MULTIPLICATION OF VULGAR FRACTIONS.. RULE'. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of clifferent integers to the same; then multiply all the nunierators together for a new numerator, and all the denominators together for, a new denominator. EXAMPLES. 1. Multiply by Answers. 41 2. Multiply by S. Multiply 54 by 4. Multiply 4 of 7 by 31 5. Multiply by 6. Multiply of 8 by 1 of 5 7. Multiply s by 91 691 8. Multiply off byť of 3 9. What is the continued product of 1 of }, 7,5and of f? Ans. 435 15+ 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. EXAMPLIS. * Ans. 4 x 5 1. Divide & by i Thus, 3 x 7 2. Divide £7 by Answers. 1*' 3. Divide of by 591 4. What is the quotient of 17 by ;? 5. Divide 5 by to 74 6. Divide 4 of of } by of 7. Divide 45 by of 4 8. Divide 71 by 127 Divide 52054 by of 91 RULE OF THREE DIRECT IN VULGAR FRACTIONS. RULE. PREPARE the fractions as before, then stare your questium agreeable to the Rules already laid down in the Rule of Tliree in whole numbers, and invert the first terin in the proportion; then multiply all the three terms continually together, and the product will be the answer, in the same naine with the second or middle term. EXAMPLES. s. d. qrs. come to 1. If { of a yard cost of a pound, what will is of an Ell English :ost? iyd.=of; of 1=46 or ] Ell English. EU. As į :::'s And *xxissió£=10 3 1 Ans. 2. It of a yard cost ; of a pound, what will 401 yasi Ans. £ 59 Ss. 6 d. 3. If 50 bushels of wheat cost 1731. what is it per bushel ? Ans. is. Ocl. i fyrs. 4. If a pistareen be worth 14} pence, what are 100 pistareen's worth : 5. A merchant seld 54 pieces of cloth, each containing 2011 yos. at 9s. gl. per gard; what dil the whole amount 6. A person having of a vessel, sells g of his share for 3121. ; what is the whole vessel worth : Ans. 6780 7. If of a ship be worth of her cargo, valued at B vool. what is the whole slip and cargo worth? Ans. £10031 14s. 112'd. Ans. 46 INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as before, then invert the third terin, and multiply all the three ternys 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. Yds. As 11:51: And 7x+x==1647 Ans. 2. If a man perform a journey in 3 days, when the day is 124 hours long; in how many days will he do it when the day is but 9.3hours. Ans. 4 ans days. 3. If 13 men in 11 days, mow 214 acres, in how many days will 8 men do the same. Ans. 1831 days. 4. How much in length that is 7} inches broad, will make a square foot ? Ans. 20 inches. 5. If 254s. will pay for the carriage of an cwt. 1451 miles; how far may 61 cwt. be carried for the same mo. Ans. 22 miles. 6. How many yards of baize which is 1+ yards wide, will line 187 yards of camblet | yd. wide ? Hins. 1 lyds. 1qr. i} na. 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. 1. If / of a yd. cost of a pound; what will 154 yds. come to? 1,875 1,583+an 15 £. s. d. yrs. As ,875 : ,583 : : 15,75 : 10,494=10 9 10 2.-4 Anss 2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds. ? Ans. £.378 8. If 4kyde. cost 3s. 41d. what wil: 30{ yds. cost ! Ans. 4.1 48 4d >s 1 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts. what will 9 Gwt. 3 qrs. cost at the same rate ? cwt. 8 cwt. $ As 1,4 :: 10,09 : : 9,75 : 70,269=870, 26cts. 9m. + 5. If 19 yards cost 25,75 dols. what will 4354 yards come to ? Ans. 8590, 21cts. 7 toni. 6. If 345 yards of tape cost 5 dols. 17 cents, 5m. what will 1 yard cost ? Ans. ,015=1fcts. 7. It'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.=83, 91cts. 8. How many yards of ribbun can I buy for 25$ dols. if 294 yds. cost 41 dollars ? Ans. 178) yards. 9. If 1783 yds. cost 25$ dollars, what cost 297 yards ? Ans. 841 10. If 1,6 cwt. of srigar cost 12 dols. 12 cts. what cost 8 hhds. each 11 cwt. 3 qrs. 10,12 lb. ? Ans. 269,072 dols.=8269, 7cts. 2m. + SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS. 51 ,04 Hate per cent. Ratio. | Rate per cent. Ratio, 3 -,03 ,055 4 6 ,06 ,065 7 ,07 Ratio is the simple interest of 1l. 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? 52,8625 Ans.=852, 86cts. 24m. 2. What is the interest of 645l. 10s. for 3 years, at 6 per cent. per annum ? £645,5 x06x3=116,190=£116 3s. 9d. 2, tqrs. Ans. 3. What is the interest of 121l. 88. 6d. for 45 years, at 6 per cent. per annum ? Ans. £32 15s. 8d. 1,56qrs. 4. What is the amount of 536 dollars 39 cents, for 1} per Ans. 8.584,6651. 5. Required the amount of 648 dols. 50 cts. for 123 yrs. at 55 per cent. per annum ? Ans. S110S, 26cts. + CASE II. The amount, time and ratio given, to find the principal. RULE. Multiply the ratio by the time, add vnity to the product for a divisor, by which sum divide the amount, and the quotient will be the princiñal. years at 6 EXAMPLES. 1. What principal will amount to 1255,975 dollars, in 5 years, at 6 per cent. per 8 ,06x5+1=1,30) 1235,975(950,75 Ans. 2. What principal will amount to 875l. 19s. in 9 years, at 6 per cent. per annum ? Ans. £567 10s. 3. What principal will amount to 626 dols. 6 cts. in 13 years, at 7 per cent. : Ans. $340,25=8340, 25cts. 4. What principal will amount to 956l. 08. 4,1251. in 8+ years, at 54 per cent. ? Ans. £645 155. CASE III. The amount, principal and time given, to find the ratio. RULE.--Subtract the principal from the amount, di vide the remainder by the product of the time and prin. cipal, and the quotient will be the ratio. 1. At what rate per cent. will 950,75 dols. amount to 1235, 975 dols. in 5 years ? XAMPLES. |