MULTIPLICATION OF VULGAR FRACTIONS. RULE. Reduce whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of differen integers to the same; then multiply all the numerators together for a new numerator, and all the denominators to gether for a new denominator. 9. What is the continued product of 3 of 3, 7, 51 and of & ? Ans. 4 DIVISION OF VULGAR FRACTIONS. RULE. Prepare the fractions as before; then, invert the divisor and proceed exactly as in Multiplication :-The products will be the quotient required. RULE OF THREE DIRECT IN VULGAR RULE. Prepare the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in 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. 1. If of a yard cost of a pound, what will of an Ell English cost? Ell. of of }=2% or ¦ Ell English. syd. Ell. £. s. d. qrs. As 5 And XX-£-10 3 1 54 = Ans. 2. If g of a yard cost of a pound, what will 403 yards come to ? Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 1737. what is it per bushAns. 7s. Od. 143 grs. pence, what are 100 pista el? 4. If a pistareen be worth 14 reens worth? Ans. £6 of cloth, each containing 5. A merchant sold 5 pieces 24 yards at 9s. d. per yard; what did the whole amount to? Ans. £60 10s. Od. 33 qrs. 6. A person having of a vessel, sells of his share for 3127.; what is the whole vessel worth? Ans. £780 7. If of a ship be worth of her cargo, valued at 80007. what is the whole ship and cargo worth? Ans. £10031 14s. 11d. 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 3 yard wide, will line 5 yards of cloth which is 13 yard wide ? Yds. yds. yds. 2 ง 335 Yds. As 12:53 And x=316 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? 3. If 13 men in 11 days, mow 21 days will 8 men do the same? 4. How much in length that is 7 make a square foot? Ans. 4 days. acres, in how many Ans. 183 days. inches broad, will Ans. 20 inches. 5. If 254s. will pay for the carriage of a cwt. 145¦ miles; how far may 61 cwt. be carried for the same money? Ans. 22 miles. 6. How many yards of baize which is 1 will line 187 yards of camblet yard wide? yards wide, Ans. 11 yds. 1 qr. 1 na. RULE OF THREE DIRECT IN DECIMALS. RULE. Reduce your fractions to decimals, and state your ques tion as in whole numbers; multiply the second and third together; divide by the first, and the quotient will be the an swer, &c. EXAMPLES. 1. If of a yard cost of a pound; what will 153 yards. 1,875,583 - and 3=,75 £. s. d. qrs. come to ? Yds. £. Yds. £. As ,875,583 :: 15,75: 10,494-10 9 10 2,24 Ans. 2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds? Ans. £378 3. If 41 yards cost 3s. 44d. what will 305 yards cost? Ans. El 4s. 3d. 3 qrs.+ 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts., what will 9 cwt. 3 qrs. cost at the same rate? cit. As 1,4 $ cwt. 10,09 :: 9,75: 70,269=$70, 26 cts. 9 m.+ 5. If 19 yards cost 25,75 dollars, what will 435 yards come to ? Ans. $590, 21 cts. 72 m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5 m., what will one yard cost? Ans. ,015-11 cts. 7. If a man lay out 121 dollars 23 cts. in merchandise, and thereby gains 39,51 dollars, how much will he gain in laying out 12 dollars at the same rate? Ans. $3,91 $3, 91 cts. 8. How many yards of riband can I buy for 254 dols. if 293 yards cost 4 dollars? Ans. 178 yards. 9. If 178 yds. cost 25 dollars, what cost 293 yards? Ans. $41 10. If 1,6 cwt. of sugar cost 12 dols. 12 cts., what cost 3 hhds., each 11 cwt. 3 qrs. 10,12 lb. ? Ans. 269,072 dols.=$269, 7 cts. 2 m.+ SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS. Ratio is the simple interest of 17. 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 toge ther, and the last product will be the interest required. EXAMPLES. 1. Required the interest of 211 dols. 45 cts. for 5 years, at 5 per cent. per annum? $cts. 211,45 principal. 10,5725 interest for one year. 52,8625 Ans.=$52, 86 cts. 21 m. 2. What is the interest of 6457. 10s. for 3 years, at 5 per cent. per annum? £645,5×06×3=116,190=£116 3s. 9d. 2,4 qrs. Ans. 3. What is the interest of 1217. 8s. 6d. for 4 years, at 6 per cent. per annum? Ans. £32 15s. 8d. 1,36 qrs. 4. What is the amount of 536 dollars, 39 cents, for 13 years, at 6 per cent. per annum ? Ans. $584,6651. 5. Required the amount of 648 dollars 50 cents for 123 years, at 5 per cent. per annum? CASE II. Ans. $1103, 26 cts. 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. EXAMPLES. 1. What principal will amount to 1235,975 dollars, in 5 years, at 6 per cent. per annum? $ ,66×5+1=1,30, 1235,975(950,75 Ans. 2. What principal will amount to 8737. 19s. in 9 years, at 6 per cent. per annum? Ans. £567 10s. 3. What principal will amount to $626, 6 cents in 12 years, at 7 per cent. ? Ans. $340,25-$340, 25 cts. amount to 9567. 10s. 4,125d. in Ans. £645 15s. 4. What principal will 83 years, at 51 per cent.? CASE III. The amount, principal and time given, to find the 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. 1. At what rate per cent. will 950,75 dollars amount to 1230,975 dollars in 5 years? |