14. The national debt of England amounts to about 279 milions of pounds sterling; how long would it take to count this debt in dollars (<s. 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 À Vulgar Fraction, is represented by two numbers picaed one above another, with a line drawn between them, thus, 1, 1, &c. signifies three-fourths, five eights, &c. The figure above the line, is called the numerator, and that below it the denominator, 5 Numerator. Thus, { 8 Denominator: 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 the least or lowest terms, when it is expressed by the least numbers possibļe, as $ when reduced to its lowest terms will be i, and it is equal to 4, &c. PROBLEM I. 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 quotients 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 terms. Ans. } EXAMPLES. 1. Reduce 146 to its lowest terms. (3) (2) -8) 4=*=*= the Answer. 2. Reduce 19; to its lowest terms. Ans. 3. Reduce th to its lowest terms. Ans. 4. Reduce its to its lowest terms. Ans. $ 5. Abbreviate 44 as much as possible. Ans. if 6. Reduces to its lowest terms. Ans. 7. Reduce 44* to its lowest terms. Ans. } 8. Reduce o to its lowest terms. 9. Reduce it to its lowest terms. Ans. 18 10. Reduce it to its lowest terms. Ans. PROBLEM II. To find the value of a fraction in the known parts of the integer, as to coin, weight, measure, &c. RULE. Multiply the numerator by the common parts of the integer, and divide by the denominator, &c. IAMPLES. 1. What is the value of g of a pound sterling ? Numer, 2 20 shillings in a pound. 3 Denom. 3)40(13s. 4d. Ans. 3 10 1 12 5)1204 12 2. What is the value of tf of a pound sterling? Ans. 188, 5d. 2 13 qrs. 3. Reduce $ of a shilling to its proper quantity; Ans. 410 4. What is the value off of a shilling? Ans. 4;d. $. What is the value of t of a pound troy? Ans. Daz 3a. 6. How much is of a hundred weight ? Ask-. 3qrs. 716. 1020z. 7. What is the value of of a mile ? Ans. 6fur. 26 po. 11ft. 8. How much is of a cwt. ?" Ans. 3qrs. 3lb. loz 124dr. 9. Reduce of an Ell English to its proger quantity Ans. 207 10. How much is 4 of a hhd. of wrine? Ans. 54gal. 11. What is the value of n of a day? Ans. 16h. 36min. 55 Ksec, 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. 1. Reduce 133. 6d. 2qrs. to the fraction of a pounds. 20 Integrel part 13 6 2 given sum. 12 12 EXAMPLES. 960 Denominator. 650 Num. Ans. ht=4*£. 2. What part of a hundred weight is 3qrs. 141b. ? 3qrs. 1416.=9816. Ans. if= 3. What part of a yard is 3qrs. 3na. ? Ans. if 4. What part of a pound sterling is 13s. 4d.? Ans. Í 5. What part of a civil year is 3 weeks, 4 days? Ans. 3 6. What part of a mile is 6fur. 26po. 3yds. 2ft. fur. po. yds. ft. feet. 6 26 3 2=4400 Num. a mile =5280 Denom. Ans. 444= 7. Reduce 7oz. 4pwt. to the fraction of a pound troy. Ans. 8. What part of an acre is 2 roods, 20 poles ? Ave. 6 9. Reduce 54 gauons to the traction of a hogshead of Ans. Wine. 10. What part of a hogshead is 9 gallons ? Ans. } 11. What part of a pound troy is 10oz. 10pwt: 10grs Ans: 449 DECIMAL FRACTIONS. A D cimal Fraclion is that whose denominator is unit, with a cypher, or cyphers annexed to it, Thus, 160item, &c. &c. The integer is always divided either into 10; 100, TO00, &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; tum ,45; 786 ,725, &c. But if the numerator has not so many places as the denominator has cyphers, put so many cyphers before • it, viz. at the left hand, as will make up the defect; so write it, thus, ,05 ; and, co thus, ,006, &c. Note. The point prefixed is called the separatrix, Decima's 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 he in the first place after writs, for separating point) ii signifies tentirs; it in the second, . hundredths, &c. decreasing in each place a tenfold proportion, as in the following NUMERATION TABLE. Miljions. Tens, parts.' X. Thousandth 76 Decimals. Cyphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure continues to possess the same place : so ,5 50 and ,500 are all the same value, and equal to ió or . But cyphers placed at the left hand of decimals, decrease their value in a tenfold proportion, by removing them further from the decimal point. Thus, ,5,05,005, &c. are five tenth parts, five hundredth parts, five thousandth parts, &c. respectively: It is therefore evident that the magnitude of a decimal fraction, compared with another, does not depend upon the number of its figures, but upon the value of its first left hand figure: for instance, a fraction beginning with any figure less than ,9 such as ,899229, &c. if extended to an infinite number of figures, will not equal ,9. 1. Place the numbers whether mixed or pure decimals, under each other, according to the value of their places. 2. Find their sum as in whole numbers, and point off 80 many places for the decimals, as are equal to the greatest number of decimal parts in any of the given numbers EXAMPLES 1. Find the sum of 41, 653+36,05+24,009+1,6 $41,653 Thus, 36,05 24,003 ? 1,6 Şum, 103,312 which is 103 integers, and 1026 parts of a unit. Or, it is 103 units, and 3 tenth parts, 1 bund. dredth part, and 2 thousandth parts of a unit, or 1. Hence we may observe, that decimals, and FEDERAL MONEY, are subject to one, and the same law of notation, and consequently of operation. |