.375 100 37.500 10 5.000 2. What is the value of .1361 of a £.? 3. What is the value of .235 of a day? Ans. 28. 8d. Ans. 5 hours 38min. 24sec. 4. What is the value of .42 of a gallon? Ans. 1qt. 1.36pt. 5. What is the value of .253 of a shilling? Ans. 3.036d. 6. What is the value of .436 of a yard? Ans. 1gr. 2.976na. 7. What is the value of .9 of an acre? Ans. 3R. 24P. RULE OF THREE IN DECIMALS. Rule. State the question as the rule of three in whole num bers, only observe, when you multiply and divide, to place the decimal points according to the rules of multiplication and division of decimals. Question. How do you perform operations in the rule of three in decimals? Examples. 1. If 4.2lb. of coffee cost 8s. 2.3d., what cost 639.25lb.? 2. When 1.4 yard cost to, at the same price? Ans. 13s., what will 15 yards come Ans. £6 19s. 3d. 1.71gr. 3. If I sell 1 qr. of cloth for 2 dollars 34.5 cents, what 18 it per yard? Ans. $9 38cts. 4. A merchant sold 10.5 cwt. of sugar, for 108.30 dollars, for which he paid 84 dollars 39.12 cents: what did he gain per cwt. by the sale? Ans. $2 27cts. 7m.-t 5. How many pieces of cloth, at 20.8 dollars per p'ece, are equal in value to 240 pieces, at 12.6 dollars per piece? Ans. 145.38+ pieces.. 6. If, when the price of wheat is 74.6 cents per oushel, penny roll weighs 5.2 oz., what should it be per bushel when the penny roll weighs 3.5 oz.? Ans. $1 10cts. 8m.+ the POSITION. By this rule, we are able to discover true numbers, by working with supposed ones as though they were real. Position is of two kinds, Single and Double. Single Position is when it is necessary to make use of only one supposed number; Double Position is when it is necessary to make use of two supposed numbers. SINGLE POSITION. Rule. 1. Suppose a number, and work with it as though it was the real one, and observe the result.-Then, 2. As the result of that operation, Is to the supposed number, So is the number given, To the number required. DOUBLE POSITION. Rule. 1. Suppose a number, and work with it as directed in the question, as though it were a real number, until you obtain the result, which will be the error. 2. Suppose some other number, and proceed in the same way to find a second result or error. 3. Multiply the first result or error by the second supposed number, and the second result or error by the first supposed number. 4. Observe whether the errors are both of the same kind; i. e. both too great, or both too little. 5. If the errors are alike, divide the difference of the products by the difference of the errors, and the product will be the true number or answer. But if the errors are one too great and the other too little, divide the sum of the products by the sum of the errors, and the product will be the true number or an How many kinds of Position are there? When is Double Position used? What is first to be done, when you commence an operation by Single Position? After having ascertained the result of the operation, how do you proceed? How do you first proceed, when commencing an operation in Double Position? After having obtained the first error, how do you proceed? When you to be done? have obtained the second error, what is then What have you to consider, after you have multiplied the second supposition by the first error, and the first supposition by the second error? When you have observed whether the errors are both of the same kind, how do you proceed, if they are both of the same kind? But if they are not both of the same kind, how do you proceed? SINGLE POSITION. Examples. 1. A gentleman having received a number of coins, 1 says,,,, and of the number is 87: what number of coins was there? Suppose he had 180 2. A certain box contains a number of dollars, 1, 1, 1, of which is 690: how many was in the box? and Ans. 1200. 3. The ages of A., B., and C. amount to 133 years; B. is older than C., and A. is older than B.: what are 183 their separate ages? Ans. A. 56, B. 42, and C. 35yr. 4. A person bought 3 pipes of wine for 350 dollars; No. 1 cost double the sum that No. 2 did, and No. 2, three times the price that No. 3 did: what was the price of each? Ans. No. 1, $210; No. 2, $105; No. 3, $35. 5. A gentleman being asked his age, replied, if the years of my life were doubled, and three-fifths of the product divided by 3, the result would be 14: what was his age? Ans. 35 years. 6. A person lent a sum of money at 53 per cent. simple interest, and at the expiration of 4 years and 8 months he received for interest £201 5s.: what was the sum lent? Ans. £750. 7. A cistern has two cocks to supply it with water; by the first it may be filled in 45 minutes, and by the second in 55 minutes; it has likewise a discharging cock, by which it may, when full, be emptied in 30 minutes: if these 3 cocks be left open, in what time will the cistern be filled? Ans. 2h. 21m. 25 sec. DOUBLE POSITION. 1. Bought cloth for a cloak, at 6 dollars per yard, and baize to line it at 1 dollar; the number of yards was 12, and the cost 42 dollars: how many yards were there of each? First, suppose there were 8 yards of cloth, at $6=48 42 proof. 2. A. and B. receive the same salary: A. saves onethird of his every year, but B., by spending 250 dollars per annum more than A., finds at the expiration of 7 years that he is 350 dollars in debt: what is their income, and what does each spend per annum? Their income, $600. 650. 3. A labourer engaged himself for 50 days, on condition that for every day he worked he should receive 1 dollar, but for every day that he was idle he should for N |