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. EXAMPLES. 1. Multiply by jinswers *= 2. Multiply by 3. Multiply 5 by : 4. Multiply s of 7 by 31 5. Multiply 133 by la 23 6. Multiply of 8 by 1 of 5 13 7. Multiply 7} by 91 693 8. Multiply of } by of 34 9. What is the continued product of of, 7, 51 and ļof ? Ans. 4 DIVISION OF VULGAR FRACTIONS. RULE. PREPARE the fractions as before ; then, invert the di visor and proceed exactly as in Multiplication :- The pro ducts will be the quotient required. EXAMPLES. 4 x 5 1. Divide by Thus,of Ans. 3 X 7 2. Divide 11 by Answers, 11%s 1 3. Divide of by 4. What is the quotient of 17 by { ? 594 5. Divide 5 by G 7 6. Divide { of of by off 31 7. Divide 45 by of 4 8. Divide 71 by 127 9. Divide 52054 by 4 of 91 711 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. s. d. qrs. el ? 1. If of a yard cost of a pound, what will is of an Ell English cost ? Syd.=of of }=48 or Ell English. 2. If of a yard cost of a pound, what will 40 yds. come to ? Ans. £59 6s. 6 d. 3. If 50 bushels of wheat cost 1731. what is it per bush Ans. 78. Od. 133qrs. 4. If a pistareen be worth 143 pence, what are 100 pistareens worth ? Ans. £6 5. A merchant sold 51 pieces of cloth each containing 24} yds. at Is. 1d. per yard ; what did the whole amount Ans. £60 10s. od 3 qrs. 6. A person having of a vessel, sells of his share for 3121. ; what is the whole vessel worth? Ans. £780 7. If of a ship be worth of her cargo, valued at 8000l. what is the whole ship and cargo worth? Ans. £10031 148. 11dd. to ? INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as bez fore, then invert the third term, and multiply all the three terros 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 1 pyard wide ? Yds. yds. yds. Yds. As 13:51::3 AudixuX=335=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. 449 days. 3. If 13 men in 113 days, mo: 21 acres, in how many days will 8 men do the samı ? Ins. 1837 days. 4. How much in length that is 7} inches broad, will make a square foot ? Ans. 20 inches. 5. If 25£s. will pay for the carriage of a cwt 1451 miles ; how far may 6.1 cwt. be carried for the same mo Ans. 22,6 miles. 6. How many yards of baize which is 14 yards wide, will line 187 yards of cau let yd. wide ? Ans. 11yds.. 1gr. lna. ney 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. f. s. 1. If j of a yd. cost of a pound ; what will 15% yds come to ? 13,875,73,583+ and =,75 Yds. £. Yds. £. d qrs. 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 4 yds. cost 3s. 4}d. what will 30 yds. cost ? ins. £1 . 48. 3d. 3978. + 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts. what will 9 curt. 3 qrs. cost at the same rate ? cut. 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 coine to ? Ans. $590, 21cts. 7;,m. 6. If 345 yards of tape cost 5 duls. 17 cents, 5m. what will one yard cost? Ans. ,015=1}cts 7. If a man lay out 121 dols. 23 cts. in merchandise, 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 riband can I buy for 25. dols. if 29 yds. cost 41 dollars ? Jus. 1785 yards. 9. If 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. 209, 072 dols. =$269, 7cts. 2m -- SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS. Rate per cent. 1 Rutio. | Rute per cent. Ratio. 3 ,03 5 ,055 6 ,065 ,07 Ratio is the simple interest of il. for one year ; or in federal money, of $1 for one year, at the rate per cent. agreed ,06 6 on. RULE. Multiply the Principal, Ratio and time continually to gether, and the last product will be the iterest required. EXAMPLES. 1. Required the interest of 211 dols. 45 cts. for 5 years, 5 per cent. per annum ? P $ cts. ,05 Ratio, 10,5725 Interest for one year. 5 Multiply by the time. 52,8625 Ans.=$52, 86cts. 20. 2. What is the interest of 6451. 10s. for 3 years, at i per cent. per annum? £615,5x06x3=116,190=6116 38. 9d. 2,4qrs. Ans. 3. What is the interest of 1211. 8s. 6d. for years, a 6 per cent. per annum ? Ans. £32 153. 8d. 1,364rs. 4. What is the amount of 536 dollars 39 cents, for 1: years at 6 per cent. per annum ? Ans. $584,6651. 5. Required the amount of 648 dols. 50 cts. for 127 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, ad unity to the produc for a divisor, l:y which sum divide the amount, and the quo tient will be the principal. EXAMPLES, 1. What principal will amount to 1235,975 dollars, ii. 5 years, at 6 per cent. per annum ? $ ,06x5+1=1,30, 1235,975 950,75 Ans. 2. What principal will amount to 873. 198. in 9 years, ai Oper cent. per annum ? Ins. £567 10s. 3. What principal will amount to 626 dols. 6 cts. in 12 years, at 7 per cent ? Ans. $340,25=$340, 25c1s. 4. What principal will amount to 9507. 10s. 4,125d. in 8 years, at 5 per cent. ? Ans. 1645 158. CASE III. RULE.-Subtract the principal from the amount, di ville the remainder by the product of tlre time and principal, and the quotient will be the ratio. EXAMPLES. 1 At what rate per cent. will 950,75 dols, amount to 75 dols, in 5 years ? |