RULE OF THREE DIRECTIN VULGAR FRACTIONS. RULE. PREPARE the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three m whole numbers, and invert the first term in the proportion ; then multiply all the three terms continually together, and the product will be the answer, in the same name with the second or middle term. EXAMPLES. s. d. grs. 1. If of a yard cost of a pound, what will is of an Ell English cost? byd.= of of }= or, En English. Ell. £. Ell. As :::* And ****5=1**£=10 3 14 Ans. 2. If of a yard costs of a pound, what will 40 yds. come to? ins. £,59 8s. 6.d. 3. If 50 bushels of wheat cost 17.. what is it per bushel Ans. 7s. Od. izgrs. 4. If a pistareen be worth 14; pence, what are 100 pise tareens worth? 5. A merchant sold 59 pieces of cloth, each containing 24 yds. at 9s. id. per yard ; what did the whole ainount tos Ins. £00 10s. Od. Sqrs. 6. A person having of a vessel, sells of his share for what is the whole vessel worth? Ans. £780 7. If of a ship be worth s of her cargo, valued at 8000l. what is the whole ship and cargo worth? ains. £ 10031 145. 11d. Ans. £6 3121.; INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together, the product will be the answer. EXAMPLES. 1. How much shalloon that is var! wide, will lme 5) yards of cloth which is 15 yard wide ? Yds. yds. yds. Tus. As 13:53:: And xx=N=16,1 Ans. 2. If a man perform a journey in 3 days, when the day is 12 hours long: in how many days will he do it when the day is but 9 hours. Ans. 4 days. 3. If 13 men in 11 days, mow 21 ) acres, in how many days will 8 men do the same. jus. 1993 days 4. How much in length that is 73 inches broad, will make a square foot: us, 20 inches. 5. If 25?s. will pay for the carriage if an cwt. 1451 miles; how far may őj ciit. be carried for the same mo 70s. 229 miles, 6. How many yards of baize which is 14 yards wide, will line 187 yards of camblet vd. wide cis. 11gids. 197. 1} m. ina ney ? RULE OF THREE DIRECT N DECIMALS. RULE. REDUCE your fractions to decimais, and state your question as in whule numbers : vultiply the second and third together; divide by the first, and the quotient will be the answer, &c. EXAMPLES. 1. If of a yd. cost je of a pound ; what will 154 yds. come to? =,875 15,585-tani =,75 Vds. Yus. fo fo. s. d. qrs. As ,875 : ,583 :: 15,75 : 10,494-10 9 10 2,24 Aus 2. If 1 pint of wine cost 1,2s. what cust 12,5 hlids.? 2:25. 6.373 S. If 4fyds. cost 33. 4. d. what will 85 sils. antes Ans. £. ? - 3. 2013. - 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts. what will 9 cwt. 3 qrs. cost at the same rate ? swt. cwt. $ As 1,4 : : 10,09 : : 9,75 : 70,269=$70, 26cts. 9m. + 5. If 19 yards cost 25,75 dols. what will 435} yards come to ? Ans. $590, 21cts. 75m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5m. what will 1 yard cost? Ans. ,015=1 cts. 7. If a man lays out 121 dols. 23 cts. in merchandize, and thereby gains 39,51 dols. how much will he gain in laying out 12 dollars at the same rate ? Ans. 3,91 dols.=93, 91cts. 8. How many yards of ribbon can I buy for 25} dols. if 29% yds. cost 41 dollars ? Ans. 1785 yards. 9. I 1784 yds. cost 25} dollars, what cost 29 yards ? Ans. $4 10. If 1,6 cwt. of sugar cost 12 dols. 12 cts. what cost 3 hhds. each 11 cwt. 5 qrs. 10,12 lb. ? Ans. 269,072 dols.=$269, cts. 2m. + SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS. Ratio is the simple interest of 11. for one year; or in federal money, of $1 for one year, at the rate per cent. agreed on. RULE. Multiply the Principal, Ratio and time continually together, and the last produce will be the interest required. EXAMPLES. 1. Required the interest of 211 dols. 45 cts. for 5 year 21 50e7 cent. per ansum? T Scts. ,05 Ratio. 10,5725 Interest for one year. 5 Multiply by the time. years, at 6 at 51 per cent. per 52,8625 Ans.=$52, 86cts. 2m. 2. What is the interest of 6451. 10s. for 3 years, at 6 per cent. per annum ? 4645,5X06xS=116,190=4116 Ss. 9d. 2,4grs. Ans. per Ans. $584,6651 annum? Ans. $1103, 26cts. + CASE II. The amount, time and ratio given, to find the principal. RULE. Multiply the ratio by the time, add unity to the product for a divisor, by which sum divide the amount, and the quotient will be the principal. 1. What principal will amount to 1235,975 dollars, in 5 years, at 6 per $ ,06x5+1=1,30)1235.975(950,75 Ans. 2. What principal will amount to 8731. 198. in 9 years, at 6 per cent. per annum? Ans. £567 10s. 3. What principal will amount to 626 dols. 6 cts. in 19 years, at 7 per cent. ? Ans. $340,25=8340, 25cts. 4. What principal will amount to 9561. 10s. 4,125d. in 81 years, at 54 per cent. ? Ins. £645 15s. CASE 11. The amount, principal and time given, to find tie ratio. RULE. Subtract the principal from the amount, divide the remainder by the product of the time and principal, and the quotient will be the ratio. EXAMPLES. per cent. EXAMPLES. At what rate per cent. will 950,75 dols. ániount to 975 dols. in 5 years? From the amount 1235,975 Ans. 2. At what rate per cent. will 5671. 10s. amount to 8731. 195. in 9 years ? Ans. 6 per cent. 3. At what rate per cent. will 340 dols. 25 cts. amount to 626 dols. 6 cts. in 12 years ? Jns. 7 per cent. 4. At what rate per cent. will 6451. 15s. amount to 956). 10s. 4,125d. in 83 years? Fins. 53 per cent. CASE IV. The amount, principal, and rate per cento gire!, to find the time. RULE. Subtract the principal from the amount; divide the remainder by the product of the ratio and principal; and the quotient will be the time. EXAMPLES. 1. In what time will 950 dols. 75 cts. amount to 1235 dollars, 97,5 cents, at 6 per cent. per annum? From the amount $1235,975 235,9050 Ans. 9 years. 2. In what time will 5671. 10s. amount to 8731. 19s. at 6 per cent. per annum? 3. In what time will 340 dols. 25 cts. amount to 626 dols. 6 cents at 7 per cent. per annum ? Ans. 12 years. 4. In what time will 645l. 153. amount to 9561. 10s. 4,125d. at 55 per ct. per annum ? Ans.3,75=9years. TO CALCULATE INTEREST FOR DAYS. Multiply the principal by the given number of days, and that product by the ratio; divirle the last product ty 3.65 (the number of days in a year) and it wili give the interest required |