DIVISION OF VULGAR FRACTIONS. RULE. Prepare the given numbers (if they require it) by the rules of reduction, and invert the divisor, then proceed as in Multiplication. EXAMPLES. 1. Divide by 5×945 num. 3×20=60 den. 15. 20 2. Divide by . 3. Divide 672 by 135. 4. Divide 7935 24 by 18 5. Divide by 3 of 6. Divide of 16 by 7. Divide Facit. of ៖ .Facit 19 of by 3 of 8. Divide 9 by of 9. Divide by 4 10. Divide 16 by 24.... 11. Divide 5205 by of 91 -12. Divide 3 by 91. Facit 24. . THE SINGLE RULE OF THREE DIRECT, IN VULGAR FRACTIONS. ULE. Reduce the numbers as before directed in Reduction. State the question as in the Rule of Three in whole numbers, and invert the first term of the proportion, then multiply the three terms continually together, and the product will be the answer. EXAMPLES. 1. If ‡ of a yard cost 1⁄2 of a £. what will of a yard come to at that rate? yard yd. £. Ans. 15s. 2. If for 4×5X 9180 num. or -453 45/15 of a yard cost? Ans. 14s. 8d. what will 10 yards Ans. £...19...10 3. of 1s. buy? 4. If lb. costs. how many pounds will Ans. 1 lb. 216-27 12 ells cost at Ans. £7...0...85. 15 Ans. 3...0...9 160 3. If ell of Holland cost. what will that rate? 6. If 12 yards of cloth cost 15s. 9d. what will 48 cost at the same rate? 7. If of an cwt. cost 284s.. what will 7 cwt. cost at the same rate? Ans. £118...6...8. 8. If 3 yards of broad cloth cost £a...}, what will 10 yards cost? Ans. £9...12. 9. If of a yard cost of a £. what will of an ell English come to at the same rate? 7 Ans. £2. 10. If 1 lb. of cochineal cost £1...5, what will 36 lb. come Ans. £45...17...6. to? 11. If 1 yard of broad cloth cost 15s., what will 4 pieces cost, each containing 27 yards?? Aus, £...14...31 12. Bought 3 pieces of silk, each containing 24 ells, at 65....03. per ell, I desire to know what the whole quantity cost? -Ans. £25...17...2. SINGLE RULE OF THREE INVERSE, IN EXAMPLES. IF 48 men can build a wall in 24 days 4, how many men can Ans. 6 men 48 do the same in 192 days? 2. If 25s. will pay for the carriage of 1 cwt. 145 miles 1, how far may 6 cwt. be carried for the same money? Ans. 22 miles 3. If 31 yards of cloth, that is 1 yard wide, be sufficient to make a cloak, how much must I have of that sort which is yard wide, to make another of the same bigness? Ans. 43 yards. 1. If 3 men can do a piece of work in 4 hours, in how many hours will 10 meu do the same work? Ans. 1 hour. 5. If a penny white loaf weigh 7 oz. when a bushel of wheat cost 5s. 6d. what is the bushel worth when a penny white loaf weighs but 24 oz. ? 6. What quantity of shalloon that is yards of cloth that is 1 yard wide? Ans. 15s. 4d. t. yard wide will line 7 Ans. 15 yds. DOUBLE RULE OF THREE IN VULGAR FRACTIONS. EXAMPLES. Fa carrier receives £2 for the carriage of 3 cwt. 150 miles, how much ought he to receive for the carriage of 7 cwt. 3 qrs. 450 toiles? Ans. £1...16...9.. 2. If £100 in 12 months gain £6 interest, what principal will gain £33 in 9 months? Ans. £75. 3. If 9 students spend £107 in 18 days, how much will 20 students spend in 30 days? Ans. £39...18...4 360 4. A man and his wife having laboured one day, earned 4s. §, how much must they have for 10 days, when their two sons helped them? Ans. £.. 17...11. time will £11 Ans. 10 months. £141, what weight Ans. 15 cut. 5. If £50 in 5 months gain £2, what quire to gain £1}{ ? 6. If the carriage of 60 cut. 20 miles cost san I have carried 30 miles for £5? 130 n re (T. S.) Promiscuous Questions in Vulgar Fractions. In reducing a compound fraction to single one, the work may frequently be considerably shortened by cancelling the fractions; that is by dividing the numerator and denominator of any two terms by the same number. 1. Reduce & and to a common denominator. 150 to its lowest terms. 2. 3. 4. 5. 6. 7. 8. 9. 10. ཌ 25 to an improper fraction. of of to a single fraction. of of of one pound to its real value. 4920 of a pound to the fraction of a penny. to a fraction of the same value, whose numerator shall be 75. to a fraction of the same value, whose denominator shall be 100. 252 11. 27 273 12. 25 13. 14. 15. 16. 17. to a simple fraction. to a simple fraction. of a pound sterling to its proper quantity. 42d Add and together and of a pound sterling together. of a pound to g of a shilling. of of of a pound take of of a crown, 28. If of a yard cost of a pound, what will a yard cost? 29. 1f 6 be 194, what will 19 be? 30. An old gentleman spent half of his fortune, and left the re mainder to A. who spent half of it, and left the remainder to B, who spent one fifth of what he received, and left C& of the old gentleman's property, what sum had each person at the first if a had £1000? 31. A gentleman had nine sons and one daughter, to whom he left of his property, which was £50, and of what he received with his wife, whose fortune was of £4750. Now the eldest son was to have four times as much as the the youngest, and the daughter and the youngest but one were to have each half as much as each of the other six brothers, and each of the six received of the gentleman's fortune, what did each receive? 32 Reduce 33 Add 31. and § to a common denominator. and of a pound together. 35. Reduce to its lowest terms, to which add . 36. 1998 5005 to an improper fraction. 250 234 to its proper terms. of of g to a single fraction. of of to a single fraction. of a penny to the fraction of a pound. 12% of a pound to the fraction of a penny. to a fraction of the same value whose numerator shall be 15. to a fraction of the same value whose denominator shall be 20. 37. 38. 39. 40. 41. 42. 43. 44. of a pound to its proper quantity. 4d to the fraction of a shilling. 49. Add and together. 57. If of a yard cost of a pound, what will 58. I 3 yards of lace cost £13, what will 10 59. If of a yard cost 15s. what will 3 yards Divide 940 pounds, and four times the half of 30 pounds, in such a manner that A may receive of, and B may have of of what remained, and D to have what was left. 62. Place four 3's in such a manner that they will make just 34. 63. Divide 19 by 92 multiplied by 1 + 64. Add to 10. 65. If I lend my friend £34 for of a year, how much ought he to lend me for 5 of a year, in order that I may neither gain nor lose in the use of cash? 66. Reduce 5s. to the decimal, and also to the fraction of a pound. 67. 69. 2s. 6d. to the decimal, and also to the fraction of a pound. 10s. to half its value in decimals, and also in fractions. 69. Divide by TUTOR'S ASSISTANT. PART III. DECIMAL FRACTIONS. IN Decimal Fractions the integer or whole thing as one pound, one yard, one gallon, &c. is supposed to be divided into ten equal parts, and those parts into tenths, and so on without end. So that the denominator of a decimal being always known to consist of an unit, with as many cyphers as the numerator has places, therefore is never set down; the parts being only distinguished from the whole numbers by a comma prefixed: thus ,5 which stands for 10,25 for 25,,123 for 123 1000. But the different value of figures appears plainer by the following table: Whole numbers. Decimal parts. 2 3 4 5 6 7 7 6 Millions Tens. C Thousands. X Thousands. Thousands. -Units. Parts of Tens. Parts of Hundreds. Parts of X Thousands. From which it plainly appears, that as whole numbers in crease in a ten-fold proportion to the left hand, decimal parts decrease in a ten-fold proportion to the right hand: so that cy phers placed before decimal parts decrease their value, by removing them farther from the comma, or unit's place; thus,5 is 5 parts of ten, or ;,05 is 5 parts of 100, or;,005 is 5 parts of 1000, or to; 0005 is 5 parts of 10000, or 0 But cyphers, after decimal parts, do not alter their value. For,‚5, ,50, ,500, &c. are each but of the unit. 5 5 A FINITE DECIMAL is that which ends at a certain number of places; but an INFINITE is that which no where ends. A RECURRING DECIMAL is that wherein one or more figures are continually repeated, as 2,75222. And 52,275275275 is called a COMPOUND RECURRING de CIMAL. Note, a finite decimal may be considered as infinite, by making cyphers to recur; for they do not alter the value of the decimal. In all operations, if the result consists of several nines, reject them, and make the next superior place an unit more: thus for 26,25999 write 26,26. In all circulating numbers, dash the last figure, as in 86,54666. |