PROBLEM V. To find the Value of any decimal of a pound (£) by Inspection. RULE. Double the first figure, or figure of tenths, for shillings; then if the second figure be 5, or more, deduct 5 from it, and reckon another shilling; then call the remaining figures in the second and third places so many farthings, subtracting I when they are above 12, and 2 when they are above 36. EXAMPLES. 1. Find the value of ,785 of a pound. Double 7, the first figure, or tenths, for s. 14s. Then the second figure being more than 5, we deduct 5 from it, and add 1 to the shillings. Then the remaining figures, 35, we call so many qrs.; abating 1 because they are more than 12 and less than 36, leaves 34qrs. And 34qrs. 8d. 2qrs. 1s. 66 66 66 66 8d. 2qrs. Ans. 15s. 8d. 2qrs. Ans. 17s. 6d. 2. Reduce,875 of a pound to shillings, pence and farthings. 3. Reduce ,095 of a pound to its proper quantity. Ans. 1s. 103d. 4. Find the value of £,230. Note. When the decimal has but two places of figures, annex a cipher to it, or suppose a cipher to be annexed. 5. Find the value of ,76 of a pound. 6. Find the value of ,34 of a pound. 7. Find the value of ,95 of a pound. Questions. 1. What is a Decimai Fraction? 2. How is the integer divided? 3. How is the true value of a decimal fraction expressed? 4. If the numerator has not so many places as the denominator has ciphers, how do you write it? 5. By what does each figure take its value? What is the first figure on the Ans. 15s. 24d. right hand of units, or the separatrix? -the second?-the third ?-the fourth? &c. 6. What effect do ciphers have when placed on the right of decimals? 7. When placed on the left, what effect do they have? 8. On what does the magnitude of a decimal fraction depend? 9. How are decimals read? 10. When whole numbers and decimals are expressed in the same number, what is it called? 11. What is the Rule for Addition of decimals?-for Subtraction? 12. What is the Rule for Multiplication of decimals? 13. What is the Rule for Division of decimals? tion to its equivalent decimal? II. How do you reduce quantities of several denominations to a decimal of the highest? III. How do you find the decimal of any number of pounds, shillings, pence and farthings, by Inspection? IV. How do you find the value of a decimal in whole numbers of a lower denomination? V. How do you find the value of any I. How do you reduce a Vulgar frac- decimal of a pound by Inspection? REDUCTION OF CURRENCIES. Formerly the pound was of the same value in Great Britain and all the American Colonies, (now States,) and the dollar reckoned at 4s. 6d. But the Legislatures of the different States issued bills of credit, which depreciated in their value, in some States more, and in others less, which caused the currencies of the several States to differ from each other. Thus, a dollar is reckoned In the New England States, also Virginia, Kentucky, and Tennessee, at 6s. called New England currency. In New York, North Caroli- at 8s., called New York na and Ohio, currency. In N. Jersey, Pennsylvania, at 7s. 6d., called PennsylDelaware and Maryland, S In South Carolina and Geor gia, } } vania currency. at 4s. 8d., called Georgia currency. In Canada and Nova Sco- Į at 5s., called Canada cur tia, PROBLEM I. rency. To reduce the currencies of the several States in which a dollar is an even number of shillings, to Federal money, 1. When the sum consists of pounds only, annex a cipher to the pounds, and divide by half the number of shillings in a dollar, the quotient will be dollars, &c. 2. If the sum consists of pounds, shillings, pence, &c. reduce the pounds and shillings to shillings, and the pence and farthings to the decimal of a shilling; annex this decimal to the shillings, with a point between; then divide the whole by the number of shillings in a dollar, and the quotient will be dollars, cents, mills, &c. EXAMPLES. 1. Reduce £348, New England currency, to Federal money. 3)3480 Ans. $1160 Annexing a cipher to £348 reduces them to tenths of pounds=3480 tenths. Then a dollar, New England currency, 3 tenths of a pound. And 3480 tenths, divided by 3 tenths, the quotient is 1160 dollars. is 2. Reduce £145, New York, &c., currency, to Federal money. 4) 1450 362,5 is We annex a cipher to the pounds, as before; then a dollar in this currency 8 of a pound,£,4. Therefore we divide by 4, and the quotient is 362 dollars; and to the remainder we may annex a cipher, and divide, which gives Ans. $362 50cts. 3. Reduce £25 6s. 83d., New England currency, to Federal money. 50 cents. £25 6s. 6)506,7291 84,4548+ 43 128,75 ,7291 Ans. $84 45cts. 4m. This sum, consisting of pounds, shillings, pence, &c., we reduce the pounds and shillings to shillings, and the pence and qrs. to the decimal of a shilling and divide by the number of shillings in a dollar. 4. Reduce £56 11s. 91d., New York currency, to Federal 5. Reduce £35 11s. 6d., Connecticut currency, to Federal money. Ans. $118 58c. 3m.+ 6. Reduce £28 11s. 6d. Virginia currency, to Federal money. Ans. $95,25. 7. Change £419 10s. 8d., New York and Ohio curAns. $1048 83c. 8m.+ rency, to Federal money. 8. Reduce £721 9s. 114d., Massachusetts money, to Federal money. Ans. $2404 98c. 9m.+ 9. Change £145, New York, &c., currency, to Federal money. Ans. $362 50cts. 10. Change £134, New England currency, to dollars. Ans. $446 66c. 6m.+ 11. Reduce £14 6s. 4 d., New York, &c., currency, to Federal money. Ans. $35 79c. 68m.+ 12. Reduce £9 11s. 4d., New England currency to Federal money. Ans. $31 88c. 8m.+ PROBLEM II. To reduce New Jersey, Pennsylvania, Delaware and Maryland currencies to Federal money. RULE. Reduce the shillings, pence, &c., to the decimal of a pound; annex this decimal to the pounds; then multiply by 8 and divide the product by 3, the quotient will be dollars, &c. EXAMPLES. 1. Reduce £41 19s., Pennsylvania currency, to Federal money. 41,95 8 3)335,60 Ans. $111,862 19s. reduced to the decimal of a pound, (by Inspection, see Rule, page 106,) are equal to £,95, &c. A dollar, this currency, is 7s. 6d. 90d. and a pound 240d., and 24; therefore a dollar is of a pound, and to divide by, we X by 8 and÷by 3. 90 0 2. Reduce £14 6s. 8d., New Jersey, &c., currency, to Federal money. Ans. $38 22c. 2m. + 3. Change £9 6s. 3d. to Federal money. Ans. $24,833. 4. Reduce 19s. 113d. to Federal money. Ans. $2 66c. 1m.† Ans. 48dols 5. Reduce £18 to Federal money. 6. Reduce 18 Pennsylvania shillings to Federal money Ans. 2dols. 40cts 7. Reduce £25 13s. 41d. to Federal money. Ans. 68dols. 45cts PROBLEM III. To reduce South Carolina and Georgia currency to Fed eral money. RULE. I. Reduce the shillings, pence, &c. to the decimal of å pound, as in problem 2. Then multiply by 30, and divide the product by 7; the quotient will be dollars, &c. EXAMPLES. 1. Reduce £45 19s. Georgia currency, to Federal money. vide by the numerator. Ans. $47 85cts. 6m.+ 3. Reduce 18 Georgia shillings to dollars, &c. Ans. $3 857+ 4. Change £918s. 61. South Carolina currency, to Federal money. Ans. $42 54 4+ 5. How many dollars, &c. is there in 12s. 6d. South Carolina currency. Ans. $2 67 84. 6. Reduce £28 19s. to Federal money. Ans. $124 07+ 7. Reduce £94 14s. 8d. to Federal money. PROBLEM IV. Ans. $405 99 8+ To reduce Canada and Nova Scotia Currency to Federal money. |