CASE V. To subtract compound numbers. 1. From 1 of a £. take of a £. Value of 11 £. = 12s. 8d. | 33 common denominator. Value of ; £. 4s. 5 d. 24 Ans. 8s. 313d. 11 To perform this question, we find by Case X. Sect. 13 XI. the value of 1£.=12s. 33 8id.; and also of £. =4s. 5}d.; we then find a common denominator of the fractional part, by multiplying together their denominators, 11 and 3=33 ceed as in Case II., Sect. XIII. Hence the following We then pro RULE. Find the value of the fractions in integers; then subtract as in the foregoing rules. а a a 2. From í of a ton take of a cwt. Ans. Iqr. 26lb. 14oz. 108 dr. 3. From į of an ell English take ã of a yard. Ans. 3qr. Ona. 24in. 4. From of a mile take 1 of a furlong. Ans. 1fur, 5rd. 10ft. 10in. 5. From of a degree take of a mile. 을 ៖ a Ăns. 49m. Ofur. 13rd. 11ft. 9in. 1gbar. 6. From i of an acre take of a rod. 言 Ans. 1R. 17p. 22yd. 2ft. 108in. 7. From i of a cord take i of a cord. Ans. 91ft. 1602jgin. 8. From is of a hhd. of wine there leaked out of it; what remained? Ans, 6gal. 3qt. Opt. 1gi. 9. From Boston to Concord, N. H. the distance is 72 miles; having travelled of this distance, how much remains ? Ans. 30m. 6fur. 34rd. 4ft. 8in. 1 bar. 10. From of a year take of a week. Ans. 101da. 5h. 54m. 174sec. 11. From t of an acre take of a foot. Ans. 1R. 18p. 5yd. 4ft. Oin. a a SECTION XIV. MULTIPLICATION OF VULGAR FRACTIONS. CASE I. OPERATION. To multiply one fraction by another. 1. If 1 apple cost of a cent, what will 2 apples cost? 3? 2. If 1 orange cost 1{ cents, what will 2 cost? 3? 4? 5? 3. If 1 pound of sugar cost | of a dollar, what will 2lbs. cost? 3? 4? 5? 6? 7? 8? 9? 10? 4. If 1 pound of chalk cost of a cent, what cost 2lbs.? } 5. Multiply ] by 7X3 21 Ans. 8 X 5 When one number is multiplied by another, it is evident, that the multiplicand is repeated as many times as there are units in the multiplier. The multiplier in this case is ß. The multiplicand, I, being less than a unit, is therefore to be repeated 3 times. If, therefore, we multiply the denominator, 8, by 5, we make the fraction to be to, which is only of the value of 3. If we now multiply the last numerator, 7, by 3, we shall increase its value 3 times; that is, a is 3 times the value of %, and is of z. We may therefore analyze the question and say, 1 of y=%; and of ] is 3 times=ixt =*; therefore % is of 3. Hence the following RULE. Prepare the fractions as in Addition, and multiply the numerators for a new numerator, and the denominators for a new denominator; if the result be an improper fraction, reduce it to its equivalent whole number. 57 6. Multiply it by 3. 7. Multiply = by 238. Multiply : by . 9. Multiply is by 1. 10. Multiply i by 4. 11. Multiply by 18. Ans. 3. 12. Multiply 1: by 1. Ans. 4. Ans. 3. 13. Multiply by 8. 14. Multiply to by 17tt. Ans. 151. Ans. 635. 15. Multiply s by 714. Ans. 10084 16. Multiply 87 by 113. Ans. 31368 17. Multiply 16113 by 1925. Ans. 78%. 18. Multiply 4 of 94 by 1 of 17. Ans. 403}. 19. Multiply 1 of 7 by it of 874. Ans. 264. 20. Multiply 7 by 3%. 21. Multiply 8 by z. Ans. 6. 22. Multiply 12 by 4. Ans. 84. 23. Multiply 15 by i. Ans. 8. 24. A merchant owns of a ship; he sells i of his share to A. What part is that of the whole? Ans. 22. CASE II. OPERATION. To multiply a mixed number by a whole number. 1. Multiply 7 by 9. In performing this question, we multiply the 5 of 7 the numerator by the multiplier, 9, and find the 9 product to be 45. This product we divide by 8, 68% the denominator of the fraction, and find the quo tient to be 5, which we carry to the product of 9 times 7. The remainder, 5, we write over the divisor, 8. Hence the following RULE. Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction, and as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, anything remains, let it be a numerator and the divisor a denominator to a fraction to be affixed to the product. 2. Multiply 87 by 7. Ans. 603. Ans. 82. 7. Multiply 237 by 11. Ans. 2575. 8. Multiply 47 \ by 15. Ans. 7091 9. Multiply 37% by 18. Ans. 679. 10. Multiply 67813 by 24. Ans. 16294. 11. What will 23pounds of lead cost, at 8 cents a pound? Ans. $ 1.91. 12. What will 154 pounds of sugar cost, at 12 cents a pound? Ans. $1.885 13. What will 29% cwt. of hay cost, at $ 1.12 per cwt.? Ans. $32.943. 14. What will 9% yards of broadcloth cost, at $ 8 per yard? $ Ans. $79.00. 15. What will 1776 tons of potash cost, at $ 97 per ton? Ans. $ 1703.561 16. What will 311 tons of plaster of Paris cost, at $ 12.75 Ans. $ 40.18Ms. 17. What will 17. dozen candles cost, at 16 cents a dozen? Ans. $ 2.783. 18. What will 273 pounds of bar soap cost, at 7 cents a pound? Ans. $ 1.913. 19. What will 297 dozen of axes cost, at $ 11.62 per dozen? Ans. $343.75. 20. Bought 28 bales of cotton cloth, each bale containing 314 yards; what will be the cost, at 16 cents per yard? Ans. $ 140.56. per ton? 59 112* $ SECTION XV. DIVISION OF VULGAR FRACTIONS. CASE 1. To divide one fraction by another. 1. If 2 peaches cost of a cent, what will 1 peach cost? 2. If 1 orange cost 3 apples, what part of an orange will 1 apple buy? 3. If is of a yard of cloth cost 1 dollar, what will of a yard cost? \ yard? 4. A certain teacher divided | an orange between 8 of his pupils; what part did each receive? 5. A quarter of a dollar is divided equally between 4 persons, what part does each receive? 6. Among how many boys, must 8 apples be distributed to give each of an apple? 1 / OPERATION. 7. Divide 4 by . 1x==131 Ans. By multiplying the numerator of the dividend 4, by the denominator of the divisor 8, the dividend is reduced to eights; and then by multiplying the denominator of the dividend, 7, by 3, the numerator of the divisor, one third of the eights are taken. Hence we deduce the following RULE. Prepare the fractions as in Addition; incert the divisor, and proceed as in Multiplication. Ans. 1185 23 775 Ans. 36 407 Ans. 1158 Ans. . 4940 8. Divide ; by s. BX ==* Ans. 9. Divide ii by . Ans. 1. 10. Divided by is. Ans. 13 11. Divide , by . Ans. .. 12. Divide it by 11. 13. Divide is by 14. Ans. 68 175 14., Divide zi by is. Ans. 114. 15. Divide is by 74. 16. Divide i by 16%. 17. Divide 11by 4. Ans. 20. 18. Divide 214 by 184. 19. Divide 171 by 2836. 20. Divide 161 by. 145. Ans. 1172 21. Divide 11 of 1 by of it. Ans. 12. 22. Divide, of 7 i by i of 17%. 23. Divide , of 15 by is of 22. Ans. 675 24. Bought of a coal mine for $3675, and having sold of it, I gave of the remainder to a charitable society, and divided the residue between 7 poor persons; what was the share of each? Ans. $ 50 for each poor person. 25. Of an estate valued at $ 5000, the widow receives 1, the oldest son of the remainder; the residue is equally divided between 7 daughters; what is the share of each daughter? Ans. $15845 49 Ans. 3850 1305 |