5. Add 4. Add 121 32 and 43 together. NOTE 1. In adding mixed numbers that are not compounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed numbers. 6. Find the sum of 53 74 and 15. I find the sum of 2 and to be 21=111 7. Add and 17 together. 8. Add 25, 81 and 1 of 3 of 3 Ans. 33 NOTE 2. To add fractions of money, weight, &c. reduce fractions of different integers to those of the same. Or, if you please you may find the value of each frac tion by Case VIII. in Reduction, and then add them in their proper terms. 9. Add of a shilling to of a pound. 1st method. SUBTRACTION OF VULGAR FRACTIONS. RULE.* PREPARE the Fraction as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required. 7. From 144 take of 19 8. From 7 take 240 Answers. 9. From of a pound, take of a shilling. of. Then from 11 31 208 135 378 10 171 1.7 12 O remains. take. Ans. £. NOTE In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper £. take 3 shillings. Ans. 5s. 6d. 23 grs. of an oz. take of a pwt. Ans.11pwt. 3gr. Ans. 1gr. 27lb. 6oz. 10 dr. 13. From 3 weeks, take of a day, and of of of Ans. 3w. 4da. 12ho. 19min 174sec. an hour. * In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number. Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number, 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 nume rators together for a new numerator, and all the denominators together for a new denominator. S. Multiply of 2 by & of 32 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 di visor and proceed exactly as in Multiplication :-The pr ducts will be the quotient required. 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 of a yard cost of a pound, what will of an Ell English cost? yd. of 4 of 8 or Ell English. Ell. £. Ell. s. d. qrs. As And 2××£.10 3 11⁄2 Ans. 2. If of a yard cost of a pound, what will 40 yds. come to ? Ans. £59 Ss. 6d. 3. If 50 bushels of wheat cost 1737. what is it per bushel? Ans. 78. Od. 123grs. 4. If a pistareen be worth 143 pence, what are 100 pistareens 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 32qrs. 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 her cargo, valued at 80007. what is the whole ship and Ans. cargo worth? £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 3 yard wide, will line 51 yards of cloth which is 1 yard wide ? Yds. yds. yds. 24 Yds. As 13:51:3 And 7××335=164 Ans. 2. If a man perform a journey in 3 days, when the day is 12 hours long; in how many when the day is but 9 hours? 3. If 13 men in 11 days, mov 21 days will 8 men do the same? 4. How much in length that is 7 make a square foot ? ney F days will he do it Ans. 4days. acres, in how many Ans. 1833 days. inches broad, will Ans. 20 inches. cwt 1451 5. If 25s. will pay for the carriage of a miles; how far may 6 cwt. be carried for the same mo Ans. 22 miles. 6. How many yards of baize which is 14 yards wide, will line 187 yards of can let yd. wide? Ans. 11yds.. 1gr. 1ļna. 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. 12 1. If of a yd. cost of a pound; what will 153 yds 7,8757,583+ and 3,75 Yds. £. £. s. d qrs. 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 4 yds. cost 3s. 41d. what will 30 yds. cost? Ans. £1 4s. 3d. 3grs. + |