30)254 S. 8 14° 180 Degrees. 10800 Minutes. 60 648000 Seconds. Ans. 180°. 10800'. 648000": LAND OR SQUARE MEASURE. 1. In 34 acres, 2 roods, and 17 poles, how many roods and perch es? OPERATION. Acres. R. poles. PROOF. 4|0)553|7 4)138 17 34 2 17 34 2 17 dollars? 1. In 48 guineas, how many Ans. 224. 2. In 100 dollars, 40 guineas, 64 moidores, and 6 pence, how many pounds sterling? Ans. £201 4 6. 3. It is required to divide 100 guineas, into pieces consisting of pounds, crowns, and dollars, of each an equal number; how many such pieces will it make ? Aus. 90 & 10s. 4. A gentleman had nine purses, and in each purse had 17 dollars; how many dollars had he? Ans. 153. 5. What number subtracted from the square of 86, will leave 17 times 34 ? A s. 6818. A 6. What is the sum, and what is the difference of six dozen dozen, and half a dozen dozen ? Ans. 936 sum. 792 difference. 7. What is the difference between half a foot solid, and a solid half foot? 8. In one square mile, how many square feet? Aus. 648 in. Ans. 27878400. 9. It is required to divide 35 shillings and 6 pence, between a man a woman, and a boy, so that the man may have 9 times as much as the woman, and the woman 7 times as much as the boy; how much had each for their share? Ans. Man 31s. 6d. Woman 3s. 6d. Boy 6. 10. A gentleman setting out on a journey, carried along with him 8 Johannes, being £3 12s. each, 17 guineas; 13 half guineas, 14 crowns, 10 half crowns, 15 shillings, and 9 six pences; and finds, on his return, by his pocket book, that he had spent £49 4s. how much did he take out, and how much did he bring home? Ans. Carried out £59 4s. Brought home £10. 11. Queen Elizabeth of England, came to the throne the 17th of November, 1558, and died the 24th of March, 1603, in the 70th year of her age; what year was she born, and how many months, of 28 days each, did she reign, reckoning 365 days, 6 hours to a year? Ans. She was born in the year 1533, and reigned 578 months, 2 weeks and 1 day. to 12. A farm containing 26 acres is to be laid out in small divisions, of 3 roods and 10 poles each, how many small divisions will there be ? Ans. 32. 13. Suppose a man's expences in one year, to be £180, what is that per calender month ? 14. In 96 firkins of beer, each firkin 9 gallons, how 54 gallons per hhd. ? 15. How many sparrows, 10 for a penny, would worth £20 ? See the work. 1|0=1d. £20 Ans. £15. many hhds. of Ans. 16. pay for an ox, Ans. 48000. 240 48000 VULGAR FRACTIONS. 1 29 : FRACTIONS, or broken numbers, are expressions for parts of a whole number, or unity, (one) and are expressed by two numbers, placed one above the other, with a line drawn between them as, ,, ., &c. signifying, one-fourth, one-half, three fourths, &c. The figure below the line is called the denominater, because it shews into how many parts the unit or integer is divided; and gives name to the fraction The number above the line shews how many of these parts the fraction contains, and is therefore called the numerator. As in the fraction of £3, a pound sterling is the unit, integer, or whole; and the denominator, 4, shews that the pound is broken or divided into four equal parts, viz. 4 crowns; and the numerator, 3, shews that the fraction contains three of these parts, that is, three crowns; and so the value of this fraction is fifteen shillings. Hence it follows, COROLLARY 1st. 1st. When the numerator of a fraction is less than the denominater, the value of such a fraction is less than unity, or the integer. 2d. When the numerator is greater than the denominator, the value of the fraction is exactly an unit or integer. 3 When the numerator is equal to the denominator, the value of the fraction is more than an unit; and so often as the denominator is contained in the numerator, so many units or wholes are contained in the fraction. If, therefore, the numerator of a fraction be divided by the denominator, the quotient will be a number of units or integers, and the remainder so many parts. The numerator of a fraction is to be considered as a dividend, and the denominator as a divisor, and the fraction itself may be taken to denote the quotient. COROLLARY 2d. From this view of a fraction it is evident that if the numerator and denominator of a fraction be either both multiplied or both divided by the same number, the products or quotients will retain the same proportion to each other; and consequently the new fraction thence arising will be of the same value as the given one. Thus the numerator, and denominator of the fraction &, multiplied by 2, produces, and divided by 4 the quotient will be, both of which fractions are of the same value as 2. |