twelfths ? 11 twelfths ? What is a pound worth ? 11. If a yard of silk is worth 80 cents, what are 104 yards MULTIPLICATION AND DIVISION OF FRACTIONS. 87 a a day; LESSON IV. 1. When corn is worth 3 fourths of a dollar a bushel, how many dollars will 8 bushels cost? How many dollars will 12 bushels cost ? 2. If a boy can earn 3 fifths of a dollar in a day, how many dollars can he earn in 5 days? How many dollars can he earn in 10 days ? 3. A man worked 10 days for 6 fifths of dollar how many dollars did he earn in the 10 days ? 4. William paid 3 eighths of a dollar for a pair of gloves, and 8 times as much for a hat; how many dollars did he pay for his hat ? 5. A lady paid 7 eighths of a dollar for a pair of shoes, and 8 times as much for a bonnet; how many dol lars did she pay for her bonnet ? 6. A man paid 5 eighths of a dollar for a bushel of corn; how many dollars must be pay for 8 bushels ? 7. Mary is 10 years old, and her age is just 2 thirds the age of Susan; how old is Susan ? 8. A boy paid 10 cents for 5 sixths of a pound of rai what would a pound cost, at the same rate ? 9. A trader purchased a quantity of oats and corn; he paid 35 cents per bushel for the oats, which was 7 tenths as much as he paid per bushel for the corn. What was the price of the corn per bushel ? 10. A farmer paid 27 dollars for a cow, which was 3 eighths of what he paid for a horse ; how many dollars did he pay for his horse ? 11. A trader sold a gold watch for 96 dollars, which was 8 sevenths of what the watch cost him ; what the cost of the watch ? 12. Mary is 12 years old, and 5 sixths of Mary's age is 2 thirds of Caroline's age ; how old is Caroline ? 13. A piece of cloth containing 12 yards was sold for 60 dollars, which was 5 fourths of what it cost; what did it cost? What was the gain on each yard ? 14. A man sold a horse for 63 dollars, which was 7 eighths of what the horse cost him ; what was the cost of the horse? How much did he lose ? sins; was LESSON V. Fractions (or fractional parts of the same thing or number) having the same name or denominator are added and subtracted in the same manner as whole numbers are added and subtracted. 1. 1 half and 2 halves and 3 halves and 4 halves, less 6 halves, are how many halves? How many whole ones? 2. 2 thirds and 4 thirds and 5 thirds and 7 thirds, less 6 thirds, are how many many whole ones? 3. 3 fourths and 5 fourths and 6 fourths and 10 fourths, less 8 fourths, are how many fourths ? whole ones? 4. 2 fifths and 3 fifths and 4 fifths and 6 fifths, less 10 fifths, are how many fifths ? How many whole How many ones? 5. 8 sixths and 7 sixths and 5 sixths and 4 sixths, less 12 sixths, are how many many whole ones? 6. 3 sevenths and 4 sevenths and 5 sevenths and 9 sevenths, less 7 sevenths, are how many sevenths? How many whole ones? 7. 10 eighths and 9 eighths and 7 eighths and 4 eighths, less 6 eighths, are how many eighths? How many whole ones? 8. 4 ninths and 5 ninths and 6 ninths and 7 ninths and 8 ninths, less 3 ninths, are how many ninths ? whole ones? 9. 9 tenths and 8 tenths and 7 tenths and 6 tenths and 5 tenths and 3 tenths, less 8 tenths, are how many tenths? How many whole ones ? 10. 4 elevenths and 5 elevenths and 6 elevenths and 10 elevenths, less 3 elevenths, are how many elevenths ? How many whole ones? 11. 10 twelfths and 9 twelfths and 8 twelfths and 7 twelfths and 6 twelfths, less 4 twelfths, are how LESSON VI. When fractions having different names or denominators are to be added or subtracted, they must first be changed to fractions having the same name or denominator. This may be done by multiplying the numerator and denominator of one or both of the given fractions by such number as will produce the same number for a denominator of each fraction. 1. What is the sum of 1 and 1 ? What the difference ? =, and and a À, their sum. Á less 4 =4, their difference. 2. What is the sum of and ? What the difference ? f = is, and = i + 2 = 1 = 11, their sum. 12 12 their difference. 3. What is the sum of į and ş? What the difference ? 4. What is the sum of and į? What the difference ? 5. What is the sum of and g? What the difference? 6. What is the sum of and ģ? What the difference ? 7. What is the sum of and ? What the difference ? 8. What is the sum of į and ? What the difference? 9. What is the sum of and ? What the difference? 10. What is the sum of į and ? What the difference ? 11. Harriet purchased of a yard of cloth at one store, and I of a yard at another. How many fourths of a yard did she purchase ? how many yards ? 12. Augusta paid of all her money for a shawl, and } of it for a bonnet; what part of her money had she remaining ? 13. Henry purchased a pine-apple, and gave $ of it to his sister, and of it to his brother; what part of it had he left? 14. A man having undertaken to perform a job of work, did of it the first day, f of it the second day, and the remainder of it the third day; what part of it did he do the third day? 15. A market-woman sold õ of all her apples to one man, and } of them to another; what part of them had she remaining unsold ? 8* FEDERAL MONEY. Federal money is the national currency of the United States. The denominations of Federal money are, the eagle, E.; the dollar, $; the dime, d.; the cent, c.; and the mill, m. The gold coins are, the eagle, the double-eagle, the half-eagle, the quarter-eagle, and the dollar. The silver coins are, the dollar, the half-dollar, the quarter-dollar, the dime, the half-dime, and the three-cent piece. The copper coins the cent and the half-cent. 1 eagle =10 dollars. $. 1 dollar Ty of 1 eagle. 1 dollar = 10 dimes. d. 1 dime = 1 of 1 dollar. 1 dime 10 cents. 1 cent It of 1 dime. 1 cent =10 mills. 1 mill It of 1 cent. m. The following table exhibits the value of the fractional parts of one dollar, expressed in cents, which are in com mon use. C 26 of a dollar 5 cts. of a dollar 25 cts. It of a dollar 64 cts. of a dollar 33} cts. is of a dollar 8} cts. of a dollar 37) cts. It of a dollar 10 cts. of a dollar 50 cts. of a dollar 124 cts. of a dollar 624 cts. of a dollar 163 cts. of a dollar 75 cts. of a dollar 20 cts. } of a dollar 874 cts. In New York, and some other states, the denominations of money in common use are dollars, shillings, and pence; the dollar being equal to 8 shillings or 100 cents, the shilling 122 cents, and the penny 1 cent. 1 shilling, or of a dollar, = 124 cents. |