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 3 of 3 by 5 of 32 Answers. 693 9. What is the continued product of 3 of 3, 7, 5 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. EXAMPLES. 1. Divide by 2. Divide by 3. Divide IT by by 3. Divide of 4 by 3 4. What is the quotient of 17 by &? 5. Divide 5 by 7 6. Divide of 3 of 7 by 1 of 3 7. Divide 45 by 5 of 4 8. Divide 71 by 127 9. Divide 52057 by # of 91 RULE OF THREE DIRECT IN VULGAR FRACTIONS. 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 g of a yard cost of a pound, what will of an Ell English cost? As gyd.=3 of 4 of 1-20 or 3 Ell English. Ell. £. Ell. 13 And 9 5 T03 s. d. grs. £10 3 14 Ans. 2. If of a yard cost of a pound, what will 40 yds. come to ? Ans. £59 8s. 61d. 3. If 50 bushels of wheat cost 173. what is it per bushel P Ans. 7s. Od. 123grs. 4. If a pistarcen be worth 143 pence, what are 100 pistareens worth? Ans. £6 5. A merchant sold 54 pieces of cloth, each containing 24 yds. at 9s. d. per yard; what did the whole amount to ? Ans. £60 10s. Od. 33qrs. 6. A person having 3 of a vessel, sells of his share for 312. what is the whole vessel worth? 9 Ans. £780 7. If of a ship be worth 3 of her cargo, valued at 80001. what is the whole ship aud cargo worth? Ans. 10031 14s. 11 d. 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 51 yards of cloth which is 14 yard wide ? Yes. yds. yds. 335 Ids. As 18:5: And 7××÷==16, 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 44 days. 285 3. If 13 men in 113days, mow 21 acres, in how many days will 8 men do the same. Ans. 1823 days. 4. How much in length that is 73 inches bread, will make a square foot ? Ans. 20 inches. 5. If 253s. will pay for the carriage of an cwt. 145) miles; how far may 63 cwt. be ney? 6. How many yards of baize will line 187 yards of camblet miles. carried for the same mo- Ans. 11gas. 1qr. 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. come to ? EXAMPLES. 2 1. If of a yd. cost 7, of a pound; what will 154 yds. 7,875 7,583+and 3=,75 Yds. £ Yds. £. £. s. d. grs. A9,875,583 :: 15,75: 10,494-10 9 10 2,24 Aus 2. If 1 pint of wine cost 1,2s. what cost 12.5 hids. ? Ans. £.373 8. If 44yds. cost 3s. 41d. what will 305 yds. Cus★ ? Ans. £.. Syrs.-f 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts. what will 9 cwt. 3 qrs. cost at the same rate? come to ? $ cwt. 8 swt. As 1,4 10,09: : 9,75: 70,269 $70, 26cts. 9m.+ 5. If 19 yards cost 25,75 dols. what will 435 yards Ans. 8590, 21cts. 7-m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5m. what will 1 vard cost? Ans. ,0151cts. 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. I 178 yds. cost 25 dollars, what cost 29 yards? Ans. $44 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.=$2C9, 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 yearså 5 per cent, per annum? 10,5725 Interest for one year. 52,8625 Ans. $52, 86cts. 24m. 2. What is the interest of 6451. 10s. for 3 years, at 6 per cent. per annum ? £645,5×06×3=116,190-116 Ss. 9d. 2,4qrs. Ans. 3. What is the interest of 1211. 8s. 6d. for 4 years, at per cent. per annum ? Ans. £32 15s. 8d. 1,36qrs. 4. What is the amount of 536 dollars 39 cents, for 11⁄2 years, at 6 per cent. per annum ? Ans. $584,6651 5. Required the amount of 648 dols. 50 cts. for 12 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. 5 EXAMPLES. 1. What principal will amount to 1235,975 dollars, in 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=8340, 25cts. 4. What principal will amount to 956l. 10s. 4,125d. in 83 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. At what rate per cent. will 950,75 dols. âmount to 975 dola in 5 years? |