22. What number multiplied by of 1⁄2 will make 77? Ans. 11 23. How many persons can you relieve, with 23 shillings each, out of £12 12s. 6d. ? Ans. 106 Ans. 365 26. Divide 1 by a fraction, which has 1 for its numerator and 365 for its denominator. RULE OF THREE, DIRECT AND INVERSE RULE.-State the question, by Rule 2nd, in whole numbers; and reduce the given quantities, if required, to simple fractions, having the 1st and 2nd terms in the same denomination; then multiply the 2nd and 3rd terms together, and divide the product by the first, and the quotient will be the answer, in the same denomination as the third term is left in. EXAMPLES. 1. Bought 3 cwt. 2 qrs. 14 lb. of sugar for £8 13s. 4d.; what is the value of 53 cwt. at the same rate? 2. If 3 yards of cloth, that is 12 yards broad, will make a cloak; how many yards of shalloon, that is yards wide, will line it? 3. Bought 2 yards? 5 × 4 × 2 yards for 4. What is the value of £13? = : 13 :: 3 49 10 1, and 34 = 2. = 4 yds. 33 qrs. Ans. 12s. 6d. ; what is the value of Ans. £1 19s. 7d. of a yard of cloth, if 23 yards cost Ans. 5s. 1d. § 5. Bought 5 yards for £4 15s., what is the value of 3 yards? 6. Bought Ans. £2 18s. 71d of a yard for of a £. what is the value of Ans. £1 1s. 10 d. of an English ell? 7. Bought of a Flemish ell for 7s. 6d. ; what will 2 yds. cost, at the same rate? Ans. £2 6s. 8d. 8. How much in length, that is yards wide, is equal to 203 yards in length and yards wide? 9. Bought 7 yards, 3 qrs. of cotton which contained 9 yards 2 qrs. of stuff width of the cotton? Ans. 23 yds. 311⁄2 qrs. to line a garment, wide; what was the Ans. 3 qrs. 2 n. in length and 15 feet 10. A floor measures 18 feet 6 inches 9 inches in width; how many yards of carpet, which measures 23 feet wide, will cover it? Ans. 35 yds. 11 in. 11. What is the value of 33 yards of cloth, if I give £4 6s. 8d. for 93 yards? Ans. £1 10s. 12. Bought 3 cwt. 3 qrs. 14 lb. of sugar for £10 13s. 4d.; what is the valne of 3 qrs. 14 lb. of the same? Ans. £2 8s. 2d. 13. Bought of a mine, and sold of my share for £520; required the value of the whole mine. Ans. £1300 14. Bought of a mill for £2400; what is the value of the remainder? Ans. £4000 of cloth for 12s. 6d. ; Ans. £11 16s. 3d. 6d. for 9 months 6d., to requite his 15. Bought of 3 of 1⁄2 of an English ell what is the value of 77 yds. of the same? 16. Borrowed of my friend £36 2s. how long must I lend him £25 17s. kindness? ; Ans. 12 months 17. Borrowed of my friend £25 12s. 6d. for 8 months; what length of time shall I lend him £100 to requite his kindness? Ans. 2 months 18. Bought 73 yards of cloth for £7 2s. 6d. ; what will 4 pieces cost, each measuring 243 yards, 19. A gentleman gave his son John son Thomas of the remainder; and was £2000, to his daughter; required the value of the estate. at the same rate? Ans. £88 4s. 31d. of his estate; to his the remainder, which each son's share, and Ans. £15000 John's, £8000 Thomas', and £25000 whole. 20. A gentleman gave of his estate to his son, of the remainder to his daughter, and the residue in small legacies; when these legacies came to be paid, the son received £13000 more than the daughter. What was each child's share, the sum left in small legacies, and value of the testator's property? -Ans. £25000 son's, £12000 daughter's, £3000 small legacies, and £40000 whole property. DOUBLE RULE OF THREE IN VULGAR FRACTIONS. Rule as per whole numbers. EXAMPLES. 1. Received £1 17s. 6d. for the interest of £75 for six months; what will be the interest of £125 for nine months? 2. Paid £2 13s. 4d. for the carriage of 25 cwt. 2 qrs. 14 lbs. 120 miles,-how much can I have carried 3624 miles for £3 6s. 8d.? 205 cwt., 1203 = 433 Here 25 cwt. 2 qrs. 14 lbs. = 25ğ = miles, £2 13s. 4d.=23 = }, 3621449 miles, and £3 6s. 8d. =3} = £50. Then 3×4 × 205 × 48% × 10 8 × 1449 × 2 qr. 19 lb. 3 8 X 4 X 3 2050 = 10 cwt. 3. If 13 men in 7 days, earn £3 10s.-how much will 10 men earn in 30 days? Ans. £11 Os. 2117 NOTE. For practice, the student may solve, by fractions, the questions given in the simple rules in Compound Proportion. DECIMAL FRACTIONS. . A DECIMAL FRACTION has for its denominator a unit, with as many ciphers annexed to the right of it, as the numerator contains figures; and is expressed by writing the numerator only, with a point placed before it; as.1; } = 5; .75, &c. 75% In Decimal fractions, unity is divided into ten equal parts, called tenths, and these tenths are each subdivided into ten other equal parts, called hundredths; each of these hundredths into ten equal parts called thousandths, &c. decreasing in value, from left to right, in a tenfold proportion. Here 23 is a whole number and .4 5 6 7 8 9 1 5 a decimal, with the point or period placed before it. The above table may be decomposed as follows: NOTE.-Ciphers placed to the right hand of a decimal neither increase nor decrease its value, as .5 denotes five tenth's or 5 10 1 = 2 But ciphers placed to the left hand of a decimal, decrease its value. 1 2 5 Thus .5 = 10 5 1 .05 = .005 = Decimals are divided into 3 sorts, viz. Finite, Infinite, and Repetends. 1. A Finite Decimal is one which terminates, as .5; .25; .75; &c. |