4. Add 124 33 and 4 together. Ans. 17 Ans. 17 Ans. 2011 5. Add 4 of 95 and 7 of 14 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. 7. Add and 17 together. 8. Add 25, 84 and of of Ans. 55 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 fraction by Case VIII. in reduction, and then add them in their proper terms. 9. Add of a shilling to of a pound. SUBTRACTION OF VULGAR FRACTIONS. RULE.* PREPARE the fractions as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required. 1. From take of take EXAMPLES. of 2. From 3. From take 16 4. From 14 take 13 11 42 31 208 Answers. 137 5. What is the difference of and 17? 6. What differs from? 7. From 144 take of 19 8. From 7 take 37 O remains. 42 , if 9. From of a pound, take of a shilling. of. Then from . take. Ans. £. NOTE. In fractions of money, weight, &c. you may, i you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms. 10. From take 37 shilling. Ans. 5s. 6d, 24qrs. 11. From of an oz. take of a pwt. 12. From of a cwt. take Ans. 1gr. 27lb. 6oz. 10 dr. 13. From 33 weeks, take of a day, and of of of Ans. Sw. 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 numerators together for a new numerator, and all the denominators together for a new denominator. 8. Multiply of by of 34 of ? 13 69 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. 3. Divide of by 4. What is the quotient of 17 by 4? 5. Divide 5 by 7% 6. Divide of off by of 7. Divide 4 by of 4 8. Divide 71 by 127 9. Divide 5205 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 of a yard cost of a pound, what will of an Ell English cost? {yd.={ of 4 of 3=20 or 1 Ell English. Ell. £. Ell. come to 54 s. d. qrs. As And 2×2×5£10 3 14 Ans. 2. If of a yard cost of a pound, what will 403 yds, Ans. £59 8s. 61d. 3. If 50 bushels of wheat cost 173l. what is it per bushel ? Ans. 7s. Od. 23qrs. 4. If a pistareen be worth 143 pence, what are 100 pistareens worth? Ans. £6 5. A merchant sold 54 pieces of cloth, each containing 244 yds. at 9s. d. per yard; what did the whole amount Ans. £60 10s. Od. 33qrs. 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 2000, what is the whole ship and cargo worth? 8000 Ans. £10031 14s. 11d. to? 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 yard wide, will line 51 yards of cloth which is 14 yard wide ? Yds. yds. yds. Yds. As 15 And 7×11ק=385=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. Anst days. 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 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 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. 1qr. 13 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 ? Yds. As ,875,583 :: 7,8757,583+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 44yds. cost 3s. 44d. what will 30g yds. cost? Ans. f.1 4s. Sd. Sqrs.+ |