201 10 How many dollars in 300£? In 900£? A $4000. 14. What will 1 ton of clover-seed cost, at 5 mills an ounce› A. $179,20. 15. At 2 cents an inch, what will 1 yard of cloth cost? A 72 cents. 16. Reduce 1 tun to gills. A. 8064 gills. 17. Reduce 20 bushels to pints. A. 1280 pints. 13. Reduce 4 tons to drams. A. 2293760. 19. How many barley-corns will reach across the Atlantic Ocean, allowing it to be 3000 miles? A. 570240000. 20. How many times will a watch click in 20 years, if it click at the usual rate of 60 times in a minute? A. 631152000. 21. A father left legacies to his children as follows: to Thomas, 75£ 14 s 6 d., to William 3 times as much as Thomas, to his daughter Mary as much as Thomas, and to Susan, his youngest child, as much as all the rest, lacking 20£ 13 s. 8 d., how much did each receive? A. William 227 3 s. 6 d., Mary 12£ 12 s. 5 d., Susan 294£ 16s. 9 d. 1827. Mr. Charles Testy 15. To Lewis P. Child, Dr. Jan. 1. To 3 yds. Linen Cloth, at 1 s. 6d. a yard, Feb. 28. Mar. 9. £25 18 s. 3 d. Halifax, April 1, 1827. Received payment, Lewis P. Child. FRACTIONS. ¶ XXXIV. 1. If one third () of an apple cost 2 cents, 2 If one third cost 3 cents, what will a whole one cost? If cents? 3. If you pay 3 cents for one fifth (†) of an orange, what will a whole orange cost? 4. If you pay 2 dollars for one eighth () of a ticket, wha will a whole ticket cost? Q. How many halves to an apple, or any thing? Q. How many thirds? Fifths? Eighths? Sixteenths? Q. When an apple, or any thing, is divided into two equa parts, would you call one of these parts a half or a third? Into 3 equal parts, what is one part called? Q. Into 4 parts, what is one part called? Q. When an apple, or any thing, is divided into two equal parts, how would you express one part, on the slate, in figures? A. I set the 1 down, and draw a line under it; then write the 2 under the line. Let me see you write down, in this manner, on the slate, one half. One third. One fourth. One fifth. One sixth. Two sixths. Three sixths. Three eighths. Eight twelfths. Q. What are such expressions as these called? A. Fractions. Q. When, then, any whole thing, as an apple, a unit, &c. is broken or divided into equal parts, what are these parts called? A. Fractions. Q. Why called fractions ? A. Because fraction signifies broken. Q. You have seen, that, when any whole thing is divided in to 3 parts, these parts are called thirds; into 4 parts, callea Fourths: what, then, does the fraction take its name or `denëmination from? 1. From the number of parts into which any thing is divided. Q. When an apple is divided into 6 parts, and you are de sirous of giving away 5 parts, how would you express these parts? A. . Q. What is the 6 (in †) called ? A. The denominator. Q. Why so called? A. Because it gives the name or de nomination to the parts. Q. What is the 5 (in †) called? A. Numerator. Q. Why so called? A. Because it numerates or numbers the parts. Q. Which is the numerator, then? A. The number above the line. " Which is the denominator? A. The number below the line. Q. What, then, does the denominator show? A. The number of parts a unit, or any thing, is divided into. 103 Q. What does the numerator show? A. How many parts are taken, or used. Q. In the expressions, 18, 1, o, which are the numerators, and which are the denominators ? Q. If you own of a vessel, how many parts is the vessel supposed to be divided into? and how many parts do you swn? 1. 40 parts, and I own 28 parts. Q. Is of an apple more than of it? Q. What fraction, then, is greater than? Than? Than Q. From these remarks, what appears to be a correct definition of fractions? 7. They are broken parts of a whole num ber.. Q How are they represented? A. By one number placed above another, with a line drawn between them. Q. In Simple Division, you recollect, that the remainder was represented in like manner; what, then, may justly be considered the origin of fractions? A. Division. Q. What may the numerator be considered? A. The divi dend. Q. What may the denominator be considered? A. The di visor. Q. What, then, is the value of a fraction? A. The quotient of the numerator divided by the denominator. Q. What is the quotient of 1 dollar divided among Q. What is the quotient of 7 divided by 8? Q. What does express ? A. The quotient, of which A. f. men? A. By the sign 2 is the dividend. 3 is the divisor. 1. If 3 apples be divided equally among 8 boys, what part of one apple will each boy receive? be of an apple apiece, and 3 apples would be 3 times as 1 apple among 8 boys would much; that is, of an apple apiece 2. If 4 oranges be divided equally among 8 boys, what part Ans. f. of an orange is each boy's part? 1 orange among 8 boys , and 4 oranges are 4 times as much; that is, t, Ans. If oranges among 7 boys? A. 4. 9 oranges among 13 boys? 20 oranges among 37 boys? 3. One orange among 2 boys is of an orange apiece; ho. much is 1 divided by 2, then? Ans. . How much is 1 divided by 3? A. The quotient of 5 divided by 6? A. t. Of 3 by 5? Of 7 by 9? Of 8 by 13? Of 11 by 15? 4. What part of one apple is a third part of 2 apples? A third part of one apple is, and a third part of 2 apples must be twice as much; that is, of 1 apple. A. 3. 5. What part of 1 apple is one fourth (1) part of 3 apples? op apples is of 3 apples is 3 times as much as of apple; that is, & of 6. What part of one apple is of 3 apples? A. . What part of 1 apple is † of 4 apples? A. . t of 4 apples is what part of 1 apple? Ans. †. A PROPER FRACTION. Q. We have seen that the denominator shows how many parts it takes toʻmake a whole or unit; when, then, the numerator is less than the denominator, is the fraction greater, or less, than a whole thing or unit ? A. It must be less. Q. What is such a fraction called? A. A Proper Fraction. Q. How may it always be known? A. The numerator is less than the denominator. Q. What kind of fractions are 4, 4, 7, &c.? AN IMPROPER FRACTION. Q. When the numerator is us large, or larger than the denominator, as, §, 1f., it is plain, that the fraction expresses 1 whole, or more than 1 whole, what is such a fraction called A. An Improper Fraction. Q. How may it be known? A. The numerator is greater than the denominator. Q. What kind of fractions are §. 42, §, &c A MIXED NUMBER. Q. What is a mixed number? A. A fraction joined with a whole number. Q. What kind of fractions are 15, 16, &c. What kind of fractions are cach of the following expres sions, viz. 15, 21, 81, 8, 7, 5? 1 XXXV. To change an Improper Fraction to a Whole or Mixed Number. 1. How many whole apples are there in 6 thirds () of an apple? In 8 quarters ()? In ? In ? In 2? In ? In 488 ? 2 How many weeks in 4 of a week? In ? In 47 ? In 4! In $? 3. How many pints in gills? In 32 gills In 4 gills/ In 12 gills' 4. How much is of a dollar? A. $1. Is ? A. 1 and == 14. Is ? Is ? Is 17? Is 24? Is 25? Q. What is the finding how many whole things are contain ed in an improper fraction called? A. Reducing an improper fraction to a whole or mixed number. 1. James, by saving of a dollar a day, would save in 33 days; how many dollars would that be? OPERATION. 16)33 Ans. 2 dollars. In this example, as + make 1 dollar, it is plain, that as many times as 16 is contained in 33, so many dollars it is. 16 is contained 2 times and 1 over; that is, 21 dollars. RULE I. What, then, is the rule for reducing an improper fraction to a whole or mixed number? A. Divide the numerator by the denominator. More Exercises for the Slate. 2. A regiment of soldiers, consuming of a barrel of pork a day, would consume in 28 days of a barrel; how many barrels would that be? 9. 53 barrels. 3. A man, saving of a dollar a day, would save in 365 days 265; how many dollars would that be? A. $73. 4. Reduce 18 to a mixed number. A. 20. 5. Reduce 6. Reduce 7. Reduce 8. Reduce 6384 to a mixed number. A. 7219. to a mixed number. A. 43. 9. Reduce to a mixed number. 4. 2314. 272 10. Reduce 17 to a whole number. A. 144. ↑ XXXVI. To reduce a Whole or Mixed Number to an Improper Fraction. 1. How many halves will 2 whole apples mɛke? Will 4? Will 6? Will 20? Will 100? 2. How many thirds in 2 whole oranges In 3? In 34 In 8? In 12? Will 3 In 2? In 2 |