table, we shall obtain the value of £1 in dollars. Consequently, we deduce this RULE. I. Reduce the shillings and pence, if any, to a decimal of a pound, by Rule under Art. 99. 11. Multiply the pounds and decimals, if any, by the fractions of the preceding table, after inverting them; the products will be in dollars and decimals of a dollar. By what fraction must we multiply Sterling money to reduce it to Federal money What fraction do we multiply by to reduce Georgia currency to Federal money ? By what do we multiply to reduce Canada currency? By what to reduce New England currency? By what to reduce Pennsylvania currency? By what to reduce New York currency? EXAMPLES. 1. Reduce £75 15s. 6d. of the respective currencies mentioned in the preceding table, to Federal money. £75 15s. 6d. £75-775, which multiplied by the respective fractions 40, 30, 4, 40, 4, and 4, gives the following answer: Ans. £75 15s. 6d. New England currency 252-58. 2. Reduce £80 5s. 3d. of the different currencies to Federal money. 3. Reduce £1000 of the different currencies to Federal Ans. £1000. Canada currency New England currency= 3333 3331. = = 2500. 106. The following are the rates at which some of the foreign coins are estimated at the custom-houses of Florin or Guilder of the United Netherlands $0.40. Thaler of Prussia and N. States of Germany $0.69. Pound of British Provinces, Nova Scotia, New Brunswick, Newfoundland, and Canada. $4.00. 107. The quotient arising from dividing one quantity by another of the same kind or denomination, is called a ratio. Thus, the ratio of 12 to 2=2=6. 12 to 32-4. 12 to 4-2-3. 12 to 6-2-2. 12 to 12=1=1. Hence, we see that the ratio of two quantities shows how many times greater the one is than the other. It is therefore evident, that there cannot exist a ratio between two quantities of different denominations. There is no ratio between 12 feet and 3 pounds, for we cannot say how many times 12 feet is greater than 3 pounds. But there is a ratio between 12 feet and 3 feet, which is There is the same ratio between 12 pounds and 3 pounds. The ratio is itself an abstract number; it is not a denominate number. The ratio of 12 feet to 3 feet is 4 units simply; it is neither 4 feet nor 4 pounds, but simply 4 times 1; showing that 12 feet is 4 times as great as 3 feet. In this way we find The ratio of 10 yards to 5 yards ==2. = =2. 8 inches to 4 inches When the ratio of two quantities is the same as the ratio of two other quantities, the four quantities are in proportion. Thus, the ratio of 8 yards to 4 yards, is the same as the ratio of 12 dollars to 6 dollars; therefore, there is a proportion between 8 yards, 4 yards, 12 dollars, and 6 dollars. The usual method of denoting that four terms are in proportion, is by means of points, or dots. Thus, the above proportion is written 8 yards 4 yards: 12 dollars: 6 dollars; in which two dots are placed between the first and second terms, and between the third and fourth; and four dots between the second and third. The proportion is read 8 yards is to 4 yards as 12 dollars is to 6 dollars. Of these four terms, the first and fourth are called extremes; the second and third are called means. Since in a proportion the quotient of the first term divided by the second, is equal to the quotient of the third term divided by the fourth, we have, using the above proportion, 8 yards 12 dollars) 4 yards 6 dollars If we reduce these fractions to a common denominator, (ART. 40,) they will become 8×6 4x6 12 × 4 or, omitting the com mon denominator 4×6, which is in effect multiplying each fraction by 4×6, we have 8×6 or 48=12×4 or 48; that is, the product of the extremes is equal to the product of the means. 8×6=48 = 12. Hence, if the product of the extremes be divided by either mean, the quotient will be the other mean. 12×4 -8. Hence, if the product of the means be divided by either extreme, the quotient will be the other extreme. From the above properties, we see that if any threeof the four terms which constitute a proportion are given, the remaining term can be found. 108. The method of finding the fourth term of a proportion, when three terms are given, constitutes the RULE OF THREE. |
