OF THE SINGLE RULE OF THREE DIRECT, IN VULGAR FRACTIONS. "How is the Rule of Three in Fractions performed? A. The operation of the Rule of Three in Fractions, both Single and Double, Vulgar and Decimal, are exactly agreeable to the principles laid down in the same rules in Whole Numbers. lb? Q. How are the following examples proved? A. By changing the order of them. EXAMPLES. 1. If lb. of sugar cost of a shilling, what cost Answer, s. 4d. 3qrs. 43. 2912 Ans. 15s 8d 38 Ans. 18s 100. 2. If ell cost. what cost 1 ell? 3. If ell cost. what cost 1 ell? 4. If 2 oz. silver cost 15s 5d. what cost oz. Answer, 6s id 3qrs 2. 5. If 6 yards cost 18s. what cost 9 yards ? Ans. 17. 5s. 7d. 1qr32. 6. If I dollar be worth 563d. what are 500 dols. worth? Answer, 1177 18s 4d. 7. If 1 yd cost 9s. what cost 16 yds ? Ans. 5l 17s. 8. If pistole be 17s., what are 100 pistoles? A. 867. 9. If oz. cost 1. what cost 1 oz ? Ans. 1 5s 8d. 10. If an ingot of silver weighs 16 oz. 1, what is it worth at 5s 6d. per oz.? Answer, 4l 12s od 1qr 23. 11. If C. cost 147. 4s. what will 7C. cost? 1187. 6s. 8d. Ans. 12. If of an ell cost of 19s. what cost 7 ells ? Answer, 71 7s 9d 1qr 3. 13. If 8lb of tobacco cost 4s 9d, what cost 1lb? Answer, 7d. 14. If lyd. broad cloth cost 15s, what will 4 pieces each containing 27 yards cost? Ans. 85/ 10s 1d. & 15. A mercer bought 3 pieces of silk, each containing 24 yards at 68 od per yard-I demand the value of the 3 pieces at that rate? Answer, 257 14s 6d 2qr 42. 16. If lb. less by cost 13d, what cost 14 lb. less by of 2 lb ? Answer, 498 od 23. 17. A merchant had 5C he would barter for tea, at 8s much tea must be given for the sugar? Ans. 431 491. 18. Bought 120 lb. of tea at 8s 70/ what was the gain per cent? Ans. 351 58 3d 3qrs 7743. sugar, at 6d 2 per lb. which per b. T demand how per lb. and sold it for OF THE SINGLE RULE OF THREE IN VERSE, IN VULGAR FRACTIONS. 1 IF F 34 yards of cloth, that is 1 yard wide, be sufficient to make a cloke; how much must I have of that sort which is of a yard wide, to make a cloke of the same bigness? Answer, 47 yards. 2. If 16 men finish a piece of work in 28 days, how long will 12 men require to do the same work? swer, 37 3. If 36 days. An yard in breadth require 20 yards long to make a garment; what length will of a yard wide require to make the same? Answer, 344 4. How many pieces of merchandize, at 20s.per pieee, are to be given for 240 pieces 4, at 128.2 per piece? Answer, 149, 34 pieces. wide, 5. How many yards of canvas that is 1 yard will be sufficient to line 20 yards of Say, that is of a yard wide? Answer, 12 yards of canvas. OF THE DOUBLE RULE OF THREE IN VULGAR 1 FRACTIONS. IF 9 F9 students spend 101 in 18 days; how much will 20 students spend in 30 days? Ans. 391 18s 4d-300 ៖ 2. Three men having worked 19 days, received 8l. , how much must 20 men have for 100 days 1? Answer, 3051 Os 8d Tg. 96 3. A man and his wife having laboured 1 day, earned 4s. ; I demand how much they must have for 10 days when their two sons helped them? Ans. 4. 17s. ląd. 4. A man with his family, which in all were 5 persons, did usually drink 7 gallons of beer in a week; how much will be drank in 22 weeks, when 3 persons more come into their family? Answer, 280 40 gallons. .0 5. Seven men with their wives, upon examining into their expences for 20 weeks past, found that they laid out 401; I demand in what time 2013 may be spent by 46 men in like proportion; Answer, 3 weeks 3938 63688* 6. Three sailors having been aboard 9 months 1, received 401; I demand how much 100 sailors must receive for 28 months service? Answer 4118/ 6s od 1qrs 1403. 1165Ç་ THE SCHOOLMASTER'S ASSISTANT. PART III. . OF DECIMAL FRACTIONS. WHAT do you understand by Decimals in general? A. Any thing which is called one; as one foot, one pound one shilling, one year, &c. is conceived in imagination to be divided into ten equal parts, and every one of those parts into ten other equal parts, and so on, by a Decimal Division without end. Q. What is a decimal Fraction? A. Any number having a point placed before it, thus, .641 is a decimal. Q. How do you distinguish a whole number from a Decimal Fraction? A. Any number having a point placed after it, thus, 641. is a whole number. Q. What is a mixt number? A. Any quantity of figures having a point placed somewhere between them, thus, 6.4), or thus, 64.1, is a mixt number. Note. The Decimal points must never be omitted; because without it, a Decimal cannot be distinguished from a whole or mixt number. But when a whole number alone is given, it is as common to omit it as to insert it; as appears by several Examples following. Q. OF NOTATION OF DECIMALS. How do Decimal places increase ? A. In the same manner as whole wumbers do: that is by tens; for every place towards the left hand is ten times greater than that which is next it towards the right hand, as appears by the following table. M Q. May not Cyphers sometimes be annexed to Decimals ? A. They may, but they alter not their value: Thus, .44 and 4100 are the same. Q. May not Cyphers sometimes be prefixed to Decimal Parts? A. Yes; and then they decrease their Value by removing them farther from the point: thus .004l is less than .41. OF ADDITION AND SUBTRACTION OF DECIMALS. Q. How OW are Decimals added or subtracted? A Place the numbers according to their value, and work as in addition or Subtraction of whole numbers. Q. How are the operations proved? A. As in whole numbers. are Decimals multiplied? A. As whole numbers are. Note 1. When numbers are Multiplied, make as many decimal parts in the product as there are in two Factors taken together. 2. If Decimal places are wanted in the product, supply them with cyphers to the decimal point. 3. Observe the same Note here, which is given in Multiplication of Vulgar Fractions. Q. How are the following examples proved? EXAMPLES. 1 Multiply .612 by 4. 12 8 Multiply .00041 by .0007 9 Multiply .0027 by 41. 10 Multiply 410. by .0012 11 Multiply .07 by .07 12 Multiply 1.007 by .04! 13 Multiply 4.001 by .004 14 Multiply 004 by .004 |