EXAMPLES. 1. Reduce 15s. 7d. 2qrs. to the decimal of a pound. Ans. ,78125-15s. 7d. 2qrs? 8. d. qrs. 15 7 2 0 DEM.-The reason of the first op peration is obvious, because the given sum reduced to the lowest denomination mentioned, stands as the numerator of the integer reduced to the same denomination for a denominator; the decimal or quotient must then bear the same proportion to the integer, as the given sum bears to the integer. In the last operation it is plain, that the quotient, 5 tenths, after the first division, bears the same proportion to a penny that two farthings bear to a penny, and so of the rest, consequently the principle is the same as in the first operation. 2. Reduce 9d. 3qrs. to the decimal of a shilling. Ans. ,8125. 3. Reduce 10s. 6d. to the decimal of a pound. Ans. 525. 4. Reduce 2qrs. 3na. to the decimal of a yard. Ans. ,6875. 5. Reduce 10cwt. 3qrs. 14lb. to the decimal of a tun. Ans. ,54375. 6. Reduce £14 12s. to a decimal expression. Ans. £14,6. 7. Reduce £47 15s. 6d. to a decimal expression. Ans. £47,775. 8. Reduce 3qrs and 2na. to the decimal of an Ell English. Ans. ,7 E. E. 9. Reduce 109 days, 12 hours to the decimal of a year. Ans. ,3 of a year. 10. Reduce 3qrs. 12lb. 5oz. 1,92dr. to the decimal of a cwt. Ans. ,86. 11. Reduce 5fur. 16pol. to the decimal of a mile. Ans. ,675 of a mile. 12. Reduce 7 calendar months, to the decimal of a year. Ans. ,625, of a year. QUESTIONS ON DECIMAL FRACTIONS. What is a decimal fraction? A. It is a fraction that has for its denominator, a unit, 1, with as many ciphers annexed as the numerator has figures, and is usually expressed by setting down the numerator only, with a point before it. What is a mixed number? A. It is made up of a whole number with some decimal fraction, one being separated from the other by a point. What is a pure decimal? A.Something less than a unit, 1, with a point at the left hand. Would a pure decimal become a unit by annexing significant figures at the right? A. It would not, a pure decimal, like certain mathematical lines which always approach each other, but never meet, may continually approach towards a unit, yet never become a unit, thus 9 tenths want one tenth of a unit,99 want one hundredth of being a unit, and ,999 want one thousandth of becoming a unit; so we might carry the decimal to any number of figures whatever: it would want something of being a unit, 1, and yet continually approaching towards a unit. How do you set down decimals for adding? A. According to the value of their places: tenths under tenths, hundredths under hundredths, &c. How do you point off, in addition of decimals? A. Directly below the given decimal points. How are numbers set down in subtraction of decimals? A. The same as in addition, and point off from the difference the same for decimals. How do you point off in multiplication of decimals? A. As many figures from the right hand of the product as there are decimal places in both the factors. When you multiply by a pure decimal, is the product greater or less than the multiplicand? A. Less, because it is repeating the multiplicand by something less than a unit, What proportion does the product bear to the multiplicand? A. The same proportion that the multiplier bears to a unit. How do you point off in division of deci mals? A. As many figures from the right hand of the quotient, as the decimal places in the dividend exceed those in the divisor. When you divide by a pure decimal, is the quotient greater or less than the dividend? A. Greater Why should it be greater? A. Beuause the divisor is less than a unit, and it is evident, that the dividend will contain a part oftener than a whole. What proportion does the dividend bear to the quotient? A. The same proportion as the divisor bears to a unit. If you divide 10 by one tenth, what will be the quotient? A. 100. If you multiply 10 by one tenth, what will be the product? A. One. How do you reduce a vulgar fraction to a decimal? A. By dividing the numerator by the denominator. How do you reduce inferiour denominations to the decimal of a superiour denomination? A. I reduce the given sum to the lowest denomination mentioned for a dividend, and then reduce an integer to the same denomination for a divisor, and the quotient will be the decimal required. How do you find the value of a decimal in the inferiour denominations of the integer? A. By multiplying the decimal by the inferiour denominations of the integer, the same as in reduction descending, and pointing off from the products in each place as many figures for decimals as will equal the decimals in the given number; the figures at the left of the decimal points will be the value of the fraction in the inferiour denominations of the integer. REDUCTION OF CURRENCIES. Reduction of Currencies is finding the value of the coin or currency of one state or country in that of another. Although the same denominations and coin are generally used in the different countries and states, yet the standard value frequently differs in each. Thús, a dollar is reckoned in New York, Canada, and 89. called New York currrency. 6s. called New England currency. 4s. 8d. called Georgia currency. 7s. 6d. called Pennsylvania currency. 4s. 6d. called English or Sterling money 59. called Canada or Halifax currency. To reduce the currency of each state to Federal money. RULE.-Divide the given sum, reduced to shillings, to sixpences, or to pence, by the number of shillings, sixpences ar pence in a dollar, as it is reckoned in each state. EXAMPLES. 1. Reduce £96 New York currency to federal money. Ans. $240. £ 20 8)1920 $240 Ans. DEM. It is plain, if we reduce the given sum, and a dollar to the same denomination, and divide by the number of shillings in a dollar the quotient will be the answer, because it shows how often Ss. or 1 dollar can be subtracted from the given sum, and so on, when it is reduced to the inferiour denomination. 2. Reduce £109 3s. 8d. New England currency to fedAns. $363,94cts. 4 mills. eral money. NOTE. A dollar in New England is the same as a dollar in New York, but, a shilling or a pound in New England is more than a shilling or pound in New York; four shillings and 6d. are a dollar in England, consequently a shilling in England, is more than a shilling in New York, and £1 in England, more than a pound in New York. 3. Reduce £103 New York currency to federal money. Ans. $257,50cts. 4. Reduce £103 New England currency to federal money. Ans. $343,33cts. 3 mills. 5. Reduce £127 10s. 5d. New England currency to federal money. Ans. $425,06cts. 9 mills. 6. Change £104 12s. New York currency to federal Ans. $261,50cts. 7. Change £380 New York currency to federal money. S. Change £37 10s. Pennsylvania money. 9. Reduce £125 5s. Pennsylvania money. money. Ans. $950. currency to federal Ans. $100. currency to federal Ans. $334. 10. Reduce £73 16s. 4d. Georgia currency to federal money. Ans. $316, 35cts. 7 mills. 11. How many dollars are equal to £44 1s. 4d. Georgia ? currency: Ans. $188,85cts. 7 mills. 12. How many dollars are equal to £35 6s. Georgia ? Ans. $151, 28cts. 5m. currency 13. Reduce £5 9s. Od. 1 farthing English currency to federal money. Ans. $24,22cts. 6m. 14. Change £22 10s. English or Sterling money to federal money. Ans. $100. 15. Change £5 6s. 6d. 1qr. Canada currency to federal money. Ans. $21,30cts. 4m. 16. How many dollars are equal to £270 17s. 6d. Canada currency. Ans. $1083,50cts. 17. Change £25 Canada currency to federal money. Ans. $100. To change Federal Money to the currency of each state. RULE.-Multiply the given sum in cents, by the number of pence ín a dollar, and cut off two figures to the right of the product; those at the left hand, will be the answer in pence; and if the figures thus cat off at the right hand, be multiplied by 4, and two figures again cut off, those at the left hand will be farthings. EXAMPLES. 1. Change $135,50 cents, to New York currency. Ans. £54 4s. $cts. 135,50 96 81300 121950 12)13008,00 210)108|4 Ans. £54 4s. DEM.—It is plain, that every hundred cents in New York currency, must be diminished four in number to change them into pence, because 96 pence are equal to 100 cents; and multiplying by 96, and cutting off two of the right hand figures, lessens the given number 4 on every 100 though it retains the same value; cutting off two figures is divi ding the product by 100. NOTE. When there are mills in the given sum, multiply the same as when the given sum is in dollars and cents, and cut off three figures at the right for a decimal; then proceed exactly as in the first and second examples. cy. 2. Change 155 dollars, 9 cents to New England currenAns. £46 10s. 6d. 2qr. nearly. |