3. Reduce $1000 to equivalent values in the different 105. To reduce a sum in either of the above currencies o Federal money. It is obvious, that by inverting the fractions which express the value of $1 in pounds, as given in the preceding 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 3 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. =£ ̃5·775, which multiplied by the respective fractions 4o, 3o, †, o, §, and §, gives the following answer: Ans. £75 15s. 6d. New England currency= 252.58. Pennsylvania currency 202-06₤. 2. Reduce £80 5s. 3d. of the different currencies to Federal money. 3. Reduce £1000 of the different currencies to Federal 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 3=24. 12 to 4-2-3. 12 to 6=2=2. 12 to 12=+=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. there is a ratio between 12 feet and 3 feet, which is But 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. 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 place between the first and second |