What 2. Bought a hat for 5 D.; a vest for 2D. 12 c. 5 m.; a coat for 15 D.; and a pair of boots for 6 D. 50 c.: did they all cost? Ans. $28.625 3. Bought a quantity of goods in New-York for 575 D. 62 c. 5 m.; paid for carting the goods to the dock 1D. 25 c.; for freighting the same to Bridgeport 5D 7c.; for carrying the same to New-Milford 5 D. 25c.; and my own expenses were 10D. 12c. 5 m.: How much do the goods stand me in at New-Milford? Ans. $597.32 4. Suppose I am indebted To A twenty-six dollars, fifty cents, C sixty dollars, four cents, five mills, E two hundred dollars: How much is the amount of my debts? Examples in Subtraction of Federal Money. 1. From 85 D. subtract Ans. $296.03 $85. 4.082 4D. 8 c. 2m. Ans. $80.918 2. A merchant bought a quantity of goods for 485 D. 50 c., and afterwards sold the same for 557 D.: how much did he gain by the sale? Ans. $71.50 3. Suppose the effects of a bankrupt amount to $2000, and he owes to A 1250 D.; to B 875 D. 78 c.; to C 271 D. 18c.; and to D 40D. 75 c.: What is the deficiency? Ans. $437.71 4. From twenty-one cents take three mills. Ans. $.207, or 20 c. 7m. 5. A has an account against B, to the amount of one hundred dollars and ten cents; and B pays him forty-two dollars twelve and a half cents in cash, and agrees to give his note for the remainder-for what sum must the note Ans. $57.975 be drawn? 3. What do 20 barrels of flour amount to, at 5 D. 25 c. per barrel? $5.25×20=$105, Ans. 4. What do 174 bushels of wheat amount to, at 1 D. 20 c. a bushel? 174×$1.20 $208.80, Ans. 5. What is the value of 48.75 acres of land, if each acre be worth 15 D. 25 c.? Ans. $743.4375, or 743D. 43c. 7.5m. Note. When there are figures to the right hand of the place of mills, they are decimal parts of a mill, and of too little value to be retained in ordinary calculations. 15. Find the amount of the articles in the following bill. Note. When there is only one decimal figure in the quotient, (found by dividing any number of dollars,) it is dimes, or tenths of a dollar; and, to reduce it to cents, a cipher must be annexed; as in the foregoing example. 2. Bought 250 lb. of cheese, for 16 D. 25 c.: what did it cost me a pound? $16.25-250-$.065-6 c. 5 m. 6 c. Ans. 3. If a contribution of $27000 is to be made up in equal shares, by 625 persons, how much must each contribute? Ans. $43.20 4. Suppose a man labors a month for 12D.; how much does he have a day; there being 26 working days in a month? Ans. 46 c. 1 m.+ 5. The canal of Languedoc, in France, is 180 miles long, and cost $2400000: how much is that per mile? Ans. $13333.33+ 6. The salary of the President of the United-States is $25000 a year: how much is it a day, allowing 365.25 days to make a year? Ans. $68.446+ 7. Bought a quantity of wheat, at $1.25 per bushel, which amounted to $375. How many bushels of wheat did I buy? Ans. 300 bush. REDUCTION OF DECIMALS. CASE I. To reduce a vulgar fraction to its equivalent decimal. RULE. Divide the numerator by the denominator, as in division of decimals, and the quotient will be the decimal fraction required. EXAMPLES. 1. Reduce to its equivalent decimal. 8)1.000 Ans. .125 Note. In dividing after the manner of short division, you may suppose ciphers to be annexed to the numerator, and perform the operation without setting down the ciphers; as in the next following example. ? ? 4)3. Ans. .75 Ans. .5 Ans. .25 Ans. .666, &c.. Ans. .0833, &c. 4. Reduce to a decimal. 3 40 ? Ans. .075 Ans. .0035 3846+, .6875, and .00472+ Answers, CASE II. To find the value of a decimal fraction of any of the higher denominations of Money, Weight, or Measure, in whole numbers in the lower denominations. RULE. Multiply the given decimal by the number which 1 of that denomination makes of the next lower, and point off the proper number of decimal places in the product, as in Multiplication of Decimals. In like manner reduce the decimal part, (if any,) of this product to the next lower denomination; and so proceed through all the inferior denominations, if necessary then the last product, together with the integers, (or numbers at the left hand of the decimal points,) in the other products, will be the answer. Note 1.-This Case is similar to Reduction Descending, and the following Case to Reduction Ascending, in whole numbers. Explanation of example 1st.-I first multiply the given decimal of a pound by 20, to reduce it to shillings, and the product is 15.500 shillings. I then multiply the decimal of a shilling, viz. .500, by 12, to reduce it to pence, and the product is 6 d.; and there being no decimal of a penny to reduce to farthings, the work is done. So the answer is 15 s. 6d. What is the value, or proper quantity, 3. Of .625 of a shilling? Ans. 7d. 2q., or 7 d. 4. Of .03125 of a mile? 5. Of .125 of a foot? 6. Of .50625 of an acre? 7. Of .1875 of a sq. foot? 8. Of .125 of a cord of wood? 9. Of .182 of a gallon of wine? 10. Of .21 of a day? 11. Of .015 of a degree? Ans. 10 rods. Ans. 1in. 1.5 b. c. Ans. 2 roods, 1 sq.rd. Ans. 27 sq. in. Ans. 16 cub. ft. Ans. 1 pt. 1.824 gil. Ans. 5 h. 2 min. 24 sec. Ans. 54". Note. The addition and subtraction of decimals of different denominations, may be performed after the decimals are reduced to their proper quantities; as in the following examples. 12. What is the sum of .17 of a lb. Troy, and .87 of an ounce, reduced to their proper quantities? oz. pwt. gr. .17 lb. 2.. 0..19.2 .87 oz.- 17.. 9.6 Ans. 2.. 18..4.8 13. What is the sum of .15lb. Avoirdupois, and .25 oz.? Ans. 2 oz. 10.4 dr. L |