2. Borrowed 10 English guineas at 28s. each, and 24 English crowns at 6s. and 8d. each; how many pistoles at 22s. each will pay the debt? Ans. 20. 3. Four men brought each 177. 10s. sterling value in gold into the mint, how many guineas at 21s. each must they receive in return? Ans. 66 guin. 14s. 4. A silversmith received three ingots of silver, each weighing 27 ounces, with directions to make them into spoons of 2 oz. cups of 5 oz. salts of 1 oz. and snuff boxes of 2 oz. and deliver an equal number of each; what was the number? Ans. 8 of each, and 1 oz. over. 5. Admit a ship's cargo from Bordeaux to be 250 pipes, 130 hhds. and 150 quarter casks [hhds.] how many gallons in all; allowing every pint to be a pound, what burden was the ship of? Ans. 44415 gals. and the ship's burden was 158 tons, 12cwt. 2qrs. 6. In 15 pieces of cloth, each piece 20 yds. how many French Ells? Ans. 200. 7. In 10 bales of cloth, each bale 12 pieces, and each piece 25 Flemish Ells, how many yards? Ans. 2250. 8. The forward wheels of a wagon are 14 feet in circumference, and the hind wheels 15 feet 9 inches, how many more times will the forward wheels turn round than the hind wheels, in running from Boston to New-York, it being 248 miles? Ans. 7167. 9. How many times will a ship 97 feet 6 inches long, sail her length in the distance of 12800 leagues and ten yards? Ans. 2079508. 10. The sun is 95,000,000 of miles from the earth, and a cannon ball at its first discharge flies about a mile in 7 seconds; how long would a cannon ball be, at that rate in flying from here to the sun? Ans. 22yr. 216d 12h. 40m. 11. The Sun travels through 6 signs of the Zodiac in half a year; how many degrees, minutes and seconds? Ans. 180deg. 10800min. 648000sec. 12. How many strokes does a regular clock strike in 365 days, or a year? An's. 56940. 13. How long will it take to count a million at the rate of Ans. 333h. 20m. or 13d. 21h. 20m 50 a minute? 14. The national debt of England amounts to about 279 millions of pounds sterling; how long would it take to count this debt in dollars (4s. 6d. sterling) reckoning without intermission twelve hours a day at the rate of 50 dollars a minute, and 365 days to the year ? Ans. 94 years, 134 days, 5 hours, 20 min. FRACTIONS. FRACTIONS, or broken numbers, are expressions for any assignable part of a unit or whole number, and (in general) are of two kinds, viz. VULGAR AND DECIMAL, A Vulgar Fraction, is represented by two numbers pla ced one above another, with a line drawn between them, thus,,, &c. signifies three-fourths, five-eighths, &c. The figure above the line, is called the numerator, and that below it, the denominator, Thus {{ 5 Numerator. The denominator (which is the divisor in division) shows how many parts the integer is divided into ; and the numerator (which is the remainder after division) shows how many of those parts are meant by the fraction. A fraction is said to be in its least or lowest terms, .when it is expressed by the least numbers possible, as when reduced to its lowest terms will be, and is equal To abbreviate or reduce fractions to their lowest terms. RULE. Divide the terms of the given fraction by any number which will divide them without a remainder, and the quo tients again in the same manner; and so on, till it appears that there is no number greater than 1, which will divide them, and the fraction will be in its least term, To find the value of a fraction in the known parts of the integer, as to coin, weight, measure, RULE. &c. Multiply the numerater by the common parts of the integer, and divide by the denominator, &c. EXAMPLES. What is the value of of a pound sterling ? 1 2. What is the value of 1 of a pound sterling? Ans. 188. 5d. 2fqrs. 8 Reduce of a shilling to its proper quantity. 4. What is the value of 5 What is the value of 1 of a shilling? of a pound troy? Ans. 4 d. How much is of n hundred weight? Ans. 3qrs. 7lb. 10,20% 7. What is the value of of a mile ? 8. How much is of n cwt.? Ans. 6fur. 26p0. 11ft. Ans. 3qrs. 3lb. 1oz. 12§dr 9. Reduce of an Eil English to its proper quantity. Ans. 2qrs. 3 na 10. How much is of a hhd. of wine? 11. What is the value of of a day? 13 Ans. 16h. 36min. 55,sec. PROBLEM III. To reduce any given quantity to the fraction of any greater denomination of the same kind. RULE. Reduce the given quantity to the lowest term mentioned for a numerator; then reduce the integral part to the same term, for a denominator; which will be the frac tion required. EXAMPLES. 1. Reduce 13s. 6d. 2qrs. to the fraction of a pound. 20 Integral part 13 6 2 given sum, 2. What part of n hundred weight is 3qrs. 14lb. ? 3qrs. 14lb.=98lb. 3. What part of a yard is 3qrs. 3na.? Ans. Ans. 1 Ans. 2 4. What part of a pound sterling is 13s. 4d.? Ans. 3= 6. What part of a mile is 6fur. 26pò. 3yds. 2 ft. ? fur. po. yds. ft. feet. 6 26 3 2=4400 Num. Ans. 4411 7. Reduce 7oz. 4pwt. to the fraction of a pound troy. Ans. What part of an acre is 2 roods, 20 poles? Ans. 9. Reduce 54 gallons to the fraction of a hogshead of wine. Ans. Ans. 10. What part of a hogshead is 9 gallons? 11. What part of a pound troy is 10oz. 10pwt. 10grs.? DECIMAL FRACTIONS. Ans. 유동 A Decimal Fraction is that whose denominator is a unit, with a cipher, or ciphers annexed to it, Thus, fo, 15, T5, &c. &c. The integer is always divided either into 10, 100, 1000, &c. equal parts; consequently the denominator of the fraction will always be either 10, 100, 1000, or 10000,&c. which being understood, need not be expressed; for the true value of the fraction may be expressed by writing the numerator only with a point before it on the left hand thus, is written,5; 45%,45; 725% 725, &c. But if the numerator has not so many places as the denominator has ciphers, put so many ciphers before it, viz. at the left hano, as will make up the defect; so write r thus,,05; and thus,,006, &c. 10 NOTE. The point prefixed is called the separatrix. Decimals are counted from the left towards the right hand, and each figure takes its value by its distance from the unit's place; if it be in the first place after units, (or separating point) it signifies tenths; if in the second, hundredths, &c. decreasing in each place in a tenfold proportion, as in the following NUMERATION TABLE. |