MULTIPLICATION OF VULGAR FRACTIONS. RULE. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator. 8. Multiply of by & of 34 of P Ans. 4 9. What is the continued product of of, 7, 5 and 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? syd. As Ell. £. Ell. of 4 of =20 or Ell English. 54 s. d. qrs. And ××=.=10 8 14 Ans. 2. If of a yard cost of a pound, what will 40 yds. come to el ? Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 173l. what is it per bush Ans. 7s. Od. igrs. 4. If a pistareen be worth 143 pence, what are 100 pis tareens worth? Ans. £6 5. A merchant sold 5 pieces of cloth, each containing 24 yds. at 9s. d. per yard; what did the whole amount to? Ans £60 10s. Od. Sqrs. 号 6. A person having of a vessel, sells of his share for 312.; what is the whole vessel worth ? Ans. £780 7. If of a ship be worth of h cargo, valued at 2000l. what is the whole ship and cargo worth? Ans. 10031 14s. 11d.. INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as be fore, 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 yard wide, will line 51 yards of cloth which is 14 yard wide ? Yds. yds. yds. 7 Fds. As 13:53 And 7×11×3-385-16 Ans. 2. If a man perform a journey in 33 days, when the day is 121 hours long; in how many days will he do it when the day is but 9 hours. 3. If 15 men in 11 days, mow 21 days will 8 men do the same. 4. How much in length that is make a square foot? Ans. days. acres, in how many Ans. 18 days. 7 inches broad, will Ans. 20 inches. 5. If 254s. will pay for the carriage of an cwt. 1451 miles; how far may 6 cwt. be ney? 6. How many yards of baize will line 187 yards of camblet carried for the same moAns. 22 miles. which is 14 yards wide, yd. wide? Ans. 11yds. 1gr. 1} na. RULE OF THREE DIRECT IN DECIMALS. RULE. REDUCE your fractions to decimals, and state your question as in whole numbers; multiply the second and third together; divide by the first, and the quotient will be the answer, &c. EXAMPLES. 1. If of a yd. cost of a pound; what will 15 yds. come to ? Fds. As ,875,583 :: 1,875,583+and =,75 Yds. £. £. s. d. grs. 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. £.578 3. If 4 yds. cost 3a. 4d. what will 50 yds. cost? Ans. £.1 4s. 3d. Sqrs. + 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts. what will 9 cwt. 3 qrs. cost at the same rate? cwt. As 1,4 come to ? $ cwt. 10,09: : 9,75: 70,269-870, 26cts. 9m.+ 5. If 19 yards cost 25,75 dols. what will 435 yards Ans. $590, 21cts. 7m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5m. what will 1 yard cost? Ans. ,015=11cts. 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.=$3, 91cts. 8. How many yards of ribbon can I buy for 25 dols. if 29 yds. cost 44 dollars ? Ans. 178 yards. 9. If 178 yds. cost 25 dollars, what cost 294 yards? Ans. $4 10. If 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, 7cts. 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 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. 52,8623 Ans.=$52, 86cts. 21m. 2. What is the interest of 645l. 10s. for 3 years, at 6 per cent. per annum ? £645,5X06X3116,190-116 Ss. 9d. 2,4qrs. Ans. 3. What is the interest of 121l. 8s. 6d. for 4 years, at 6 per cent. per annum ? Ans. £32 15s. 8d. 1,36qrs. 4. What is the amount of 556 dollars 39 cents, for 13 years at 6 per cent. per annum? Ans. $584,6651. 5. Required the amount of 648 dols. 50 cts. for 124 yrs. at 5 per cent. per 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. EXAMPLES. 1. What principal will amount to 1235,975 dollars, in 5 years, at 6 per cent. per annum? ,06×5+1=1,30)1235,975(950,75 Ans. 2. What principal will amount to 873l. 19s. in 9 years, at 6 per cent. per annum ? Ans. £567 10s. 3. What principal will amount to 626 dols. 6 cts. in 12 years, at 7 per cent. ? Ans. $340,25 $340, 25cts. 4. What principal will amount to 956l. 10s. 4,125d. in 8 years, at 5 per cent. ? Ans. £645 15s. 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 dols. amount to 1235, 975 dols. in 5 years? |